- All
- 1.G.A
- 1.MD.A
- 1.MD.B
- 1.MD.C
- 1.NBT.A
- 1.NBT.B
- 1.NBT.C
- 1.OA.A
- 1.OA.B
- 1.OA.C
- 1.OA.D
- 2.G.A
- 2.MD.A
- 2.MD.B
- 2.MD.C
- 2.MD.D
- 2.NBT.A
- 2.NBT.B
- 2.OA.A
- 2.OA.B
- 2.OA.C
- 3.G.A
- 3.MD.A
- 3.MD.B
- 3.MD.C
- 3.MD.D
- 3.NBT.A
- 3.NF.A
- 3.OA.A
- 3.OA.B
- 3.OA.C
- 3.OA.D
- 4.G.A
- 4.MD.A
- 4.MD.B
- 4.MD.C
- 4.NBT.A
- 4.NBT.B
- 4.NF.A
- 4.NF.B
- 4.NF.C
- 4.OA.A
- 4.OA.B
- 4.OA.C
- 5.G.A
- 5.G.B
- 5.MD.A
- 5.MD.B
- 5.MD.C
- 5.NBT.A
- 5.NBT.B
- 5.NF.A
- 5.NF.B
- 5.OA.A
- 5.OA.B
- 6.EE.A
- 6.EE.B
- 6.EE.C
- 6.G.A
- 6.NS.A
- 6.NS.B
- 6.NS.C
- 6.RP.A
- 6.SP.A
- 6.SP.B
- 7.EE.A
- 7.EE.B
- 7.G.A
- 7.G.B
- 7.NS.A
- 7.RP.A
- 7.SP.A
- 7.SP.B
- 7.SP.C
- 8.EE.A
- 8.EE.B
- 8.EE.C
- 8.F.A
- 8.F.B
- 8.G.A
- 8.G.B
- 8.G.C
- 8.NS.A
- 8.SP.A
- HSA-APR.A
- HSA-APR.B
- HSA-APR.C
- HSA-APR.D
- HSA-CED.A
- HSA-REI.A
- HSA-REI.B
- HSA-REI.C
- HSA-REI.D
- HSA-SSE.A
- HSA-SSE.B
- HSF-BF.A
- HSF-BF.B
- HSF-IF.A
- HSF-IF.B
- HSF-IF.C
- HSF-LE.A
- HSF-LE.B
- HSF-TF.A
- HSF-TF.B
- HSF-TF.C
- HSG-C.A
- HSG-C.B
- HSG-CO.A
- HSG-CO.B
- HSG-CO.C
- HSG-CO.D
- HSG-GMD.A
- HSG-GMD.B
- HSG-GPE.A
- HSG-GPE.B
- HSG-MG.A
- HSG-SRT.A
- HSG-SRT.B
- HSG-SRT.C
- HSG-SRT.D
- HSN-CN.A
- HSN-CN.B
- HSN-CN.C
- HSN-Q.A
- HSN-RN.A
- HSN-RN.B
- HSS-CP.A
- HSS-CP.B
- HSS-IC.A
- HSS-IC.B
- HSS-ID.A
- HSS-ID.B
- HSS-ID.C
- HSS-MD.A
- HSS-MD.B
- K.CC.A
- K.CC.B
- K.CC.C
- K.G.A
- K.G.B
- K.MD.A
- K.MD.B
- K.NBT.A
- K.OA.A

- All
- 1.G.A.1
- 1.G.A.2
- 1.G.A.3
- 1.MD.A.2
- 1.MD.C.4
- 1.NBT.A.1
- 1.NBT.B.2
- 1.NBT.B.3
- 1.NBT.C.4
- 1.NBT.C.5
- 1.OA.A.1
- 1.OA.A.2
- 1.OA.B.3
- 1.OA.B.4
- 1.OA.C.5
- 1.OA.C.6
- 1.OA.D.7
- 1.OA.D.8
- 2.G.A.1
- 2.G.A.2
- 2.G.A.3
- 2.MD.A.1
- 2.MD.A.3
- 2.MD.A.4
- 2.MD.B.5
- 2.MD.B.6
- 2.MD.C.7
- 2.MD.C.8
- 2.MD.D.9
- 2.NBT.A.1
- 2.NBT.A.2
- 2.NBT.A.3
- 2.NBT.A.4
- 2.NBT.B.5
- 2.NBT.B.6
- 2.NBT.B.7
- 2.NBT.B.8
- 2.NBT.B.9
- 2.OA.A.1
- 2.OA.B.2
- 2.OA.C.3
- 2.OA.C.4
- 3.G.A.2
- 3.MD.A.1
- 3.MD.A.2
- 3.MD.B.3
- 3.MD.C.6
- 3.MD.C.7
- 3.NBT.A.1
- 3.NBT.A.2
- 3.NBT.A.3
- 3.NF.A.1
- 3.NF.A.2
- 3.NF.A.3
- 3.OA.A.2
- 3.OA.A.3
- 3.OA.A.4
- 3.OA.B.5
- 3.OA.C.7
- 3.OA.D.8
- 3.OA.D.9
- 4.G.A.1
- 4.G.A.2
- 4.G.A.3
- 4.MD.A.1
- 4.MD.A.2
- 4.MD.A.3
- 4.MD.B.4
- 4.MD.C.6
- 4.MD.C.7
- 4.NBT.A.1
- 4.NBT.A.3
- 4.NBT.B.5
- 4.NBT.B.6
- 4.NF.A.1
- 4.NF.A.2
- 4.NF.B.3
- 4.NF.B.4
- 4.NF.C.5
- 4.NF.C.6
- 4.NF.C.7
- 4.OA.A.1
- 4.OA.A.2
- 4.OA.A.3
- 4.OA.B.4
- 4.OA.C.5
- 5.G.A.2
- 5.G.B.3
- 5.G.B.4
- 5.MD.A.1
- 5.MD.B.2
- 5.MD.C.5
- 5.NBT.A.1
- 5.NBT.A.2
- 5.NBT.A.3
- 5.NBT.A.4
- 5.NBT.B.5
- 5.NBT.B.6
- 5.NBT.B.7
- 5.NF.A.1
- 5.NF.A.2
- 5.NF.B.3
- 5.NF.B.4
- 5.NF.B.5
- 5.NF.B.6
- 5.NF.B.7
- 5.OA.A.1
- 5.OA.A.2
- 5.OA.B.3
- 6.EE.A.1
- 6.EE.A.2
- 6.EE.A.3
- 6.EE.A.4
- 6.EE.B.5
- 6.EE.B.6
- 6.EE.B.7
- 6.EE.B.8
- 6.EE.C.9
- 6.G.A.1
- 6.G.A.2
- 6.G.A.3
- 6.G.A.4
- 6.NS.A.1
- 6.NS.B.2
- 6.NS.B.3
- 6.NS.B.4
- 6.NS.C.5
- 6.NS.C.6
- 6.NS.C.7
- 6.NS.C.8
- 6.RP.A.1
- 6.RP.A.2
- 6.RP.A.3
- 6.SP.A.1
- 6.SP.A.2
- 6.SP.A.3
- 6.SP.B.4
- 6.SP.B.5
- 7.EE.A.1
- 7.EE.B.3
- 7.EE.B.4
- 7.G.A.1
- 7.G.A.2
- 7.G.A.3
- 7.G.B.4
- 7.G.B.6
- 7.NS.A.1
- 7.NS.A.2
- 7.NS.A.3
- 7.RP.A.1
- 7.RP.A.2
- 7.RP.A.3
- 7.SP.A.1
- 7.SP.A.2
- 7.SP.B.3
- 7.SP.B.4
- 7.SP.C.6
- 7.SP.C.7
- 7.SP.C.8
- 8.EE.A.1
- 8.EE.A.3
- 8.EE.A.4
- 8.EE.B.5
- 8.EE.B.6
- 8.EE.C.7
- 8.EE.C.8
- 8.F.A.1
- 8.F.A.2
- 8.F.A.3
- 8.F.B.4
- 8.F.B.5
- 8.G.A.1
- 8.G.A.2
- 8.G.A.3
- 8.G.A.4
- 8.G.A.5
- 8.G.B.6
- 8.G.B.7
- 8.G.B.8
- 8.G.C.9
- 8.NS.A.1
- 8.NS.A.2
- 8.SP.A.1
- 8.SP.A.2
- 8.SP.A.3
- 8.SP.A.4
- HSA-APR.A.1
- HSA-APR.B.2
- HSA-APR.B.3
- HSA-APR.C.4
- HSA-APR.C.5
- HSA-APR.D.6
- HSA-CED.A.1
- HSA-CED.A.2
- HSA-CED.A.3
- HSA-CED.A.4
- HSA-REI.A.1
- HSA-REI.A.2
- HSA-REI.B.3
- HSA-REI.B.4
- HSA-REI.C.6
- HSA-REI.C.7
- HSA-REI.D.10
- HSA-REI.D.11
- HSA-REI.D.12
- HSA-SSE.A.1
- HSA-SSE.A.2
- HSA-SSE.B.3
- HSA-SSE.B.4
- HSF-BF.A.1
- HSF-BF.A.2
- HSF-BF.B.3
- HSF-BF.B.4
- HSF-IF.A.1
- HSF-IF.A.2
- HSF-IF.A.3
- HSF-IF.B.4
- HSF-IF.B.5
- HSF-IF.B.6
- HSF-IF.C.7
- HSF-IF.C.8
- HSF-IF.C.9
- HSF-LE.A.1
- HSF-LE.A.2
- HSF-LE.A.3
- HSF-LE.A.4
- HSF-LE.B.5
- HSF-TF.A.1
- HSF-TF.A.2
- HSF-TF.A.3
- HSF-TF.A.4
- HSF-TF.B.5
- HSF-TF.C.8
- HSF-TF.C.9
- HSG-C.A.1
- HSG-C.A.2
- HSG-C.A.3
- HSG-C.A.4
- HSG-C.B.5
- HSG-CO.A.1
- HSG-CO.A.2
- HSG-CO.A.3
- HSG-CO.A.4
- HSG-CO.A.5
- HSG-CO.B.6
- HSG-CO.B.7
- HSG-CO.B.8
- HSG-CO.C.10
- HSG-CO.C.11
- HSG-CO.C.9
- HSG-CO.D.12
- HSG-CO.D.13
- HSG-GMD.A.1
- HSG-GMD.A.2
- HSG-GMD.A.3
- HSG-GMD.B.4
- HSG-GPE.A.1
- HSG-GPE.A.2
- HSG-GPE.B.4
- HSG-GPE.B.5
- HSG-GPE.B.6
- HSG-GPE.B.7
- HSG-MG.A.1
- HSG-MG.A.2
- HSG-MG.A.3
- HSG-SRT.A.1
- HSG-SRT.A.2
- HSG-SRT.A.3
- HSG-SRT.B.4
- HSG-SRT.B.5
- HSG-SRT.C.6
- HSG-SRT.C.7
- HSG-SRT.C.8
- HSN-CN.A.1
- HSN-CN.A.2
- HSN-CN.B.5
- HSN-CN.B.6
- HSN-CN.C.7
- HSN-CN.C.8
- HSN-Q.A.1
- HSN-Q.A.2
- HSN-Q.A.3
- HSN-RN.A.1
- HSN-RN.A.2
- HSN-RN.B.3
- HSS-CP.A.1
- HSS-CP.A.2
- HSS-CP.A.3
- HSS-CP.A.4
- HSS-CP.A.5
- HSS-CP.B.6
- HSS-CP.B.7
- HSS-CP.B.8
- HSS-CP.B.9
- HSS-IC.A.1
- HSS-IC.A.2
- HSS-IC.B.3
- HSS-IC.B.4
- HSS-ID.A.1
- HSS-ID.A.2
- HSS-ID.A.3
- HSS-ID.A.4
- HSS-ID.B.5
- HSS-ID.B.6
- HSS-ID.C.7
- HSS-ID.C.8
- HSS-ID.C.9
- HSS-MD.A.2
- HSS-MD.B.5
- HSS-MD.B.7
- K.CC.A.1
- K.CC.A.2
- K.CC.A.3
- K.CC.B.4
- K.CC.B.5
- K.CC.C.6
- K.G.B.4
- K.MD.A.1
- K.MD.A.2
- K.MD.B.3
- K.NBT.A.1
- K.OA.A.1
- K.OA.A.2
- K.OA.A.3
- K.OA.A.5

# Search Results

We found 1086 results for: 6

### 2 - Peyton and Presley Discuss Addition

Peyton said, “I can solve 47 + 65” and he showed this strategy. 47 + 65 = 100 + 12 = 112 Presley s...

#### February 02, 2017

### 7 - A task related to standard 7.G.A.2

Starting at the origin, a ladybug walked 4 units east. Then she walked a distance of 3 units in an ...

#### February 10, 2016

### 6 - Locations in the Coordinate Plane

Some points are located ona square-unit grid, and coordinate axes are drawn: a) Choose any two poin...

#### December 31, 2015

### 6 - Exponent Experimentation 3

In each equation below, $x$ can be replaced with a number that makes the equation true. Find such a...

#### December 24, 2015

### 6 - Exponent Experimentation 1

Decide whether each equation is true or false, and explain how you know. $2^4=2\cdot4$ $3+3+3+3+3=3^5$...

#### December 24, 2015

### 6 - Exponent Experimentation 2

Here are some different ways to write the value $16$: $$2^4$$ $$12-(2^1+2^2)+\frac{500}{50}$$ $$2^3+2^3$$...

#### December 24, 2015

### 6 - Volumes with Fractional Edge Lengths

Make sure you have plenty of snapcubes. A dubsnapis a length equal to two snap cube edges.Build a c...

#### December 24, 2015

### 6 - Equivalent Ratios and Unit Rates

2 bottles of watercost $5.00. Fill in thetable that shows the costs for 4, 6, and 8 bottles. Find the cost for a single bottle in each case. Number of bottles Cost (\$) Cost per bottle $$2$$ $$5$$ $$4$$ $$6$$ $$8$$ 5 granolabars cost $...

#### December 24, 2015

### 6 - Nome, Alaska

The high and low temperatures, in degrees Fahrenheit,are plotted in the coordinate planefor 8 days ...

#### December 20, 2015

### 6 - Families of Triangles

There are a bunch of triangles. They all have one side that is 10 centimeters long, which we will c...

#### December 18, 2015

### 6 - Introducing Equivalent Expressions 1

Evaluate each of the following expressions: $2(4-3)^2$ $2(6-3)^2$ $2(8-3)^2$ In the expressions abo...

#### December 17, 2015

### 6 - What is the Best Way to Divide?

A group of 10 scientists won a \$1,000,000 prize for a discovery they made. They will share the pri...

#### December 17, 2015

### 6 - All, Some, or None?

For each equation, explain whether it's true for all, some, or no values of $a$. Explain how you kn...

#### December 15, 2015

### 6 - Which Goes with Which?

Decide which of the following equations best represents each situation. $$x + 2= 10$$ $$x=10+2$$ $$2\cdot10=x$$...

#### December 15, 2015

### 6 - Make Use of Structure

Think about what theseequations mean, and find their solutions.Write a sentence explaining how you ...

#### December 15, 2015

### 6 - Reciprocity

Telulahas 10 times as much iced teaas Nikki. We can represent this with a diagram: or a multiplicat...

#### December 02, 2015

### 6 - 12 Rectangular Units

Here is a large rectangle made up of 12 smaller rectangles. This rectangle could represent the equa...

#### December 02, 2015

### 6 - 2 Units Wide and 3 Units Long

Here is a rectangle that is 2 units wide and 3 units long and has an area of 6 square units. If the...

#### December 02, 2015

### 6 - Tenths of Tenths and Hundredths of Hundredths

A large square hasboth sides subdivided into $10$ equal pieces. If the large square has a sidelengt...

#### December 02, 2015

### 6 - How Much in One Batch?

10 cups of flour make 5batches of cookies. How many cups of flour in one batch? Here area diagram a...

#### December 02, 2015

### 6 - How Many Batches/What Fraction of a Batch?

A batch of cookies requires2 cups of flour. How many cups are needed for 3 batches? Here area diagr...

#### December 02, 2015

### 6 - Estimating Products of Decimals

Decide which valueis closest to the answer for each of the following questions. Explain your reason...

#### December 02, 2015

### 6 - Adding Base Ten Numbers, Part 3

In the picture below, a small square represents a unit, a long, thin rectangle represents a bundle ...

#### December 02, 2015

### 6 - Adding Base Ten Numbers, Part 2

Add: 4,000 + 5,000 600 + 200 20 + 50 8 + 1 0.3 + 0.4 0.07 + 0.02 0.001 + 0.006 0.0005+ 0.0003 4628....

#### December 02, 2015

### 6 - Adding Base Ten Numbers, Part 1

The diagram below can be used to represent 40 + 80 = 120 if a small square represents 10 and a grou...

#### December 02, 2015

### 6 - Dividing by a Fraction is the Same as Multiplying by its Reciprocal

Part 1: Match each of the three equations with one of the two diagrams below. Explain how the diagr...

#### December 02, 2015

### 6 - Simple Unit Conversion Using Ratio Reasoning

Malik is using a cookbook to make a recipe, but he can not find his measuring cups! He has, however...

#### November 25, 2015

### 6 - Equivalent Ratios 2

In a marching band there are 24 trombones and 15 snare drums. Heather says, “The ratio of trombones...

#### November 12, 2015

### 6 - Apples to Apples

Alice and Claire go apple picking. When they are done, Claire has 3times as many apples in her bask...

#### November 03, 2015

### 6 - Same and Different

For all of these questions, it may be helpful to draw a diagram. A steady speed A snail went 6 inch...

#### November 03, 2015

### 6 - Sweet Tea

If you have a cup of tea, will it be sweeter if you addone teaspoon of sugar or two? If you have tw...

#### November 03, 2015

### 6 - Constant Speed

Callie biked 12miles in 3 hours. Carterbiked 10miles in 2 hours. Represent each person's trip with ...

#### November 03, 2015

### 6 - Baking Bread 2

A recipe forbread calls for 4 cups of flour, 1 pint of water, 2 tablespoons of yeast, and 1teaspoon...

#### November 03, 2015

### 6 - Equivalent Ratios 1

Rubi was paid \$24 to sweep 4 walks.Which of the following can be represented by an equivalent rati...

#### November 03, 2015

### 6 - Many Ways to Say It

Paint Abigail mixed 2 cups of white paintwith 6 tablespoons of blue paint. Which of the following s...

#### November 03, 2015

### 6 - Baking Bread 1

A bread recipe calls for 5cups of flour and 2 teaspoons of yeast. How much flour and how much yeast...

#### November 03, 2015

### 6 - Representing a Context with a Ratio

A recipe calls for 2 cups of tomato sauce and 3 tablespoons of oil. We can say that the ratio of cu...

#### November 03, 2015

### HSA - Graphing from Factors I

Graph the functions given by the equations $y= (x-1)(x+2)(x-5)$ and $y = 3(x-1)(x+2)(x-5)$with a vi...

#### October 22, 2015

### HSA - Graphing from Factors II

Emery graphs the function $f$ given by $f(x) = (x-1)(x+2)(x-50)$ on his graphing calculator and get...

#### October 22, 2015

### HSA - Quadratic Sequence 2

The first three steps of twovisual patterns are shown below. The number of tiles in step $n$ of Pat...

#### October 22, 2015

### HSA - Quadratic Sequence 1

The first three steps of three visual patterns are shown below. Here are functions that define how ...

#### October 22, 2015

### 3 - Dajuana's Homework

It usually takes Dajuana 45 minutes to do her homework.If she starts her homework at 5:30 PM, what ...

#### October 21, 2015

### 3 - Kiri's Multiplication Matching Game

The game is played with one to four players. To play, two decks of cards are needed: the "matching"...

#### October 21, 2015

### HSA - Quadratic Sequence 3

The first three steps of twovisual patterns are shown below. The number of tiles in step $n$ of Pat...

#### October 19, 2015

### HSA - Zero Product Property 4

The Zero Product Property states that if the product of two numbers is zero, then at least one ofth...

#### October 19, 2015

### HSA - Zero Product Property 3

The Zero Product Property (ZPP) states that if the product of two numbers is zero, then at least on...

#### October 19, 2015

### HSF - Boom Town

The population of Pittsburgh was about 12,600 in 1820.Between 1820 and 1840 the population grew exp...

#### October 08, 2015

### HSF - Allergy medication

Every day Brian takes 20mg of a drug that helps with his allergies. His doctor tells him that each ...

#### October 08, 2015

### HSF - Identifying Quadratic Functions (Vertex Form)

The figure shows a graph of the function$f(x)=x^2$. a) For each of the graphs of quadratic functio...

#### October 08, 2015

### 6 - 24 Unit Squares

The area of each figure shown is 24square units. On grid paper, find a way to draw more figures wit...

#### September 29, 2015

### 6 - Areas of Special Quadrilaterals

Of the polygons shown, which have equal areas? Explain how you know.

#### September 29, 2015

### 6 - Areas of Right Triangles

Explain why theright triangle shown has an area of exactly 20 square units. The "legs" of a right t...

#### September 29, 2015

### HSF - Decaying Dice

“Exponential decay” describes a situation in whicha quantity decreases following a certain pattern....

#### September 28, 2015

### - All Your Base Are Belong to Us

When Esther tuned into a video game tournament being broadcast online, 64players remained in the to...

#### September 28, 2015

### HSF - Predicting the Past

Leo leaves his house one morning and notices a small plant growing in the yard that he has never no...

#### September 28, 2015

### 8 - Reflections, Rotations, and Translations

In this task, using computer software, you will apply reflections, rotations, and translationsto at...

#### September 11, 2015

### HSS - Guess The Probability

An instructor in a classroom of 40 students gave each of the 40 students a bag of 10 chips. In each...

#### September 11, 2015

### HSS - Last Person Standing

An instructor in a classroom of 40 students gave each of the 40 students a bag of 10 chips. In each...

#### September 11, 2015

### HSS - Types of Statistical Studies

The following are some common methods of data collection in statistical studies that involve people...

#### September 11, 2015

### HSF, HSA - F-LE, A-CED Paper Folding

A commonclaim is that it is impossible to fold a single piece of paper in half more than 7 times (t...

#### September 06, 2015

### HSF, HSA - Identifying Quadratic Functions (Standard Form)

The figure shows a graph of the function$f(x)=x^2$. a) For each of the graphs of quadratic functio...

#### September 06, 2015

### HSF - Identifying Exponential Functions

Anexponential functionis a function of the form $f(x)=ab^x$ for positive real numbers $a$ and $b$. ...

#### September 04, 2015

### 3 - Find 1 Starting from 5/3, Assessment Variation

The number line below shows two numbers, 0 and $\frac53$. Where is 1 on this number line? http://ww...

#### August 31, 2015

### HSF - Basketball Bounces, Assessment Variation 2

SCREEN I In science class, some students dropped a basketball and allowed it to bounce. They measur...

#### August 31, 2015

### 2 - High Jump Competition

Presley jumped 36 cm on her first jump in the high jump competition. On her second jump, she jumped...

#### August 05, 2015

### 2 - Determining Length

Materials ruler, meter sticks, yard sticks, measuring tape paper crayons Actions Part 1 Explain tha...

#### August 05, 2015

### 1 - Equal Shares

Materials Paper cut outs of rectangles, circles, and squares Blank paper Actions Part One: Give eac...

#### August 05, 2015

### 4 - Comparing Fractions Using Benchmarks Game

This activity is designed for pairs of students. Itusesa set of cards and a fraction mat which are ...

#### July 29, 2015

### 3 - Comparing Fractions Game

This activity is designed for pairs of students. They will require a set of cards (which are suppli...

#### July 29, 2015

### 2 - Partitioning a Rectangle into Unit Squares

Materials • Copies of a rectangle with edges marked (one for each student/ group, see attached blac...

#### July 15, 2015

### 2, 1 - Ford and Logan Add 45+36

Actions Part One: Solve the problem and explain your thinking. 45+36 Part Two: Ford and Logan each ...

#### July 15, 2015

### 8 - Similar Triangles I

The two triangles picturedbelow have three pairs of congruent angles: Are these two triangles sim...

#### July 06, 2015

### 8 - Similar Triangles II

Triangles $ABC$ and $PQR$ below share two pairs of congruent angles as marked: Explain, using dil...

#### July 06, 2015

### HSF - F-IF From the flight deck

This task is in the form of classroom instructions; it is not intended to be distributed to student...

#### July 04, 2015

### HSF - F-IF Graphing Stories

In this activity we will investigate the relationship between different quantities that are shown i...

#### July 04, 2015

### 1 - Number Square

Part 1 The teacher explains the Number Square: In this big number square, the numbers in the little...

#### July 01, 2015

### HSF - The Aquarium

PART 1: Below is an illustration of an aquarium. When the faucet is on, the water flows into the aq...

#### June 30, 2015

### HSF, HSN - Solar Radiation Model

One online source suggests thatexploiting solar energy makes sense in an area that receives $9\frac{kWh}{m^2}$...

#### June 30, 2015

### HSF - Words - Tables - Graphs

Below are4 verbal descriptions, 3 graphs, and 3 tables of values. Match each of the following descr...

#### June 13, 2015

### HSF - The story of a flight

The graphs below show three different quantities recorded by the flight computer during a flight of...

#### June 13, 2015

### HSF - Playing Catch

Here is a graph that somebody drew for the height of a ball over time. Write a story that could hav...

#### June 13, 2015

### HSF - Lake Sonoma

California is in the fifth year of a drought. Towns have been asked to decrease water use across th...

#### June 13, 2015

### HSF - Hoisting the Flag 2

Every morning at summer camp, one of the campers has to hoist the camp flag to the top of the flagp...

#### June 13, 2015

### HSF - Hoisting the Flag 1

Every morning at summer camp, one of the campers has to hoist the camp flag to the top of the flagp...

#### June 13, 2015

### HSF - Containers

Here are 6 containers that are being filled with water at a constant rate, and9 graphs that represe...

#### June 12, 2015

### 5 - To Multiply Or Not to Multiply, Variation 2

Some of the problems below can be solved by multiplying $\frac18\times\frac25$, while others need a...

#### June 08, 2015

### 5 - Mrs. Gray's Homework Assignment

1/4 mile Track 1 lap = 1/4 mile Part One Mrs. Gray gave a homework assignment with a fraction probl...

#### June 08, 2015

### 5 - Connecting the Area Model to Context

The diagram below represents one whole. Part One Write a multiplication story that could be solved ...

#### June 08, 2015

### 5 - Scaling Up and Down

The fifth grade teachers are in charge of planning the annual Davis Elementary Fun Run. The teacher...

#### June 08, 2015

### 5 - Cross Country Training

The members of a cross country team like to continue training on their own during the summer. Nero ...

#### June 08, 2015

### 5 - Sharing Lunches

Alex, Bryan, and Cynthia are about to eat lunch, and they have two sandwiches to share. Draw a pict...

#### June 08, 2015

### 1 - Doubles?

Abel said, How 6 + 6 should be 11: Because 5 + 5 is 10 and 6 is one more than 5 and 11 is one more ...

#### June 06, 2015

### 6 - Evaluating Ratio Statements

The ratio of the number of boys to the number of girls at school is4:5. There are 270 students at t...

#### June 03, 2015

### 5 - Cornbread Fundraiser

The 5th graders want to raise money for their overnight camping trip by selling cornbread during th...

#### June 01, 2015

### 5 - Comparing Heights of Buildings

The Burj Khalifa(Dubai) is about 2$\frac{1}{2}$ times as tall as the Eiffel Tower (Paris) . The Eif...

#### June 01, 2015

### 6 - Hunger Games versus Divergent

The 150 students at Skokie School were asked if they prefer seeing the movie Hunger Games or Diverg...

#### June 01, 2015

### 6 - Perfect Purple Paint I

Jessica gets her favorite shade of purple paint by mixing 2 cups of blue paint with 3 cups of red p...

#### June 01, 2015

### 7 - Perfect Purple Paint II

Jessica gets her favorite shade of purple paint by mixing 1/3 cup of blue paint with 1/2 cup of red...

#### June 01, 2015

### 6 - Party Planning

Arianna is making origami swans for her friend's birthday party. She wants to make 9 swans, one for...

#### June 01, 2015

### 6 - Fizzy Juice

When Sam and his friends get together, Sam makes orange soda by mixing orange juice with soda (spar...

#### May 31, 2015

### 5 - New Park

Part 1: There are two design proposals for a new rectangular park in town. In design one, $\frac{3}{4}$...

#### May 22, 2015

### 4 - Extending Multiplication From Whole Numbers to Fractions

Write a story problem that can be solved by finding\(5\times4\). Draw two different diagrams that s...

#### May 22, 2015

### 6 - Describing Distributions

Data Set 1 consists of data on the time to complete an assignment (in minutes) for 25 sixth graders...

#### April 28, 2015

### 6 - Is It Center or Is It Variability?

Statistical questions are questions that can be answered by collecting data and where we anticipate...

#### April 28, 2015

### HSS - Scratch 'n Win Blues

Many large retail stores and restaurants offer special discounts and free gifts to customers throug...

#### April 26, 2015

### HSS - Fred's Flare Formula

Roadside flares are often used by motorists to warn oncoming drivers of obstacles in the roadway an...

#### April 08, 2015

### 7 - College Athletes

Below are the heights of the players on the University of Maryland women's basketball team for the ...

#### April 05, 2015

### 5 - Breaking Apart Composite Solids

Students will need two different color markers or crayons to complete this task. John was finding t...

#### March 30, 2015

### 5 - What do these shapes have in Common?

The picture below is called a Venn Diagram. Each circle (A, B, and C) contain shapes that all share...

#### March 30, 2015

### 8 - Approximating pi

Different cultures through history have used many different rational numbers to approximate $\pi$. ...

#### March 14, 2015

### 6 - Wallpaper Decomposition

Jamie is planning to cover a wall with red wallpaper. The dimensions of the wall are shown below: ...

#### February 26, 2015

### 5 - Why Do We Need an Order of Operations?

State the meaning of each of the following expressions and draw a picture that represents it. $$(3\times5)+4$$...

#### February 23, 2015

### 7 - Cider versus Juice - Variation 2

Assuming you like juice and cider equally, which product is the better deal? Suppose the juice boxe...

#### February 23, 2015

### 7 - Rescaling Washington Park

Your computer shows you a map of Washington Park in Eugene, Oregon. The scale in the bottom right c...

#### February 23, 2015

### 6 - Walking the Block

Here is a map of part of Downtown Salt Lake City. You are starting at the corner of 11th Ave. and D...

#### February 23, 2015

### 7 - Gym Membership Plans

In January, Georgia signed up for a membership at Anytime Fitness. The plan she chose cost \$95 in ...

#### February 23, 2015

### 6 - Extending the Number Line

Draw a line on graph paper. Make a tick mark in the middle of the line and label it 0. Mark and lab...

#### February 22, 2015

### 6 - Mean or Median?

Bobbie is a sixth grader who competes in the 100 meter hurdles. In eight track meets during the sea...

#### February 22, 2015

### 6 - Height Requirements

At SeaWorld San Diego, kids are only allowed into the Air Bounce if they are between 37 and 61 inch...

#### February 21, 2015

### 7 - Cider versus Juice - Variation 1

The price of a gallon of apple cider is \$7.00. The price of eight 4.23-ounce juice boxes is \$2.39...

#### February 21, 2015

### 7 - Double Discounts

Emily has a coupon for 20 percent off of her purchase at the store. She finds a backpack that she l...

#### February 21, 2015

### 7 - Drill Rig

A water well drilling rig has dug to a height of –60 feet after one full day of continuous use. Ass...

#### February 21, 2015

### 6 - Comparing Test Scores

In Mrs. Sanchez' math classroom, more people sit on the right-hand side of the room than the left. ...

#### February 21, 2015

### 7 - Why is a Negative Times a Negative Always Positive?

Some people define $3\times5$ as $5+5+5$, which has a value of $15$. If we use the same definition ...

#### February 21, 2015

### 7 - Wedges of a Circle

Martin and Muriel finished a project for class showing one way to see why the area of a circle is g...

#### February 21, 2015

### 6 - Math Homework Problems

Over a two week period, Jenna had the following number of math homework problems given each day:$$20,\,0,\,7,\,10,\,1,\,11,\,0,\,25,\,15,\,1.$$...

#### February 21, 2015

### 6 - Average Number of Siblings

The number of siblings for a group of sixth grade students is shown below: $$1,\, 0,\, 2,\, 1,\, 6,\, 0,\, 2,\, 0,\, 1,\, 10. $$...

#### February 21, 2015

### 6 - Statistical Questions

Last night, Jennifer and her family went out for dinner. The questions below came up on their way t...

#### February 21, 2015

### HSS - Restaurant Bill and Party Size

The owner of a local restaurant selected a random sample of dinner tables at his restaurant. For ea...

#### January 07, 2015

### HSS - Two-Way Tables and Probability

Each student in a random sample of seniors at a local high school participated in a survey. These s...

#### January 07, 2015

### HSS - Support for a Longer School Day?

Each student in a random sample of students at a local high school was categorized according to gen...

#### January 07, 2015

### HSS - Margin of Error for Estimating a Population Mean

Background: Researchers have questioned whether the traditional value of 98.6F is correct for a typ...

#### January 06, 2015

### 5 - Always, Sometimes, Never

Decide whether each of these statements is always, sometimes, or never true. If it is sometimes tru...

#### January 05, 2015

### 5 - Sidewalk Patterns

Cora and Cecilia each use chalk to make their own number patterns on the sidewalk. They make each o...

#### December 09, 2014

### 5 - Chavone's Bathroom Tiles

Chavone is remodeling her bathroom. She plans to cover the bathroom floor with tiles that are each ...

#### December 09, 2014

### 3 - India's Bathroom Tiles

India is remodeling her bathroom. She plans to cover the bathroom floor with tiles that are each 1 ...

#### December 09, 2014

### 3 - Introducing the Distributive Property

Part I. a. How many circles are there in all? Write down a number sentence that shows how you thoug...

#### December 09, 2014

### 4 - Rounding on the Number Line

The number 8,263 lies between 8,260 and 8,270 on the number line. Label all the other tick marks be...

#### December 08, 2014

### 6 - How many staples?

Can you find an inconsistency in the information on this box of staples? Explain.

#### December 05, 2014

### 6 - Exam scores

Alyssa took a math test with 20 questions and she answered 16 questions correctly. In order get an ...

#### December 05, 2014

### 8 - Different Areas?

Below is a picture of an 8 by 8 square divided into four polygons: The green and yellow polygons ...

#### November 22, 2014

### 6 - Nets for Pyramids and Prisms

Below is a net for a three dimensional shape: The inner quadrilateral is a square and the four tria...

#### November 22, 2014

### 6 - Reflecting points over coordinate axes

Below are some points in the coordinate plane: Find the coordinates of the points. Reflect the po...

#### November 22, 2014

### 6 - Integers on the Number Line 2

Below is a number line with 0 and 1 labeled: Find and label the numbers $-2$ and $-4$ on the number...

#### November 22, 2014

### 6 - Batting Average

Before a game, Jake's batting average was exactly 0.350. That is, the decimal expansion of the frac...

#### November 22, 2014

### 6 - Unit Conversions

There are many resources available on the computer to help converting between different units. This...

#### November 22, 2014

### 6 - Plotting points in the coordinate plane

For each set of points below, draw and label a set of coordinate axes and plot the points: $(1,2), (3,-4), (-5,-2), \left(0,2\frac{1}{2}\right)$...

#### November 22, 2014

### 6 - Bag of Marbles

In a bag of marbles, $\frac{3}{5}$ of the marbles are blue and the rest are red. If the number of r...

#### November 22, 2014

### 6 - Which detergent is a better buy?

A store has two different brands of laundry detergent. Brand A can do 80 loads of laundry and costs...

#### November 22, 2014

### 6 - Speed Conversions

Jessica sees the following speed limit sign while visiting Australia where the units for speed are ...

#### November 22, 2014

### 6 - Ticket Booth

A school carnival ticket booth posts the following sign: Which amount of tickets offers the best...

#### November 22, 2014

### 7 - Distributive Property of Multiplication

Lucia uses the picture below to explain the distributive property for the expression (3+1) $\times$...

#### November 22, 2014

### 7 - Circumference of a Circle

Draw circles with diameters as indicated below and measure their circumferences to complete the fol...

#### November 22, 2014

### 7 - Approximating the area of a circle

Below is a picture of a circle of radius $r$ and a square of side length $r$: Show that $$2 \leq\frac{\text{Area(Circle)}}{\text{Area(Square)}} \leq4.$$...

#### November 22, 2014

### 8, 7 - Scaling angles and polygons

For each shape below, draw a scaled copy with a scale factor of 2. Explain why your drawing is accu...

#### November 22, 2014

### 8, 7 - Repeating or Terminating?

Tiffany said, I know that 3 thirds equals 1 so $\frac13 +\frac13+\frac13 = 1$. I also know that $\frac13=0.333\ldots$...

#### November 22, 2014

### 8 - A scaled curve

Below are two curves with some labeled points. Curve B is a scaled version of curve A: this means...

#### November 22, 2014

### 7 - Differences of Integers

Ojos del Salado is the highest mountain in Chile, with a peak at about 6900 meters above sea level....

#### October 26, 2014

### 8 - Finding the distance between points

Plot the points (5,3), (-1,1), and (2,-3) in the coordinate plane and find the lengths of the three...

#### October 26, 2014

### 8 - Creating Similar Triangles

In triangle $ABC$ below, $\angle B$ is a right angle and $|AB| = |BC|$: Draw a line segment joini...

#### October 26, 2014

### 8 - Rigid motions and congruent angles

In the picture below, $\ell$ and $k$ are parallel lines: Show that angle $a$ is congruent to angl...

#### October 26, 2014

### 8 - Choosing appropriate units

A computer has 128 gigabytes of memory. One gigabyte is $1 \times 10^9$ bytes. A floppy disk, used ...

#### October 26, 2014

### 8 - Introducing Functions

For each situation below, fill in the missing information in the tables. A parking meter takes only...

#### October 26, 2014

### 8 - Same Size, Same Shape?

For each pair of figures, decide whether these figures are the same size and same shape. Explain yo...

#### September 26, 2014

### 7 - Decimal Expansions of Fractions

Sarah learned that in order to change a fraction to a decimal, she can use the standard division al...

#### September 02, 2014

### HSA - Non-Negative Polynomials

A non-negative polynomial $f$ is a polynomial which never takes negative values, that is, $f(x) \geq 0$...

#### August 25, 2014

### 8 - Street Intersections

Market Street runs parallel to Main Street and both are intersected by 5th Avenue as shown below: ...

#### August 19, 2014

### 8 - Sizing up Squares

Below is a picture of a right triangle on a square grid: In the next picture, quadrilaterals hav...

#### August 17, 2014

### HSG - The Great Egyptian Pyramids

Three of the great Egyptian pyramids are pictured below. Each is a square pyramid. Calculate the mi...

#### August 13, 2014

### 8 - Are They Similar?

Determine, using rotations, translations, reflections, and/or dilations, whether the two polygons b...

#### August 08, 2014

### 8 - Effects of Dilations on Length, Area, and Angles

Consider triangle $ABC$. Draw a dilation of $ABC$ with: Center $A$ and scale factor 2. Center $B$ a...

#### August 06, 2014

### 3 - Valid Equalities? (Part 2)

Decide if the equations are true or false. Explain your answer. 4 x 5 = 20 34 = 7 x 5 3 x 6 = 9 x 2...

#### July 22, 2014

### HSG - Opposite Angles in a Cyclic Quadrilateral

A cyclic quadrilateral is a quadrilateral whose vertices all lie on a circle. An example is picture...

#### July 19, 2014

### HSG - Identifying Translations

Suppose $\triangle DEF$ below can be obtained from $\triangle ABC$ by a translation: Explain why $ABED$...

#### July 14, 2014

### HSG - Tangent of Acute Angles

Below is a picture of a right triangle: In terms of the picture, what are $\sin{\angle P}$, $\cos{\angle P}$...

#### July 14, 2014

### HSG - Trigonometric Function Values

For which acute angles $a$ is $\sin{a} = \cos{a}$? Explain. For which acute angles $a$ is $\sin{a} = \cos{2a}$...

#### July 11, 2014

### HSG - Constructing Special Angles

The goal of this task is to estimate the measure of angles in triangles with integer side lengths. ...

#### July 11, 2014

### HSG - SSS Congruence Criterion

Suppose $\triangle ABC$ and $\triangle DEF$ share three corresponding congruent sides as pictured b...

#### July 08, 2014

### HSG - Congruent and Similar Triangles

In triangles $ABC$ and $DEF$ below $m(\angle A) = m(\angle D)$, $m(\angle B) = m(\angle E)$ and $|\overline{AB}| = |\overline{DE}|$...

#### July 08, 2014

### 5 - Millions and Billions of People

Historians estimate that there were about 7 million people on the earth in 4,000 BCE. Now there are...

#### July 07, 2014

### HSG - Congruent angles made by parallel lines and a transverse

In the picture below $\ell$ and $k$ are parallel: Show that the four angles marked i...

#### July 07, 2014

### HSG - Identifying Rotations

Below is triangle $ABC$ and a rotated image triangle $DEF$. Explain how to identify the center of r...

#### July 07, 2014

### HSG - Sum of angles in a triangle

Suppose $ABC$ is a triangle in the plane as pictured below: Suppose $M$ is the midpoint of $\overline{AC}$...

#### July 07, 2014

### HSG - Congruent angles in isosceles triangles

Below is an isosceles triangle $ABC$ with $|AB| = |AC|$: Three students propose different arguments...

#### July 07, 2014

### HSG - Horizontal Stretch of the Plane

Suppose $f$ is the map of the plane which takes each point $(x,y)$ to the point $(x-3,y)$ and $g$ i...

#### July 07, 2014

### HSA - Who wins the Race?

Alice and Briana each participate in a 5-kilometer race. Alice's distance covered, in kilometers, a...

#### July 07, 2014

### HSG - Volume of a Special Pyramid

The four diagonals of a cube with side length $\ell$ meet in a point $P$, and divide the cube into ...

#### July 07, 2014

### HSG - Circumscribed Triangles

Below is a picture of a triangle circumscribed about a circle: Suppose we are given a circle $X$ an...

#### July 07, 2014

### HSF - Solving Problems with Linear and Exponential Models

Raphael deposits \$10,000 in a bank account which earns 5% interest, compounded annually. If he mak...

#### July 07, 2014

### HSA - Ideal Gas Law

A certain number of Xenon gas molecules are placed in a container at room temperature. If $V$ is th...

#### July 07, 2014

### HSA - Uranium 238

Uranium 238 is a radioactive material with many applications in nuclear technology. It decays expon...

#### July 07, 2014

### HSG - Volume formulas for cylinders and prisms

The volume of a rectangular prism of length $l$, width $w$, and height $h$ is $l \times w \times h$...

#### July 05, 2014

### HSF - Moore's Law and Computers

PersonalComputer hard disk capacity has grown at a remarkably steady exponential rate for several d...

#### July 04, 2014

### HSA - Canoe Trip

Jamie and Ralph take a canoe trip up a river for $1$ mile and then return. The current in the river...

#### July 04, 2014

### HSA - An Extraneous Solution

Megan is working solving the equation $$\frac{2}{x^2-1} - \frac{1}{x-1} = \frac{1}{x+1}.$$ She says...

#### July 03, 2014

### 3 - How Heavy?

Students will need various items, a balance scale, a large set of cubes such as unifix or snap cube...

#### July 01, 2014

### HSF - Special Triangles 2

Use the unit circle and indicated triangle below to find the exact value of the sine and cosine of ...

#### May 20, 2014

### 5 - Elmer's Multiplication Error

This is Elmer’s work on a multiplication problem: Use estimation to explain why Elmer’s answer is...

#### May 18, 2014

### HSF - 1,000 is half of 2,000

A new internet organization called Illuminated Manifolds (IM) is trying to generate 2,000 insightfu...

#### May 13, 2014

### 6 - Gianna's Job

Gianna is paid \$90 for 5 hours of work. At this rate, how much would Gianna make for 8 hours of wo...

#### May 12, 2014

### 7 - Drinking the Lake

About how much water does an average person drink in a life time? Explain. What size container woul...

#### May 12, 2014

### HSG - Defining Parabolas Geometrically

Suppose $F = (0,2)$ and $\ell$ is the $x$-axis: Find the point on the $y$-axis equidistant from $F$...

#### May 09, 2014

### HSG - Slope Criterion for Perpendicular Lines

Suppose $\ell$ and $k$ are lines with slopes $m$ and $-\frac{1}{m}$ respectively where $m$ is a non...

#### May 09, 2014

### HSN - Complex Cube and Fourth Roots of 1

For each odd positive integer $n$, the only real number solution to $x^n = 1$ is $x = 1$ while for ...

#### May 08, 2014

### HSA - Graphing from Factors III

Mike is trying to sketch a graph of the polynomial $$ f(x)=x^3+4x^2+x-6. $$ He notices that the coe...

#### May 08, 2014

### HSG, HSF - Coordinates of Points on a Circle

Below is a picture of the unit circle in the plane with an angle of measure $a$: What are the coord...

#### May 06, 2014

### 3 - Three Hidden Rectangles

There are many ways to find the area of this figure. Try to find as many ways as you can to split t...

#### May 06, 2014

### HSF - Bank Account Balance

At the beginning of the week, Jessie had \$500 in her bank account. She deposited a check for \$50 ...

#### May 05, 2014

### HSG - Similar Triangles

Alicia has two triangles $ABC$ and $PQR$ whose corresponding sides are proportional as pictured bel...

#### May 05, 2014

### HSF - Calculations with sine and cosine

Complete the following table, rounding off each answer to the nearest hundredth if using a calculat...

#### May 05, 2014

### HSS - Identifying Outliers

Students were asked to report how far (in miles) they each live from school. The following distance...

#### May 03, 2014

### HSS - Measuring Variability in a Data Set

Jim has taken 4 exams in his Statistics class. Exam Score 1 92 2 84 3 96 4 100 Both the MAD (mea...

#### May 03, 2014

### HSS - Understanding the Standard Deviation

This task is divided into four parts. Part 1 Below are dot plots for three different data sets. Th...

#### May 03, 2014

### HSS - The Addition Rule

Consider the population consisting of the students at a high school who are members of the student ...

#### May 03, 2014

### HSS - Describing Data Sets with Outliers

For certain data sets, such as home prices and household or individual income,is oftendescribed usi...

#### May 03, 2014

### HSS - Describing Events

The 10 cards below provide information on the ten students on the robotics team at a high school. T...

#### May 03, 2014

### HSF - What exactly is a radian?

Definition: An angle of $1$ radian is defined to be the angle, in the counterclockwise direction, a...

#### May 02, 2014

### HSN - New Cuyama

On a road trip in California, Lisa saw a sign which made her laugh and take a picture: What is math...

#### May 02, 2014

### HSA - Powers of 11

Felicia notices what appears to be an interesting pattern between powers of 11 and powers of $x + 1$...

#### May 02, 2014

### HSN - Sums of rational and irrational numbers

Explain why the sum and product of two rational numbers is always a rational number. Kaylee says I ...

#### April 30, 2014

### HSG - Triangle Perimeters

Below is a picture of two triangles with vertices on coordinate grid points: What are the perimeter...

#### April 30, 2014

### HSG - Parallel Lines in the Coordinate Plane

Suppose $\ell$ and $m$ are parallel lines in the plane. What can you deduce about the slopes of $\ell$...

#### April 30, 2014

### HSG - Similar Quadrilaterals

Quadrilaterals $ABCD$ and $EFGH$ have three corresponding congruent angles: $m(\angle A) = m(\angle E)$...

#### April 30, 2014

### HSG - When are two lines perpendicular?

Suppose $\ell$ and $m$ are lines containing $(0,0)$ as pictured below: The unit circle is also show...

#### April 30, 2014

### 2 - Buttons odd and even

6 is even. We can write 3+3=6 to show this. 7 is odd. We can write 3+3+1=7 to show this. Count out...

#### April 29, 2014

### K - Ten Frame Addition

Materials One 10-frame per pair of students (see example below) Counters, 10 per pair of students D...

#### April 29, 2014

### HSN - Evaluating Exponential Expressions

Henry explains why $4^{3/2} = 8$: I know that $4^3$ is 64 and the square root of 64 is 8. Here is H...

#### April 29, 2014

### HSG - Midpoints of Triangle Sides

Suppose $ABC$ is a triangle. Let $M$ be the midpoint of $\overline{AB}$ and $P$ the midpoint of $\overline{BC}$...

#### April 29, 2014

### HSF - Snake on a Plane

In a video game called Snake, a player moves a snake through a square region in the plane, trying t...

#### April 29, 2014

### HSF - Bicycle Wheel

The wheels on a bicycle have a radius of 13 inches. One wheel is pictured below: The point $O$ is t...

#### April 29, 2014

### HSA - Rewriting a Quadratic Expression

What is the minimum value taken by the expression $(x-4)^2 + 6$? How does the structure of the expr...

#### April 29, 2014

### 2 - Choral Counting

Materials Chart paper Marker Actions The teacher will begin by asking a student volunteer to show 3...

#### April 22, 2014

### 1 - Peyton's Books

Materials Chart paper Word problem Peyton had 16 books to take on his trip. He lost some. Now hehas...

#### April 22, 2014

### 2 - Choices, Choices, Choices

Arianna has been saving her chore money all summer. Her mother has allowed her to spend the money o...

#### April 15, 2014

### 2 - Pet Shop

Materials Coins and dollar bills Problem with table of costs displayed Stuffed Animals at the Pet S...

#### April 15, 2014

### 2 - Using Pictures to Explain Number Comparisons

Compare each pair of numbers. Write your comparison using $\lt, =,$ or $\gt$ and in words. Explain ...

#### April 15, 2014

### 4 - Mental Division Strategy

Jillian says I know that 20 times 7 is 140 and if I take away 2 sevens that leaves 126. So 126 $\div$...

#### April 15, 2014

### 5 - Rounding to Tenths and Hundredths

A number $n$ is shown on the number line. 1. The tick marks are evenly spaced. Label them. 2. What ...

#### April 15, 2014

### 5 - Placing Thousandths on the Number Line.

Label all of the tick marks on the number line. Plot and label each of the following numbers on the...

#### April 15, 2014

### 5 - Comparing Decimals on the Number Line

Which is greater, 0.1 or 0.01? Show the comparison on the number line. Which is greater, 0.2 or 0.0...

#### April 15, 2014

### 2 - Number Line Comparisons

Plot the following numbers on the number line. $$ $$ $$ 456 \qquad \qquad 983\qquad \qquad 938 \qquad \qquad 425 \qquad \qquad 220 \qquad \qquad 202\qquad \qquad 799 $$...

#### April 04, 2014

### HSN - Giving raises

A small company wants to give raises to their 5 employees. They have $10,000 available to distribut...

#### April 01, 2014

### HSF - Hours of Daylight 1

In order to determine how effective solar panels would be at various times of the year it is import...

#### April 01, 2014

### HSF - Finding Trig Values

Suppose that $\cos\theta = \frac{2}{5}$ and that $\theta$ is in the 4th quadrant. Find $\sin\theta$...

#### April 01, 2014

### HSF - Special Triangles 1

Use the unit circle and indicated triangle below to find the exact value of the sine and cosine of ...

#### April 01, 2014

### HSF - Trig Functions and the Unit Circle

The points on the graphs and the unit circle below were chosen so that there is a relationship betw...

#### April 01, 2014

### 4 - Defining Attributes of Rectangles and Parallelograms

Look at each figure. Read each of the descriptions. Place an X in the box if it appears to describe...

#### March 30, 2014

### 2 - Many Ways to do Addition 2

Materials For each student: * A large index card * A pencil Action Part 1 The teacher will put up t...

#### March 25, 2014

### 1 - Cave Game Subtraction

Materials * A cup for each student to represent his/her cave * Counters * Recording sheet Actions T...

#### March 25, 2014

### 1 - Fact Families with Pictures

Write as many equations for each picture as you can. Use the numbers 4, 1, and 5. Here are some equ...

#### March 25, 2014

### K - Bags of Stuff

#### Materials * 10-15 quart plastic bags of various counters (different numbers of counters in eac...

#### March 25, 2014

### HSA - Rewriting equations

In each of the equations below, rewrite the equation, solving for the indicated variable If $F$ den...

#### March 20, 2014

### HSA - Visualizing Completing the Square

Enrico has discovered a geometric technique for ''completing the square'' to find the solutions of ...

#### March 20, 2014

### HSA - Estimating a Solution via Graphs

Jason and Arianna are working on solving the system of linear equations $$ \begin{align} 6x + 17y &= 100\\ 5x + 9y &= 86. \end{align} $$...

#### March 20, 2014

### HSN - Kepler's Third Law of Motion

Below is a picture of the (elliptical) orbit of a planet around the sun: The sun is at point $A$, p...

#### March 20, 2014

### HSF - Dido and the Foundation of Carthage

According to ancient legend, Dido made a deal with a local ruler to obtain as much land as she coul...

#### March 20, 2014

### HSS - Finding Probabilities of Compound Events

Cecil has two six-sided dice, a red one and a white one. If Cecil throws the two dice, what is the ...

#### March 20, 2014

### HSG - Scaling a Triangle in the Coordinate Plane

Below is a picture of $\triangle ABC$ with vertices lying on grid points: Draw the image of $\triangle ABC$...

#### March 20, 2014

### HSF - Equilateral triangles and trigonometric functions

In the picture below, the purple circle is the set of points in the plane whose distance from the o...

#### March 20, 2014

### HSF - Triangular Numbers

Below are pictures of the first three triangular numbers: In general, the $n^{\text{th}}$ triangula...

#### March 20, 2014

### K - Which is Longer?

Materials Blackline Master Pencil or Crayons Long, skinny objects to compare; for example: a pair o...

#### March 18, 2014

### K - What Makes a Teen Number?

Decompose teen numbers using 10-frames and a number equation. #### Materials * Number cards 11-19 *...

#### March 18, 2014

### 4 - Thousands and Millions of Fourth Graders

There are almost 40 thousand fourth graders in Mississippi and almost 400 thousand fourth graders i...

#### March 18, 2014

### K - Dice Addition 2

Adding two numbers to make an equation. #### Materials * One pair of dice per student * A recording...

#### March 13, 2014

### K - Goodie Bags

Compare 3 quantities and order them from least to greatest. #### Materials * 5-6 baggies of various...

#### March 13, 2014

### K - Longer and Shorter

#### Materials * One of the student's shoes to use to compare to other items. * A bin of seven to t...

#### March 13, 2014

### 7 - Cube Ninjas!

Imagine you are a ninja that can slice solid objects straight through. You have a solid cube in fro...

#### March 10, 2014

### 6, 5 - Standing in Line

Alysha really wants to ride her favorite ride at the amusement park one more time before her parent...

#### February 27, 2014

### 5 - Meerkat Coordinate Plane Task

Greetings from the Kalahari Desert in South Africa! In this activity, you will learn a lot about th...

#### February 27, 2014

### 5 - Are these equivalent to 9.52?

Isaiah is thinking of the number 9.52 in his head. Decide whether each of these has the same value ...

#### February 26, 2014

### 3 - Finding the unknown in a division equation

Tehya and Kenneth are trying to figure out which number could be placed in the box to make this equ...

#### February 18, 2014

### 3, 4 - Rounding to the Nearest 100 and 1000

Plot the following numbers on the number line: 80 328 791 1. Round each number to the nearest 100. ...

#### February 18, 2014

### 3 - Rounding to the Nearest Ten and Hundred

Plot 8, 32, and 79 on the number line. 1. Round each number to the nearest 10. How can you see this...

#### February 18, 2014

### 5 - Which number is it?

Netta drew a picture on graph paper: She said, In my picture, a big square represents 1. Since ten ...

#### February 18, 2014

### 5 - Drawing Pictures to Illustrate Decimal Comparisons

1. Which is greater, 0.01 or 0.001? Explain. Draw a picture to illustrate your explanation. 2. Whic...

#### February 18, 2014

### 4 - Rounding to the Nearest 1000

The tick marks on the number line are evenly spaced. Label them. Plot the following numbers on the ...

#### February 18, 2014

### 4 - Threatened and Endangered

Maned wolves are a threatened species that live in South America. People estimate that there are ab...

#### February 18, 2014

### , HSG - Volume Estimation

Charles and Olivia are trying to estimate the volume of water that could be held by the figure show...

#### February 17, 2014

### 5 - Tenths and Hundredths

Jossie drew a picture to represent 0.24: She said, The little squares represent tenths and the rect...

#### January 30, 2014

### HSS - Math test grades

Ari has collected data on how much her classmates study each week and how well they did on their re...

#### January 07, 2014

### HSS - False Positive Test Results

A certain test for mononucleosis has a 99% chance of correctly diagnosing a patient with mononucleo...

#### January 07, 2014

### HSF - Trigonometric functions for arbitrary angles (radians)

Below is a picture of a right triangle with $a$ the measure of angle $A$: Joyce knows that the sine...

#### January 07, 2014

### HSG - Defining Trigonometric Ratios

Below is a picture of $\triangle ABC$: Draw a triangle $DEF$ that is similar (but not congruent) to...

#### January 07, 2014

### HSN, HSF, HSG - Coordinates of equilateral triangles

Is there an equilateral triangle $ABC$ so that $\overline{AB}$ lies on the $x$-axis and $A$, $B$, a...

#### January 07, 2014

### HSG - Sine and Cosine of Complementary Angles

Suppose $0^\circ \lt a \lt 90^\circ$ is the measure of an acute angle. Draw a picture and explain w...

#### January 07, 2014

### HSN, HSA - Completing the square

Renee reasons as follows to solve the equation $x^2 + x + 1 = 0$. First I will rewrite this as a sq...

#### January 07, 2014

### HSN - Powers of a complex number

Let $z = 1 + i$ where $i^2 = -1$. Calculate $z^2, z^3,$ and $z^4$. Graph $z, z^2, z^3,$ and $z^4$ i...

#### January 07, 2014

### HSG - A Ton of Snow

Eric and Julianne are shoveling snow. After an hour of hard work, Eric remarks ''I bet we have shov...

#### January 07, 2014

### HSG - Squares on a coordinate grid

In the picture below a square is outlined whose vertices lie on the coordinate grid points: The are...

#### January 06, 2014

### HSG - Finding triangle coordinates

Below is a picture of a triangle $ABC$ on the coordinate grid. The red lines are parallel to $\overleftrightarrow{BC}$...

#### January 06, 2014

### HSG - Properties of Congruent Triangles

Below is a picture of two triangles: Suppose there is a sequence of rigid motions which maps $\triangle ABC$...

#### January 06, 2014

### HSF - Properties of Trigonometric Functions

Below is a picture of an angle $\theta$ in the $x$-$y$ plane with the unit circle sketched in purpl...

#### January 06, 2014

### HSG, HSF - Trigonometric Identities and Rigid Motions

Sketch graphs of $f(x) = \cos{x}$ and $g(x) = \sin{x}$. Find a translation of the plane which maps ...

#### January 06, 2014

### HSF - Trigonometric Ratios and the Pythagorean Theorem

In the triangle pictured above show that $$ \left(\frac{|AB|}{|AC|}\right)^2 + \left(\frac{|BC|}{|AC|}\right)^2 = 1 $$...

#### January 06, 2014

### HSF - Exploring Sinusoidal Functions

In this task we will explore the effect that changing the parameters in a sinusoidal function has o...

#### January 06, 2014

### 8 - Spiderbox

A spider walks on the outside of a box from point A to B to C to D and finally to point E as shown ...

#### November 25, 2013

### K - My Book of Five

Materials Double sided counters Markers that are the same colors as the counters Teacher-made “My B...

#### November 14, 2013

### 8 - Function Rules

A function machine takes an input, and based on some rule produces an output. The tables below show...

#### October 30, 2013

### HSG - How far is the horizon?

Milong and her friends are at the beach looking out onto the ocean on a clear day and they wonder h...

#### October 30, 2013

### HSG - Folding a square into thirds

Suppose we take a square piece of paper and fold it in half vertically and diagonally, leaving the ...

#### October 30, 2013

### HSG - Pythagorean Theorem

Below is a picture of a right triangle $ABC$ with right angle $C$ along with the point $D$ so that ...

#### October 30, 2013

### HSG - Circumference of a circle

Suppose we define $\pi$ to be the circumference of a circle whose diameter is 1: Explain why the ci...

#### October 30, 2013

### HSG - Tangent Line to Two Circles

In the picture below, points $A$ and $B$ are the centers of two circles and they are collinear with...

#### October 30, 2013

### HSG - Area of a circle

The goal of this task is to explain why the area enclosed by a circle $C$ of radius $r$ is $\pi r^2$...

#### October 30, 2013

### HSG - Fixed points of rigid motions

A rigid motion of the plane is a map of the plane to itself which preserves distances between point...

#### October 30, 2013

### HSG - Dilations and Distances

Let $f$ be the map which dilates the plane by a factor $r \gt 0$ with repsect to a center $O$. We w...

#### October 30, 2013

### HSG - Inscribing an equilateral triangle in a circle

Suppose we are given a circle of radius $r$. The goal of this task is to construct an equilateral t...

#### October 30, 2013

### HSF, HSA - Modeling London's Population

The table below shows historical estimates for the population of London. Year18011821 18411861 1881...

#### October 30, 2013

### HSF - Choosing an appropriate growth model

Below are population estimates for the larger metropolitan areas of Paris (France), Shenzhen (China...

#### October 30, 2013

### HSF - Boiling Water

Below is a table showing the approximate boiling point of water at different elevations: Elevation ...

#### October 30, 2013

### HSG - Showing a triangle congruence: a particular case

Triangles $ABC$ and $PQR$ pictured below are congruent: Show the congruence using rigid motions of ...

#### October 30, 2013

### HSG - Showing a triangle congruence: the general case

Suppose $\triangle ABC$ and $\triangle PQR$ are distinct, congruent triangles. Using the steps belo...

#### October 29, 2013

### HSG - Parallelograms and Translations

Suppose $\overline{AB}$ is a line segment and $D$ is a point not on $\overline {AB}$ as pictured be...

#### October 29, 2013

### 6 - Hippos Love Pumpkins

Hippos sometimes get to eat pumpkins as a special treat. If 3 hippos eat 5 pumpkins, how many pumpk...

#### October 23, 2013

### HSA - Bernardo and Sylvia Play a Game

Bernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected a...

#### October 21, 2013

### HSG - Defining Perpendicular Lines

Three students have proposed these ways to describe when two lines $\ell$ and $m$ are perpendicular...

#### October 14, 2013

### HSG - Origami regular octagon

Lisa makes an octagon by successively folding a square piece of paper as follows. First, she folds ...

#### October 14, 2013

### HSA - Products and Reciprocals

The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the rec...

#### October 14, 2013

### HSG - Defining Parallel Lines

Alex and his friends are studying for a geometry test and one of the main topics covered is paralle...

#### October 14, 2013

### HSG - Origami equilateral triangle

Jessica is working to construct an equilateral triangle with origami paper and uses the following s...

#### October 14, 2013

### 8 - Congruence of Alternate Interior Angles via Rotations

Suppose $\ell$ and $m$ are parallel lines with $Q$ a point on $\ell$ and $P$ a point on $m$ as pict...

#### October 14, 2013

### 8, HSG - Origami Silver Rectangle

This task examines the mathematics behind an origami construction of a rectangle whose sides have t...

#### October 14, 2013

### HSG - Orbiting Satellite

A satellite orbiting the earth in a circular path stays at a constant altitude of 100 kilometers th...

#### October 14, 2013

### HSS, HSF - Laptop Battery Charge 2

Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend...

#### October 14, 2013

### HSG - Ask the Pilot

In the July 2013 issue of United Airlines' Hemisphere Magazine the following article appeared: Writ...

#### October 13, 2013

### 5 - Fractions on a Line Plot

You and your partner will need fraction cards made from this set: Label the line-plot below with $\frac18$...

#### September 23, 2013

### 5 - Using Volume to Understand the Associative Property of Multiplication

Make sure you have plenty of snap cubes. Build a rectangular prism that is 2 cubes on one side, 3 c...

#### September 21, 2013

### 5 - You Can Multiply Three Numbers in Any Order

Make sure you have plenty of snap cubes. * Build a rectangular prism that is 2 cubes high, 3 cubes ...

#### September 21, 2013

### 1 - Link-Cube Addition

Materials * Link-cubes or snap-cubes (2 colors for each student or pair of students) * A die * Pape...

#### September 18, 2013

### 5 - Picturing Factors in Different Orders

Find all the factor pairs for 30. For each factor pair, draw a picture that shows both of the facto...

#### September 18, 2013

### HSG - Equal Area Triangles on the Same Base I

On graph paper, sketch a line segment with end points $A=(0,2)$ and $B=(0,6)$. Plot all points $C=(x,y)$...

#### September 11, 2013

### HSG - Indiana Jones and the Golden Statue

The following clip shows the famous opening scene of the movie Raiders of the Lost Arc. At the begi...

#### September 11, 2013

### HSA - Pythagorean Triples

This task will investigate the intersection points of the circle $C$ of radius 1 centered at $(0,0)$...

#### September 11, 2013

### HSA - Reasoning with linear inequalities

The following is a student solution to the inequality $$ \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. $$...

#### September 11, 2013

### HSA - Collinear points

Consider three points in the plane, $P=(-4, 0), Q=(-1, 12)$ and $R=(4, 32)$. Find the equation of t...

#### September 09, 2013

### HSS - Used Subaru Foresters II

Jane wants to sell her Subaru Forester and does research online to find other cars for sale in her ...

#### September 08, 2013

### HSS - Used Subaru Foresters I

Jane wants to sell her Subaru Forester, but doesn’t know what the listing price should be. She chec...

#### September 08, 2013

### HSS - Olympic Men's 100-meter dash

The scatterplot below shows the finishing times for the Olympic gold medalist in the men's 100-mete...

#### September 08, 2013

### 6 - Identifying Statistical Questions

Which of the following are statistical questions? (A statistical question is one that can be answer...

#### September 08, 2013

### 7 - Stay or Switch?

You are playing a video game. At the end of every level, there are three boxes. One contains 10,000...

#### September 08, 2013

### 6 - Polygons in the Coordinate Plane

The vertices of eight polygons are given below. For each polygon: Plot the points in the coordinate...

#### September 08, 2013

### 4 - Measuring Angles

Draw an angle that measures 60 degrees like the one shown here: Draw another angle that measures 25...

#### September 08, 2013

### 8 - Circle Sandwich

A square is inscribed in a circle which is inscribed in a square as shown below. Note that the vert...

#### September 08, 2013

### 7 - Map distance

On the map below, $\frac14$ inch represents one mile. Candler, Canton, and Oteen are three cities o...

#### September 08, 2013

### 7 - Differences and Distances

Conner and Aaron are working on their homework together to find the distance between two numbers, $a$...

#### September 07, 2013

### 3 - Markers in Boxes

Presley has 18 markers. Her teacher gives her three boxes and asks her to put an equal number of ma...

#### September 07, 2013

### 6 - Distances between Points

Some points are shown in the coordinate plane below. What is the distance between points B & C? Wha...

#### September 06, 2013

### 1 - Fact Families

Materials * Fact Family work sheets * Blank addition and subtraction frames (2 of each) * Numbers c...

#### September 06, 2013

### 8 - Orders of Magnitude

It is said that the average person blinks about 1000 times an hour. This is an order-of-magnitude e...

#### September 06, 2013

### 8 - Folding a Square into Thirds

Suppose we take a square piece of paper and fold it in half vertically and diagonally, leaving the ...

#### September 04, 2013

### HSF - Building an Explicit Quadratic Function by Composition

Let $f$ be the function defined by $f(x) = 2x^2 + 4x - 16$. Let $g$ be the function defined by \beg...

#### August 26, 2013

### 7 - Red, Green, or Blue?

This is a game for two people. You have three dice; one is red, one is green, and one is blue. Thes...

#### August 23, 2013

### HSA - Silver Rectangle

Below is a picture of a rectangle $ABCD$ with segment $\overline{MN}$ drawn where $M$ is the midpoi...

#### August 20, 2013

### HSF - Analyzing Graphs

Pictured below are the graphs of four different functions, defined in terms of eight constants: $a, b, c, k, m, p, q, \text{ and } r.$...

#### August 20, 2013

### 4 - Button Diameters

With a partner or group, gather a handful of round buttons from a diverse collection, and use a rul...

#### August 20, 2013

### 4 - What's My Number?

Find a number greater than 0 and less than 1,000 that: Is closer to 500 than 0, and Is closer to 20...

#### August 20, 2013

### 8 - Slopes Between Points on a Line

The slope between two points is calculated by finding the change in $y$-values and dividing by the ...

#### August 19, 2013

### 7 - Stained Glass

The students in Mr. Rivera's art class are designing a stained-glass window to hang in the school e...

#### August 19, 2013

### 5 - Multiplying Decimals by 10

Explain why $0.4\times10=4$. Explain why $3.4\times10=34$. Draw pictures to illustrate your explana...

#### August 15, 2013

### 6 - Setting Goals

Seth wants to buy a new skateboard that costs \$167. He has \$88 in the bank. If he earns \$7.25 an...

#### August 14, 2013

### 5 - Marta's Multiplication Error

Marta made an error while finding the product $84.15 \times 10$. In your own words, explain Marta’s...

#### August 13, 2013

### HSF - Graphene

Graphite is a mineral with many technological uses and it is perhaps most familiar for its use in w...

#### August 13, 2013

### HSG - Classifying Triangles

Choose two distinct points $A$ and $B$ in the plane. For which points $C$ is $\triangle ABC$ a righ...

#### August 13, 2013

### HSA - Introduction to Polynomials - College Fund

When Marcus started high school, his grandmother opened a college savings account. On the first day...

#### August 13, 2013

### 3 - Fish Tanks

Suppose there are 4 tanks and 3 fish in each tank. The total number of fish in this situation can b...

#### August 13, 2013

### 8 - Stuffing Envelopes

Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns \$14 for...

#### August 12, 2013

### 5 - Kipton's Scale

Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much wou...

#### August 12, 2013

### HSF - Running Time

Many computer applications use very complex mathematical algorithms. The faster the algorithm, the ...

#### August 12, 2013

### 7 - Who is the better batter?

Below is a table showing the number of hits and the number of times at bat for two Major League Bas...

#### August 10, 2013

### 7 - Dueling Candidates

Joel and Marisa are running for president at their middle school (grades 6-8). After the votes are ...

#### August 10, 2013

### HSA - Profit of a company, assessment variation

The profit, $P$ (in thousands of dollars), that a company makes selling an item is a quadratic func...

#### August 08, 2013

### 6, 7 - Climbing the steps of El Castillo

Chichén Itzá was a Mayan city in what is now Mexico. The picture below shows El Castillo, also know...

#### August 07, 2013

### 7 - Thunder and Lightning

Alyssa sees a lightning bolt in the sky and counts four seconds until she hears the thunder. There ...

#### August 07, 2013

### 5 - Using Operations and Parentheses

What numbers can you make with 1, 2, 3, and 4? Using the operations of addition, subtraction, and m...

#### August 07, 2013

### 5 - Measuring Cups

Lucy has measuring cups of sizes 1 cup, $\frac{1}{2}$ cup, $\frac{1}{3}$ cup, and $\frac{1}{4}$ cup...

#### August 07, 2013

### 6 - Sierpinski's Carpet

Take a square with area 1. Divide it into 9 equal-sized squares. Remove the middle one. What is the...

#### August 06, 2013

### 8 - Finding isosceles triangles

Mrs. Lu has asked students in her class to find isosceles triangles whose vertices lie on a coordin...

#### August 05, 2013

### 7 - Lincoln's math problem

If 100 dollars in one year gain $3\frac12$ dollars interest, what sum will gain \$38.50 cents in on...

#### August 01, 2013

### 8 - Laptop Battery Charge

Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend...

#### July 31, 2013

### HSF - Temperature Change

The table below shows the temperature, $T,$ in Tucson, Arizona $t$ hours after midnight. When does ...

#### July 24, 2013

### 7 - Proportionality

A text book has the following definition for two quantities to be directly proportional: We say tha...

#### July 16, 2013

### HSG - Defining Rotations

Consider the following possible definitions for rotation of the plane by an angle $a$ about the poi...

#### July 09, 2013

### HSG - Defining Reflections

Carlos finds the following definition of a reflection in a math book: The reflection $r_\ell$ about...

#### July 09, 2013

### 7 - Walk-a-thon 2

Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total d...

#### July 07, 2013

### 4 - To regroup or not to regroup

Sometimes when we subtract one number from another number we "regroup," and sometimes we don't. For...

#### June 28, 2013

### 2 - Hitting The Target Number

Materials * Number cards labeled 1-10 (attached as a PDF) Actions * Begin by playing the game as a ...

#### June 23, 2013

### 2 - Building toward fluency

Materials * Whiteboard or chart paper and markers * Empty number line or magnetic cubes lined up on...

#### June 23, 2013

### 2 - Alexander, Who Used to be Rich Last Sunday

Materials * Alexander, Who Used to be Rich Last Sunday by Judith Viorst * Plastic coins * Labels fo...

#### June 23, 2013

### 7 - The Circumference of a Circle and the Area of the Region it Encloses

What is the definition of a circle with center $A$ and radius $r$? A circle has center $A$ and radi...

#### June 21, 2013

### HSG - Equal Area Triangles on the Same Base II

Given a line segment with end points $A=(0,0)$ and $B=(6,8)$, find all points $C=(x, y)$ such that ...

#### June 21, 2013

### 4 - Who is the tallest?

Mr. Liu asked the students in his fourth grade class to measure their heights. Here are some of the...

#### June 06, 2013

### 7 - Tetrahedral Dice

Many games use dice which are six-sided and fair (meaning each face on the die is equally likely to...

#### June 05, 2013

### HSN - Complex number patterns

For this task, the letter $i$ denotes the imaginary unit, that is, $i=\sqrt{-1}$. For each integer ...

#### May 30, 2013

### HSA - Clea on an Escalator

It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to...

#### May 30, 2013

### HSF - Model air plane acrobatics

A model airplane pilot is practicing flying her airplane in a big loop for an upcoming competition....

#### May 30, 2013

### 1 - Grandfather Tang's Story

Materials * A copy of Grandfather Tang's Story by Ann Tompert * One set of tangrams for each studen...

#### May 29, 2013

### 8 - Placing a square root on the number line

Place $\sqrt{28}$ on a number line, accurate to one decimal point....

#### May 29, 2013

### 8 - Two Triangles' Area

Let $A$ be the area of a triangle with sides of length 25, 25, and 30. Let $B$ be the area of a tri...

#### May 29, 2013

### HSG - Symmetries of a quadrilateral II

There is exactly one reflection and no rotation that sends the convex quadrilateral ABCD onto itsel...

#### May 29, 2013

### HSF - Sum and Difference angle formulas

In this task, you will show how all of the sum and difference angle formulas can be derived from a ...

#### May 29, 2013

### 8 - Proportional relationships, lines, and linear equations

Lines $L$ and $M$ have the same slope. The equation of line $L$ is $4y=x$. Line $M$ passes through ...

#### May 28, 2013

### HSG - Congruence of parallelograms

Rhianna has learned the SSS and SAS congruence tests for triangles and she wonders if these tests m...

#### May 28, 2013

### HSG - Is this a parallelogram?

In quadrilateral $ABCD$ pictured below, $\overline{AB}$ is congruent to $\overline{CD}$ and $\overline{BC}$...

#### May 28, 2013

### HSG - Similar triangles

In the two triangles pictured below $m(\angle A) = m(\angle D)$ and $m(\angle B) = m(\angle E)$: Us...

#### May 28, 2013

### 7 - How Fast is Usain Bolt?

Jamaican sprinter Usain Bolt won the 100 meter sprint gold medal in the 2012 Summer Olympics. He ra...

#### May 28, 2013

### 4 - Multiples of 3, 6, and 7

Make a list of the first ten multiples of 3. Which of the numbers in your list are multiples of 6? ...

#### May 27, 2013

### 4 - Numbers in a Multiplication Table

The table below shows all the products of pairs of numbers between 1 and 9. Which numbers appear on...

#### May 27, 2013

### 3 - Shapes and their Insides

Draw a purple pentagon Draw a blue shape with 3 line segments that is not a triangle. Draw an orang...

#### May 27, 2013

### 3 - Finding the Area of Polygons

Find the area of each colored figure. Each grid square is 1 inch long.

#### May 27, 2013

### 6 - Walk-a-thon 1

Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total d...

#### May 27, 2013

### HSF - Latitude

Standard maps of the earth are broken into a grid of latitude lines (east-west) and longitude lines...

#### May 27, 2013

### HSA - How Much Folate?

Sara's doctor tells her she needs between 400 and 800 milligrams of folate per day, with part comin...

#### May 27, 2013

### HSA - Find A System

Without graphing, construct a system of two linear equations where $(-2,3)$ is a solution to the fi...

#### May 26, 2013

### HSS - The Marble Jar

Sometimes hotels, malls, banks, and other businesses will present a display of a large, clear conta...

#### May 24, 2013

### HSG - Tilt of earth's axis and the four seasons

The geometry of the earth-sun interaction plays a very prominent role in many aspects of our lives ...

#### May 24, 2013

### HSG - Explaining the equation for a circle

This problem examines equations defining different circles in the $x$-$y$ plane. Use the Pythagorea...

#### May 24, 2013

### HSG - Mutually Tangent Circles

Three circles, each having radius 2, are mutually tangent as pictured below: What is the total area...

#### May 24, 2013

### HSA - Egyptian Fractions II

Ancient Egyptians used unit fractions, such as $\frac{1}{2}$ and $\frac{1}{3}$, to represent all ot...

#### May 24, 2013

### HSA - Integer Solutions to Inequality

What is the sum of all integer solutions to $1\lt (x-2)^2\lt...

#### May 24, 2013

### HSG - Symmetries of rectangles

Jennifer draws the rectangle $ABCD$ below: Find all rotations and reflections that carry rectangle ...

#### May 24, 2013

### HSG - Symmetries of a circle

Suppose $C$ is a circle with center $O$ as pictured below: Find all lines of symmetry of the circle...

#### May 24, 2013

### HSG - Symmetries of a quadrilateral I

Suppose $ABCD$ is a quadrilateral for which there is exactly one rotation, through an angle larger ...

#### May 24, 2013

### HSG - Similar circles

For this problem, $(a,b)$ is a point in the $x$-$y$ coordinate plane and $r$ is a positive number. ...

#### May 24, 2013

### HSF - A valuable quarter

In 1901, the San Francisco mint produced only 72,664 quarters. By comparison, during other years ar...

#### May 24, 2013

### 1 - Domino Addition

Materials A large set of dominoes to affix to a whiteboard or place in a pocket chart, or a regular...

#### May 24, 2013

### 1 - Roll & Build

Materials For each pair: * 2 ten-sided dice with the numbers 0 to 9 or two spinners with the number...

#### May 24, 2013

### 8 - Animal Brains

Is there an association between the weight of an animal’s body and the weight of the animal’s brain...

#### May 23, 2013

### 2 - Polygons

* Color the inside of all the triangles blue. * Color the inside of all the quadrilaterals red. * C...

#### May 23, 2013

### 6 - Puzzle Times

Each of the 20 students in Mr. Anderson's class timed how long it took them to solve a puzzle. Thei...

#### May 22, 2013

### 7 - Heads or Tails

Each of the 20 students in Mr. Anderson's class flipped a coin ten times and recorded how many time...

#### May 22, 2013

### 2 - How Big is a Foot?

Materials * How Big is a Foot? by Rolf Myller * Masking tape * Enough 12-inch (one foot) rulers for...

#### May 22, 2013

### K - Finding Equal Groups

Material * Assorted objects to create the groups * Clear ziplock bags or small cups * Index cards a...

#### May 22, 2013

### 7 - Designs

Find the area and perimeter of the colored part of each of the six figures below. The purple, blue,...

#### May 20, 2013

### 5 - What is a Trapezoid? (Part 2)

Niko and Carlos are studying parallelograms and trapezoids. They agree that a parallelogram is a qu...

#### May 20, 2013

### 4 - What is a Trapezoid? (Part 1)

Say what a trapezoid is in your own words. Compare your definition with a partner. Is this parallel...

#### May 20, 2013

### 4 - What's the Point?

The students in Ms. Sun's class were drawing geometric figures. First she asked them to draw some p...

#### May 19, 2013

### 8 - Sammy's Chipmunk and Squirrel Observations

For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipm...

#### May 19, 2013

### 6 - Seven to the What?!?

What is the last digit of $7^{2011}$? Explain. What are the last two digits of $7^{2011}$? Explain.

#### May 19, 2013

### HSG - Paper Clip

This paper clip is just over 4 cm long. How many paper clips like this may be made from a straight ...

#### May 19, 2013

### 4 - The Geometry of Letters

Letters can be thought of as geometric figures. How many line segments are needed to make the lette...

#### May 18, 2013

### 3 - Snow Day

Alec and Felix are brothers who go to different schools. The school day is just as long at Felix' s...

#### May 17, 2013

### 3 - How Many Colored Pencils?

There are 6 tables in Mrs. Potter's art classroom. There are 4 students sitting at each table. Each...

#### May 17, 2013

### HSA - Seeing Dots

Consider the algebraic expressions below: $$ (n + 2)^2 - 4 \qquad \text{and} \qquad n^2 + 4n. $$ Us...

#### May 17, 2013

### 4 - The Locker Game

The 20 students in Mr. Wolf's 4th grade class are playing a game in a hallway that is lined with 20...

#### May 17, 2013

### 2 - Looking at Numbers Every Which Way

127 is a number. Write it as a sum of 100's, 10's, and 1's. Write its name in words. Draw a picture...

#### May 16, 2013

### 2 - Ordering Time

Materials * Sets of 3-6 "analog clock cards," enough for each student * Sets of 3-6 "digital clock ...

#### May 16, 2013

### 3 - Halves, thirds, and sixths

A small square is a square unit. What is the area of this rectangle? Explain. What fraction of the ...

#### May 16, 2013

### 8 - Heart Rate Monitoring

Serena is starting a new workout routine and wants to keep track of her heart rate to make sure tha...

#### May 16, 2013

### 4 - What shape am I?

Draw at least two examples and two non-examples of each of the quadrilaterals defined below. Parall...

#### May 16, 2013

### 8 - The Intersection of Two Lines

Draw the two lines that intersect only at the point $(1,4)$. One of the lines should pass through t...

#### May 15, 2013

### 8 - Summer Swimming

The local swim center is making a special offer. They usually charge \$7 per day to swim at the poo...

#### May 15, 2013

### 4 - Multiples of nine

Starting with 9, list the first 10 multiples of 9. In the list in part (a) what patterns do you see...

#### May 15, 2013

### 7 - Distances Between Houses

Aakash, Bao Ying, Chris and Donna all live on the same street as their school, which runs from east...

#### May 15, 2013

### 6 - Fruit Salad

A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a tot...

#### May 15, 2013

### 4 - Doubling Numerators and Denominators

How does the value of a fraction change if you double its numerator? Explain your answer. How does ...

#### May 15, 2013

### 4 - Cynthia's Perfect Punch

Cynthia is making her famous "Perfect Punch" for a party. After looking through the recipe, Cynthia...

#### May 15, 2013

### 4 - Fractions and Rectangles

What fraction of the rectangle below is shaded? Laura says that $\frac14$ of the rectangle is shade...

#### May 14, 2013

### 5 - The Value of Education

The table shows four people who earn the typical amount for their education level. NameLevel of Edu...

#### May 14, 2013

### 8 - A Triangle's Interior Angles

Given that $\overleftrightarrow{DE}\parallel\overleftrightarrow{AC}$ in the diagram below, prove th...

#### May 14, 2013

### 4 - Finding Lines of Symmetry

Each shape below has a line of symmetry. Draw a line of symmetry for each shape. Not every shape ha...

#### May 14, 2013

### 7 - Rounding and Subtracting

Xiaoli was estimating the difference between two positive numbers $x$ and $y$ (where $x\gt y$). Fir...

#### May 14, 2013

### 4 - Margie Buys Apples

Margie bought 3 apples that cost 50 cents each. She paid with a five-dollar bill. How much change d...

#### May 14, 2013

### 1 - Weather Graph Data

Materials * Completed monthly weather recording sheet * Crayons * Sentence strips with frames (see ...

#### May 13, 2013

### 1 - All vs. Only some

First pose the question: Here are four triangles. What do all of these triangles have in common? Wh...

#### May 13, 2013

### 7 - Bookstore Account

At the beginning of the month, Evan had \$24 in his account at the school bookstore. Use a variable...

#### May 13, 2013

### 5 - Cari's Aquarium

Cari is the lead architect for the city’s new aquarium. All of the tanks in the aquarium will be re...

#### May 13, 2013

### 1 - 20 Tickets

Materials 20 counters or linking cubes per pair of students pencil copy of the problem Actions The ...

#### May 05, 2013

### 1 - The Very Hungry Caterpillar

Materials The Very Hungry Caterpillar by Eric Carle The students work individually or in pairs. Eac...

#### April 24, 2013

### K - The Napping House

Materials The Napping House by Audrey Wood One ten-frame for each child (see PDF for black line mas...

#### April 23, 2013

### 1 - Growing Bean Plants

Materials - 2 clear plastic cups for each pair of students - 4 bean seeds for each pair - soil - un...

#### April 17, 2013

### 2 - Saving Money 1

Materials Popsicle sticks and rubber bands or base-10 blocks Paper and pencil for each student Acti...

#### April 03, 2013

### HSA - Delivery Trucks, assessment variation

A company uses two different-sized trucks to deliver concrete blocks. The first truck can transport...

#### April 01, 2013

### 4 - Are these right?

Which of the polygons are right triangles? Choose a measuring tool to help you determine this. The...

#### March 29, 2013

### 3 - Classroom Supplies

Your teacher was just awarded \$1,000 to spend on materials for your classroom. She asked all 20 of...

#### March 29, 2013

### HSA - A Cubic Identity

Let $a$ and $b$ be real numbers with $a>b>0$ and $\frac{a^3-b^3}{(a-b)^3}=\frac{73}{3}$. What is $\frac{b}{a}$...

#### March 29, 2013

### 8, HSG - Points from Directions

Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between point...

#### March 29, 2013

### 7 - Sitting across from Each Other

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side....

#### March 28, 2013

### HSA - Pairs of Whole Numbers

The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle...

#### March 27, 2013

### HSS - Alex, Mel, and Chelsea Play a Game

Alex, Mel, and Chelsea play a game that has 6 rounds. In each round there is a single winner, and t...

#### March 27, 2013

### HSG - Extensions, Bisections and Dissections in a Rectangle

In rectangle $ABCD$, $|AB|=6$, $|AD|=30$, and $G$ is the midpoint of $\overline{AD}$. Segment $AB$ ...

#### March 27, 2013

### HSG - Unit Squares and Triangles

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the ar...

#### March 27, 2013

### 3 - The Class Trip

Mrs. Moore’s third grade class wants to go on a field trip to the science museum. The cost of the t...

#### March 24, 2013

### 7 - The Price of Bread

Inflation is a term used to describe how prices rise over time. The rise in prices is in relation t...

#### March 24, 2013

### 2 - Visiting the Arcade

Amy went to the arcade. At the arcade, people can buy tokens to use for the games. Amy paid \$5 to ...

#### March 24, 2013

### HSF - Invertible or Not?

The table below shows some input-output pairs of two functions $f$ and $g$ that agree for the value...

#### March 22, 2013

### HSF - Basketball Bounces, Assessment Variation 1

SCREEN I In science class, some students dropped a basketball and allowed it to bounce. They measur...

#### March 19, 2013

### 7 - Molly's Run, Assessment Variation

Molly ran $\frac{2}{3}$ of a mile in 8 minutes. If Molly runs at that speed, how long will it take ...

#### March 18, 2013

### 6 - Riding at a Constant Speed, Assessment Variation

Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, How far did she ride in 1...

#### March 18, 2013

### 6 - The Escalator, Assessment Variation

Ty took the escalator to the second floor. The escalator is 12 meters long, and he rode the escalat...

#### March 18, 2013

### 3 - Fraction Comparisons With Pictures, Assessment Variation

Who correctly compares the numbers 2/3 and 2/5? Ben said that 2/3 is greater than 2/5. Lee said tha...

#### March 18, 2013

### 3 - Comparing Fractions with the Same Numerators, Assessment Variation

Choose each statement that is true. $\frac98$ is greater than $\frac{9}{4}$. $\frac{9}{4}$ is great...

#### March 18, 2013

### 3 - Comparing Fractions with the Same Denominator, Assessment Variation

Choose each statement that is true. $\frac34$ is greater than $\frac54$. $\frac54$ is greater than ...

#### March 18, 2013

### 8 - US Airports, Assessment Variation

The scatter plot below shows the relationship between the number of airports in a state and the pop...

#### March 18, 2013

### 8 - Delivering the Mail, Assessment Variation

Joshua's mail truck travels 14 miles every day he works, and is not used at all on days he does not...

#### March 18, 2013

### 7 - Buying Bananas, Assessment Version

Carlos bought $6\frac12$ pounds of bananas for \$5.20. What is the price per pound of the bananas t...

#### March 18, 2013

### 7 - Art Class, Assessment Variation

The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixt...

#### March 18, 2013

### 7 - Robot Races, Assessment Variation

The students in Carli’s class built some solar-powered robots which they raced in the cafeteria of ...

#### March 18, 2013

### 3 - Find 7/4 starting from 1, Assessment Variation

The number line below shows two numbers, 0 and 1. Where is $\frac74$ on this number line? http://ww...

#### March 18, 2013

### 3 - Find 1/4 Starting from 1, Assessment Version

The number line below shows two numbers, 0 and 1. Where is $\frac14$ on this number line? http://ww...

#### March 18, 2013

### 8 - Running on the Football Field

During the 2005 Divisional Playoff game between The Denver Broncos and The New England Patriots, Br...

#### March 17, 2013

### 7 - Gotham City Taxis

The taxi fare in Gotham City is \$2.40 for the first $\frac{1}{2}$ mile and additional mileage char...

#### March 17, 2013

### 6, 7 - Anna in D.C.

Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She le...

#### March 17, 2013

### 6, 8 - Pennies to heaven

A penny is about $\frac{1}{16}$ of an inch thick. In 2011 there were approximately 5 billion pennie...

#### March 17, 2013

### 7 - Rolling Twice

A fair six-sided die is rolled twice. What is the theoretical probability that the first number tha...

#### March 17, 2013

### 7 - Two-School Dance

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are ...

#### March 17, 2013

### 5 - Box of Clay

A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A s...

#### March 17, 2013

### 8 - Area of a Trapezoid

Quadrilateral $ABCD$ is a trapezoid, $AD = 15$, $AB = 50$, $BC = 20$, and the altitude is 12. What ...

#### March 17, 2013

### 6 - Overlapping Squares

Two congruent squares, $ABCD$ and $PQRS$, have side length 15. They overlap to form the 15 by 25 re...

#### March 16, 2013

### 8 - Partitioning a hexagon

Find a way to partition a regular hexagon into 2 congruent figures. Explain how you know the 2 figu...

#### March 16, 2013

### 5 - Minutes and Days

What time was it 2011 minutes after the beginning of January 1,...

#### March 16, 2013

### 8 - Point Reflection

The point in the $x$-$y$ plane with coordinates $(1000,2012)$ is reflected across the line $y=2000$...

#### March 16, 2013

### 2 - Frog and Toad on the number line

One day, Frog and Toad were sitting together on a lily pad. Some lily pads were in a line across th...

#### March 16, 2013

### 1 - Where Do I Go?

Materials Set of cards from 1-100, these can be purchased or created using a black marker and index...

#### March 16, 2013

### 8 - Cutting a rectangle into two congruent triangles

Below is a picture of rectangle $ABCD$ with diagonal $AC$. Draw the image of triangle $ACD$ when it...

#### March 16, 2013

### 8 - A rectangle in the coordinate plane

Below is a quadrilateral in the coordinate plane: Use the Pythagorean theorem to find the lengths o...

#### March 13, 2013

### 8, HSG - Is this a rectangle?

Is the quadrilateral with vertices $(-6, 2)$, $(-3,6)$, $(9, -3)$, $(6,-7)$ a rectangle? Explain.

#### March 13, 2013

### 8 - Bird and Dog Race

Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/...

#### March 13, 2013

### HSG - How thick is a soda can? Variation II

About how thick is a soda can? Explain which measurements you will need to take as well as extra in...

#### March 04, 2013

### HSG - Triangles inscribed in a circle

Suppose $A = (-1,0)$ and $B = (1,0)$ are points in the coordinate plane as pictured below: Suppose ...

#### March 04, 2013

### HSG - Circumcenter of a triangle

The goal of this task is to construct the circumcenter of a triangle, that is, the point which is t...

#### March 04, 2013

### HSG - Neglecting the Curvature of the Earth

Jerry and Ashley are trying to find out if it is possible to see the lowest point in the USA from t...

#### March 04, 2013

### HSF - Rainfall

The table below shows $R=f(t)$, the total amount of rain, in centimeters (cm), during a steady rain...

#### March 04, 2013

### HSS - Sarah, the chimpanzee

Many researchers have studied chimpanzees to learn about their problem solving skills. In 1978, res...

#### February 25, 2013

### HSS - Texting and Grades II

Medhavi suspects that there is a relationship between the number of text messages high school stude...

#### February 25, 2013

### 7 - Offensive Linemen

College football teams are grouped with similar teams into "divisions" (and in some cases, "subdivi...

#### February 24, 2013

### HSS - Coffee and Crime

Many counties in the United States are governed by a county council. At public county council meeti...

#### February 19, 2013

### 7 - Valentine Marbles

A hotel holds a Valentine's Day contest where guests are invited to estimate the percentage of red ...

#### February 19, 2013

### HSS - Speed Trap

A statistically-minded state trooper wondered if the speed distributions are similar for cars trave...

#### February 12, 2013

### HSS - How Do You Get to School?

All of the upper-division students (juniors and seniors) at a high school were classified according...

#### February 12, 2013

### HSS - Coffee at Mom's Diner

At Mom’s diner, everyone drinks coffee. Let $C =$ the event that a randomly-selected customer puts ...

#### February 12, 2013

### HSF - Rising Gas Prices – Compounding and Inflation

Inflation is the measure of the annual growth in the price of a good or service, computed as the pe...

#### February 11, 2013

### 1 - Field Day Scarcity

Materials * pictures of water bottle, snack, and ball (see black line master) * tools such as snap ...

#### February 10, 2013

### HSG - Building a tile pattern by reflecting hexagons

Below is a picture of a regular hexagon, which we denote by $H$, and two lines denoted $\ell$ and $m$...

#### February 09, 2013

### HSG - Building a tile pattern by reflecting octagons

Below is a picture of a regular octagon, which we denote by $O$, and two lines denoted $\ell$ and $m$...

#### February 09, 2013

### HSG - Mt. Whitney to Death Valley

The Morris family is on a road trip through California. One day they are driving from Death Valley ...

#### February 04, 2013

### HSF - A Saturating Exponential

Suppose a can of cold soda is left in a warm room on a summer day. The graph below shows the temper...

#### February 04, 2013

### HSF - Throwing Baseballs

Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given...

#### February 03, 2013

### HSA - Forms of exponential expressions

Four physicists describe the amount of a radioactive substance, $Q$ in grams, left after $t$ years:...

#### February 03, 2013

### HSA - Combined Fuel Efficiency

The US Department of Energy keeps track of fuel efficiency for all vehicles sold in the United Stat...

#### January 25, 2013

### 8 - Tile Patterns II: hexagons

A common tiling pattern with hexagons is pictured below: A regular hexagon is a hexagon with $6$ co...

#### January 23, 2013

### 8 - Tile Patterns I: octagons and squares

One interesting tile pattern (see for example this Tile Pattern) has four octagons surrounding what...

#### January 23, 2013

### HSG - Global Positioning System II

Global Positioning System or GPS devices receive input from satellites and use this information to ...

#### January 21, 2013

### HSG - Tangent to a circle from a point

Suppose $C$ is a circle with center $O$ and $P$ is a point ourside of $C$. Let $M$ be the midpoint ...

#### January 21, 2013

### HSG - Inscribing a circle in a triangle II

Suppose a circle with center $O$ is inscribed inside triangle $ABC$ as in the picture below: Also p...

#### January 21, 2013

### HSG - Inscribing a circle in a triangle I

The goal of this task is to show how to draw a circle which is tangent to all three sides of a give...

#### January 21, 2013

### HSG, HSA - Global Positioning System I

The distance between two points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is given by $$ \sqrt{(x_1 - x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2}. $$...

#### January 21, 2013

### HSG - Joining two midpoints of sides of a triangle

Suppose $ABC$ is a triangle. Let $M$ be the midpoint of $\overline{AB}$ and $\ell$ the line through...

#### January 21, 2013

### HSG - Hexagonal Pattern of Beehives

Beehives are made of walls, each of the same size, enclosing small hexagonal cells where honey and ...

#### January 21, 2013

### HSG - Running around a track II

An Olympic $400$ meter track is made up of two straight sides, each measuring $84.39$ meters in len...

#### January 21, 2013

### HSG - Running around a track I

An Olympic $400$ meter track is made up of two straight sides, each measuring $84.39$ meters in len...

#### January 21, 2013

### HSG, HSA - Regular Tessellations of the plane

A tessellation of the plane is an arrangement of polygons which cover the plane without gaps or ove...

#### January 21, 2013

### HSG - Inscribing a triangle in a circle

The circumcenter of a triangle $ABC$ is the point in the plane which is equidistant from the three ...

#### January 21, 2013

### HSG - Right triangles inscribed in circles II

Suppose $ABC$ is a triangle with angle $ACB$ a right angle. Suppose $M$ is the midpoint of segment ...

#### January 21, 2013

### HSG - Right triangles inscribed in circles I

Suppose $\overline{AB}$ is a diameter of a circle and $C$ is a point on the circle different from $A$...

#### January 21, 2013

### HSA - Sum of angles in a polygon

Below is a quadrilateral $ABCD$: Show, by dividing $ABCD$ into triangles, that the sum of the inter...

#### January 21, 2013

### HSG - Finding the Area of an Equilateral Triangle

Below is an equilateral triangle whose side lengths are each $1$ unit: Find the area of $\triangle ABC$.

#### January 20, 2013

### 8 - Areas of Geometric Shapes with the Same Perimeter

Below are pictures of an equilateral triangle, a square, a regular hexagon, and a circle each havin...

#### January 20, 2013

### HSG - How many leaves on a tree?

Amy and Greg are raking up leaves from a large maple tree in their yard and Amy remarks "I'll bet t...

#### January 20, 2013

### HSG - How many leaves on a tree? (Version 2)

Amy and Greg look for a method to estimate the number of leaves on a $35$ foot tree in their yard. ...

#### January 20, 2013

### 1 - Measure Me!

Materials * Student worksheet * Unifix cubes * Pencils * Clip boards (optional) Actions Students wi...

#### January 14, 2013

### 2 - Delayed Gratification

You won first place at your school Science Fair! You have two choices for the prize: Option 1: You ...

#### January 14, 2013

### HSG - Construction of perpendicular bisector

Let $A$ and $B$ be two distinct points in the plane and $\overline{AB}$ the segment joining them. T...

#### January 11, 2013

### HSG - Points equidistant from two points in the plane

Suppose $A$ and $B$ are two distinct points in the plane and $L$ is the perpendicular bisector of s...

#### January 11, 2013

### HSG - Solar Eclipse

A solar eclipse occurs when the moon passes between the sun and the earth. The eclipse is called pa...

#### January 11, 2013

### HSG - Angle bisection and midpoints of line segments

Suppose $P$ is the vertex of an angle and $Q$ and $R$ are points on the two angle rays so that $\overline{PQ}$...

#### January 11, 2013

### HSG - Reflections and Isosceles Triangles

Suppose $ABC$ is an isosceles triangle with side $\overline{AB}$ congruent to side $\overline{AC}$ ...

#### January 05, 2013

### HSG - Reflections and Equilateral Triangles II

Suppose $ABC\,$ is an equilateral triangle. Let $D$ be the midpoint of side $\overline{AB}$ and $E$...

#### January 05, 2013

### HSG - Reflections and Equilateral Triangles

Suppose $ABC$ is an equilateral triangle: Describe three reflections of the plane which preserve tr...

#### January 05, 2013

### HSN - Calories in a sports drink

The label on a $16.9$ ounce bottle of a sports drink indicates that one serving of $8$ ounces conta...

#### January 05, 2013

### 8 - Triangle congruence with coordinates

Triangles $ABC$ and $PQR$ are shown below in the coordinate plane: Show that $\triangle ABC$ is con...

#### January 04, 2013

### HSG - How thick is a soda can? Variation I

A cylindrical soda can is made of aluminum. It is approximately $4 \frac{3}{4}$ inches high and the...

#### January 04, 2013

### HSG - Archimedes and the King's crown

The King of Syracuse reportedly requested Archimedes' advice for determining if a crown was made wi...

#### January 04, 2013

### 5 - What is 23 ÷ 5?

Jessa has 23 one-dollar bills that she wants to divide equally between her 5 children. How much mon...

#### January 03, 2013

### 1 - Making a ten

Materials Copies of a table of sums for numbers 1 through 9: Colored markers or crayons Actions Ask...

#### January 02, 2013

### 3 - Making a ten

Below is a table showing all the ways to add the numbers from 1 to 9. Each sum which is larger than...

#### January 02, 2013

### 1 - Equality Number Sentences

Compare the number of circles in each box. If they are equal, write a number sentence. For example:...

#### January 02, 2013

### 2 - Saving Money 2

Louis wants to give \$15 to help kids who need school supplies. He also wants to buy a pair of shoe...

#### January 02, 2013

### HSS - Do You Fit In This Car?

Automobile manufacturers have to design the driver’s seat area so that both tall and short adults c...

#### January 02, 2013

### 4 - Running Laps

Cruz and Erica were both getting ready for soccer. * Cruz ran 1 lap around the school. * Erica ran ...

#### January 01, 2013

### 7 - Repeating decimal as approximation

Use long division to find the repeating decimal that represents $\frac{29}{13}$ Take the number obt...

#### December 31, 2012

### 4 - Plastic Building Blocks

Dennis and Cody are building a castle out of plastic building blocks. They will need $2\frac12$ buc...

#### December 31, 2012

### 5 - Seeing is Believing

Below is a picture that represents $9 + 2$. Draw a picture that represents $4 \times (9 + 2)$. How ...

#### December 31, 2012

### HSS - Bob's Bagel Shop

Bob’s Bagel Shop has estimated the following probabilities for the number of bagels a randomly-sele...

#### December 31, 2012

### 6 - Electoral College

Unlike many elections for public office where a person is elected strictly based on the results of ...

#### December 30, 2012

### HSS - Should We Send Out a Certificate?

Test scores on a statewide standardized test for a large population of students are normally distri...

#### December 26, 2012

### HSS - Sounds Really Good! (sort of...)

A friend of yours, Phil, writes to you asking about a new scratch-off lottery game. It costs \$10 t...

#### December 26, 2012

### 2 - Susan's Choice

Susan wanted to make a birthday card for her best friend but needed some art supplies. She emptied ...

#### December 20, 2012

### 4 - Carnival Tickets

Every year a carnival comes to Hallie's town. The price of tickets to ride the rides has gone up ev...

#### December 19, 2012

### 6 - Movie tickets

Hallie is in 6th grade and she can buy movie tickets for \$8.25. Hallie's father was in 6th grade i...

#### December 19, 2012

### 8 - Reflecting reflections

Below is a picture of a triangle on a coordinate grid: Draw the reflection of $\triangle ABC$ over ...

#### December 18, 2012

### 8 - Congruent Triangles

The two triangles in the picture below are congruent: Give a sequence of rotations, translations, a...

#### December 18, 2012

### 1 - How Long?

You will need various items to measure, a large set of cubes such as unifix or snap cubes, and a re...

#### December 18, 2012

### HSA - A Lifetime of Savings

For 70 years, Oseola McCarty earned a living washing and ironing other people’s clothing in Hatties...

#### December 17, 2012

### HSG - Shortest line segment from a point $P$ to a line $L$

Suppose $P$ is a point not contained on a line $L$. Let $Q$ be the point on $L$ so that $PQ$ meets ...

#### December 15, 2012

### HSG - Eratosthenes and the circumference of the earth

The ancient Greek scientist Eratosthenes devised the following experiment for estimating the circum...

#### December 15, 2012

### HSA - Basketball

Chase and his brother like to play basketball. About a month ago they decided to keep track of how ...

#### December 15, 2012

### 8 - Distance across the channel

In science class, Mrs. Winkler’s students are studying the water flow in a channel close to their s...

#### December 14, 2012

### 6 - Data Transfer

The data transfer rate of an Internet connection is the rate in bytes per second that a file can be...

#### December 14, 2012

### 6 - Drinking Juice, Variation 2

Alisa had $\frac12$ liter of juice in a bottle. She drank $\frac38$ liters of juice. What fraction ...

#### December 11, 2012

### HSA - Solution Sets

Given below are the graphs of two lines, $y=-0.5 x + 5\ $ and $y=-1.25 x + 8,$ and several regions ...

#### December 11, 2012

### HSG - Tangent Lines and the Radius of a Circle

Consider a circle with center $O$ and let $P\,$ be a point on the circle. Suppose $L$ is a tangent ...

#### December 08, 2012

### 3 - Geometric pictures of one half

For each of the pictures, explain how you can see that half of the square is shaded:

#### November 25, 2012

### 3 - Representing Half of a Circle

For each picture, decide whether one half of the circle is shaded or not. Explain how you know.

#### November 25, 2012

### 5 - Painting a room

Kulani is painting his room. He needs $\frac13$ of a gallon to paint the whole room. What fraction ...

#### November 14, 2012

### 4 - Using Place Value

Fill in the following blanks to: 0.17, 0.27, ______, ______, ______, ______, ______, _____ ______, ...

#### November 13, 2012

### 5 - Bowling for Numbers

Materials: * 4 dice per team * Recording sheet * Two-minute timer for each turn Action: Have studen...

#### November 12, 2012

### 7 - Equivalent fractions approach to non-repeating decimals

Malia found a "short cut" to find the decimal representation of the fraction $\frac{117}{250}$. Rat...

#### November 11, 2012

### 5 - Origami Stars

Avery and Megan are cutting paper to make origami stars. They need $\frac{1}{5}$ of a sheet of pape...

#### November 11, 2012

### 5 - Finding Common Denominators to Add

To add fractions, we usually first find a common denominator. Find two different common denominator...

#### November 11, 2012

### K - Color Week

This game can be set up two ways. Version 1 Set up one week as “color week” and send home a notice ...

#### November 11, 2012

### K - Counting Mat

Materials * Counting Mats * Small objects to count, such as bears or tiles. Action The teacher give...

#### November 11, 2012

### 8 - Congruent Rectangles

Below is a picture of two rectangles with the same length and width: Show that the rectangles are c...

#### November 11, 2012

### 8 - Reflecting a rectangle over a diagonal

Each picture below shows a rectangle with a line through a diagonal. For each picture, use the grid...

#### November 11, 2012

### 4 - Lines of symmetry for circles

Mr. Watkins asked his students to draw a line of symmetry for a circle with center $O$ pictured bel...

#### November 11, 2012

### 4 - Lines of symmetry for quadrilaterals

Below are pictures of four quadrilaterals: a square, a rectangle, a trapezoid and a parallelogram. ...

#### November 11, 2012

### K - Dice Addition 1

Materials Each pair of students needs: * One worksheet * Two markers of different colors * One pair...

#### November 06, 2012

### K - Which number is greater? Which number is less? How do you know?

Action: This task should be done as a whole group. * The teacher will show the class two groups of ...

#### October 28, 2012

### 1 - \$20 Dot Map

The attached graphic shows a map. You must get from start to finish by visiting three of the dots, ...

#### October 22, 2012

### 4 - Comparing Sums of Unit Fractions

Use <, =, or > to compare the following sums: $\frac12 + \frac14$ ________ $\frac13 + \frac15$ $\frac13 + \frac12$...

#### October 22, 2012

### 7 - Tossing Cylinders

Think about a cylindrical (or cylinder-like) object, such as a bottle lid or a roll of tape. Some p...

#### October 19, 2012

### 6 - Buttons: Statistical Questions

Zeke likes to collect buttons and he keeps them in a jar. Zeke can empty the buttons out of the jar...

#### October 19, 2012

### 5 - Banana Pudding

Carolina’s Banana Pudding Recipe 2 cups sour cream 5 cups whipped cream 3 cups vanilla pudding mix ...

#### October 16, 2012

### 7 - Measuring the area of a circle

Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter which he f...

#### October 12, 2012

### 4 - Finding an unknown angle

In the figure, $ABCD$ is a rectangle and $\angle CAD = 31^{\circ}$. Find $\angle BAC$....

#### October 12, 2012

### 2 - How Many Days Until Summer Vacation?

Materials * Paper * Pencil * Hundreds board * Base-ten blocks Actions Pose this problem to the chil...

#### October 12, 2012

### 4 - Lines of symmetry for triangles

Below are pictures of four triangles with given side lengths: For each triangle, find and draw all ...

#### October 12, 2012

### 4 - Identifying Multiples

Below is a multiplication table for single digit numbers: Use a different copy of the multiplicatio...

#### October 12, 2012

### HSN - Checking a calculation of a decimal exponent

Alicia and Zara are scientists working together. Alicia uses a calculator to evaluate $3^{1.4}$ and...

#### October 12, 2012

### HSF - Medieval Archer

A computer game uses functions to simulate the paths of an archer’s arrows. The $x$-axis represents...

#### October 10, 2012

### 8 - Music and Sports

Is there an association between whether a student plays a sport and whether he or she plays a music...

#### October 09, 2012

### 8 - Hand span and height

Do taller people tend to have bigger hands? To investigate this question, each student in your clas...

#### October 09, 2012

### 7 - Rolling Dice

Roll two dice 10 times. After each roll, note whether any sixes were observed and record your resul...

#### October 09, 2012

### 1 - Making a clock

Materials * 12 sheets of laminated paper or tag board with the numbers 1-12 * 12 sheets of laminate...

#### October 08, 2012

### 1 - Kiri's Mathematics Match Game

Students can play in groups of 2-4. An array of cards (twelve to twenty in total) is placed face do...

#### October 06, 2012

### HSS - Return to Fred's Fun Factory (with 50 cents)

In order to play a popular “spinning wheel” game at Fred's Fun Factory Arcade, a player is required...

#### October 04, 2012

### HSS - Fred's Fun Factory

A famous arcade in a seaside resort town consists of many different games of skill and chance. In o...

#### October 04, 2012

### K - Number Rods

Materials * Unifix cubes or snap cubes, composed into rods with 1-10 cubes (or any counting sequenc...

#### October 01, 2012

### 2 - Jamir's Penny Jar

Jamir has collected some pennies in a jar. Recently, he added coins other than pennies to his jar. ...

#### September 21, 2012

### 1 - Using lengths to represent equality

Materials Cuisenaire rods or paper strips cut to whole centimeter lengths Actions Students work in ...

#### September 20, 2012

### 1 - Number of the Day

Materials Large chart paper, markers, math journals, pencils, 100 chart. Directions Students will c...

#### September 20, 2012

### 8 - Texting and Grades I

Medhavi suspects that there is a relationship between the number of text messages high school stude...

#### September 20, 2012

### 7 - Mr. Briggs's Class Likes Math

In a poll of Mr. Briggs’s math class, 67% of the students say that math is their favorite academic ...

#### September 20, 2012

### 8 - What's Your Favorite Subject?

All the students at a middle school were asked to identify their favorite academic subject and whet...

#### September 20, 2012

### 5 - Salad Dressing

Aunt Barb’s Salad Dressing Recipe $\frac13$ cup olive oil $\frac16$ cup balsamic vinegar a pinch o...

#### September 15, 2012

### HSN, HSF - Accuracy of Carbon 14 Dating II

Carbon 14 is a form of carbon which decays exponentially over time. The amount of Carbon 14 contain...

#### September 13, 2012

### 8 - Calculating and Rounding Numbers

Lucia's calculator gives a value of $$ 3.14159265 $$ for $\pi$. Is the equation $$ \pi = 3.14159265 $$...

#### September 13, 2012

### HSN - Rational or Irrational?

In each of the following problems, a number is given. If possible, determine whether the given numb...

#### September 13, 2012

### HSA - Course of Antibiotics

Susan has an ear infection. The doctor prescribes a course of antibiotics. Susan is told to take 25...

#### September 13, 2012

### HSN, HSS - Accuracy of Carbon 14 Dating I

The half-life of Carbon $14$, that is, the time required for half of the Carbon $14$ in a sample to...

#### September 13, 2012

### HSA - Quinoa Pasta 3

Jerry was recently diagnosed with celiac disease. This means that he cannot eat any food containing...

#### September 13, 2012

### HSA - Quinoa Pasta 2

A type of pasta is made of a blend of quinoa and corn. How much of the pasta is quinoa and how much...

#### September 13, 2012

### HSG - How many cells are in the human body?

About how many cells are in the human body? You can assume that a cell is a sphere with radius 10$^{-3}$...

#### September 10, 2012

### 1 - Make Your Own Puzzle

Give each student scissors, an envelope, and a square of colored paper (the colored paper should be...

#### September 09, 2012

### 5 - How many marbles?

Julius has 4 blue marbles. If one third of Julius' marbles are blue, how many marbles does Julius h...

#### September 08, 2012

### 7 - Molly's Run

Molly runs $\frac{1}{3}$ of a mile in 4 minutes. If Molly continues at the same speed, how long wil...

#### September 05, 2012

### 3 - Symmetry of the addition table

Below is a table showing how to add numbers from $1$ to $3$: Cut out the table and fold it over the...

#### September 05, 2012

### HSS - Haircut Costs

Seventy-five female college students and 24 male college students reported the cost (in dollars) of...

#### September 03, 2012

### 8 - US Garbage, Version 1

The following table shows the amount of garbage that was produced in the US each year between 2002 ...

#### September 03, 2012

### HSF - Foxes and Rabbits 3

Given below are two graphs that show the populations of foxes and rabbits in a national park over a...

#### August 30, 2012

### HSF - Foxes and Rabbits 2

Given below is a table that gives the populations of foxes and rabbits in a national park over a 12...

#### August 29, 2012

### HSN - Fuel Efficiency

Sadie has a cousin Nanette in Germany. Both families recently bought new cars and the two girls are...

#### August 28, 2012

### 6 - Puppy Weights

Below are the 25 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston K...

#### August 28, 2012

### 3 - Patterns in the multiplication table

The table shows products of the whole numbers 1 through 6. Color all of the even products in the ta...

#### August 27, 2012

### 3 - Naming the Whole for a Fraction

Mrs. Frances drew a picture on the board. Then she asked her students what fraction it represents. ...

#### August 27, 2012

### 6 - Morning Walk

Sierra walks her dog Pepper twice a day. Her evening walk is two and a half times as far as her mor...

#### August 27, 2012

### 6 - Watch out for Parentheses

Evaluate the following numerical expressions. $2(5+(3)(2)+4)$ $2((5+3)(2+4))$ $2(5+3(2+4))$ Can the...

#### August 27, 2012

### HSA - Cantor Set

In this task we will investigate an interesting mathematical object called the Cantor Set. It is a ...

#### August 22, 2012

### 4 - Listing fractions in increasing size

Order the following fractions from smallest to largest: $$ \frac{3}{8}, \; \;\; \; \frac{1}{3}, \; \; \; \; \frac{5}{9}, \; \; \; \; \frac{2}{5} $$...

#### August 22, 2012

### 4 - Sugar in six cans of soda

For a certain brand of orange soda, each can contains $\frac{4}{15}$ cup of sugar. How many cups of...

#### August 21, 2012

### 5 - Painting a Wall

Nicolas is helping to paint a wall at a park near his house as part of a community service project....

#### August 21, 2012

### HSF - Carbon 14 dating in practice II

In order to use Carbon $14$ for dating, scientists measure the ratio of Carbon $14$ to Carbon $12$ ...

#### August 21, 2012

### HSG - Seven Circles III

Seven circles of the same size can be placed in the pattern shown below: The six outer circles touc...

#### August 21, 2012

### HSG - Coins in a circular pattern

Below is a table of diameters of different denominations of United States Coins: DenominationDiamet...

#### August 21, 2012

### 5 - To Multiply or not to multiply?

Some of the problems below can be solved by multiplying $\frac18\times\frac25$, while others need a...

#### August 21, 2012

### HSG - Seven Circles I

Liz places seven pennies in the arrangement shown below: She notices that each of the six outer pen...

#### August 20, 2012

### HSF, HSA - Building a General Quadratic Function

In ''Building an explicit quadratic function'' a particular quadratic function was rewritten by com...

#### August 20, 2012

### K - Longer and Heavier? Shorter and Heavier?

Materials * Several pairs of objects (see below for how to choose the pairs) * balance scale Action...

#### August 20, 2012

### HSS - The Titanic 3

On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passen...

#### August 18, 2012

### HSS - The Titanic 2

On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passen...

#### August 18, 2012

### HSS - The Titanic 1

On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passen...

#### August 18, 2012

### 6 - Running at a Constant Speed

A runner ran 20 miles in 150 minutes. If she runs at that speed, How long would it take her to run ...

#### August 17, 2012

### 6 - Friends Meeting on Bicycles

Taylor and Anya live 63 miles apart. Sometimes on a Saturday, they ride their bikes toward each oth...

#### August 17, 2012

### 8 - Ants versus humans

The average mass of an adult human is about 65 kilograms while the average mass of an ant is approx...

#### August 16, 2012

### 6 - Busy Day

The Jonas family had a really busy day. After leaving their home, Mrs. Jonas dropped son Cody at hi...

#### August 15, 2012

### HSG - Bisecting an angle

Suppose $A$ is an angle with vertex $P$, as pictured below: Draw a circle with center $P$ and with ...

#### August 15, 2012

### 3 - Comparing Fractions

Compare the fractions below. Use the symbols $\gt$, =, or $\lt$ to record your comparisons. Draw a ...

#### August 15, 2012

### HSF - Logistic Growth Model, Abstract Version

An important example of a model often used in biology or ecology to model population growth is call...

#### August 15, 2012

### HSF - Logistic Growth Model, Explicit Version

The dots in the graph below show the approximate United States Population measured each decade star...

#### August 15, 2012

### 3 - Addition Patterns

Below is a table showing addition of numbers from $1$ through $5$. In each column and each row of t...

#### August 15, 2012

### HSS - Rain and Lightning.

Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lightning and r...

#### August 14, 2012

### 2 - Which Pictures Represent One Half?

Which pictures show one half of the shape shaded? Explain. Is more or less than one half of the sha...

#### August 13, 2012

### 7 - Track Practice

Angel and Jayden were at track practice. The track is $\frac25$ kilometers around. Angel ran 1 lap ...

#### August 11, 2012

### 3 - Jon and Charlie's Run

Jon and Charlie plan to run together. They are arguing about how far to run. Charlie says, I run $\frac{3}{6}$...

#### August 10, 2012

### 1 - Hundred Chart Digit Game

Materials A 100 chart per pair of students A set of digit cards per pair of students (four each of ...

#### August 10, 2012

### 1 - Choral Counting II

Materials 100 chart or large number line, preferably one that extends beyond 100. A pointer Setup H...

#### August 10, 2012

### 3 - Comparing Fractions with a Different Whole

Bryce drew this picture: Then he said, This shows that $\frac{1}{4}$ is greater than $\frac{1}{2}$....

#### August 10, 2012

### 5 - Making S'Mores

Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mo...

#### August 10, 2012

### 7 - Sports Equipment Set

Jonathan wants to save up enough money so that he can buy a new sports equipment set that includes ...

#### August 10, 2012

### HSS - Cards and Independence

One card is selected at random from the following set of 6 cards, each of which has a number and a ...

#### August 10, 2012

### 8 - Quinoa Pasta 1

A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the perc...

#### August 10, 2012

### 8, HSN - Calculating the square root of 2

Jessica evaluates $\sqrt{2}$ on her calculator which shows a value of $$ 1.4142136. $$ She then wri...

#### August 09, 2012

### HSN - Complex Distance

In this problem, you will compute some values related to the complex numbers $2+i$ and $5-3i$. Plot...

#### August 09, 2012

### 4 - Comparing two different pizzas

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a ...

#### August 09, 2012

### 5 - Egyptian Fractions

Ancient Egyptians used unit fractions, such as $\frac{1}{2}$ and $\frac{1}{3}$, to represent all fr...

#### August 09, 2012

### 5 - Mixed Numbers with Unlike Denominators

Find two different ways to add these two numbers: $$1\frac{1}{3} + 2\frac{3}{5}$$...

#### August 08, 2012

### 8 - Introduction to Linear Functions

Decide which of the following points are on the graph of the function $y = 2x + 1$: $(0, 1), (2, 5), (\frac12, 2), (2, 1), (1, 1), (0.5, 1)$...

#### August 08, 2012

### 6 - Chocolate Bar Sales

Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of...

#### August 08, 2012

### 6 - Rectangle Perimeter 3

Sadie computes the perimeter of a rectangle by adding the length, $l$, and width, $w$, and doubling...

#### August 07, 2012

### 4 - Peaches

Alfredo picked $2\frac34$ pounds of peaches from the tree in his backyard. He gave $1\frac14$ pound...

#### August 07, 2012

### 5 - Jog-A-Thon

Alex is training for his school's Jog-A-Thon and needs to run at least $1$ mile per day. If Alex ru...

#### August 07, 2012

### 5 - Finding Common Denominators to Subtract

To subtract fractions, we usually first find a common denominator. Find two different common denomi...

#### August 01, 2012

### HSF - Building a quadratic function from $f(x) = x^2$

Suppose $f(x) = x^2$ where $x$ can be any real number. Sketch a graph of the function $f$. Sketch a...

#### July 31, 2012

### 5 - Folding Strips of Paper

Label the points on the number line that correspond to $\frac16$, $\frac26$, $\frac36$, $\frac46$, ...

#### July 30, 2012

### 4 - Using Benchmarks to Compare Fractions

Melissa gives her classmates the following explanation for why $\frac{1}{5} \lt \frac{2}{7}$: I can...

#### July 30, 2012

### HSG - Inscribing a hexagon in a circle

Let $C$ be a circle with center $O$ and a diameter meeting $C$ in points $P$ and $S$ as shown below...

#### July 26, 2012

### HSG - Inscribing a square in a circle

Let $C$ be a circle with center $O$. Suppose $\overline{PR}$ and $\overline{QS}$ are two diameters ...

#### July 26, 2012

### 5 - How many servings of oatmeal?

A package contains 4 cups of oatmeal. There is $\frac{1}{3}$ cup of oatmeal in each serving. How ma...

#### July 25, 2012

### 4 - Karl's Garden

Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Who...

#### July 24, 2012

### 6 - Comparing Temperatures

Here are the low temperatures (in Celsius) for one week in Juneau, Alaska: Monday Tuesday Wednesday...

#### July 23, 2012

### HSG - Seven Circles II

Seven circles of the same size are placed in the pattern shown below: The six outer circles touch t...

#### July 23, 2012

### 4 - Making 22 Seventeenths in Different Ways

Which of the following sums are equal to $\frac{22}{17}$? $\frac{5}{17}+\frac{4}{17}+\frac{3}{17}+\frac{10}{17}$...

#### July 15, 2012

### 4 - Writing a Mixed Number as an Equivalent Fraction

Ben wrote a mixed number as the fraction 7$\frac{1}{3}$. Here is his work: $$\begin{align} 7\frac{1}{3} &= \frac{7}{1}+\frac{1}{3} &\text{ (Step 1)} \\ &= \frac{(7\times 3)+1}{3} &\text{ (Step 2)} \\ &= \frac{21+1}{3} &\text{ (Step 3)} \\ &= \frac{22}{3} &\text{ (Step 4)} \end{align}$$...

#### July 15, 2012

### 5 - Connor and Makayla Discuss Multiplication

Makayla said, "I can represent $3\times \frac23$ with 3 rectangles each of length $\frac23$." Conno...

#### July 14, 2012

### 1 - Start/Stop Counting II

Setup Students should be seated on chairs at their tables or desks. The teacher will give a countin...

#### July 13, 2012

### 3 - The Stamp Collection

Masha had $120$ stamps. First, she gave her sister half of the stamps and then she used three to ma...

#### July 04, 2012

### HSA - Accurately weighing pennies II

In $1983$ the composition of pennies in the United States was changed due, in part, to the rising c...

#### June 29, 2012

### HSA - Accurately weighing pennies I

In $1983$ the composition of pennies in the United States was changed due, in part, to the rising c...

#### June 29, 2012

### 2 - Representing Half of a Rectangle

Ms. Nim gave her students a picture of a rectangle. Then she asked them to shade in one half of the...

#### June 25, 2012

### 8 - Converse of the Pythagorean Theorem

A Pythagorean triple $(a,b,c)$ is a set of three positive whole numbers which satisfy the equation ...

#### June 24, 2012

### 1 - Counting Circles II

Setup Have students stand and form a circle facing in toward each other. Select a counting sequence...

#### June 22, 2012

### K - Which is heavier?

Students will need various items to compare weights, a balance scale,and a recording sheet with fou...

#### June 20, 2012

### HSF - Identifying graphs of functions

Consider the following four functions $f(x) = \frac{3}{1 + e^{-3x}}$ $g(x) = 1 - \frac{e^{-x}}{2} $...

#### June 17, 2012

### K - Shape Hunt Part 2

This game is a scavenger hunt. It can be played indoors or outdoors and can be played after student...

#### June 17, 2012

### HSA - Zeroes and factorization of a non polynomial function

Sketch graphs of the functions $f$ and $F$ given by $f(x)= |x|$ and $F(x) = x^2$ for $-2 \leq x \leq 2$...

#### June 17, 2012

### HSF - Random Walk II

Imagine Scott stood at zero on a life-sized number line. His friend flipped a coin 50 times. When t...

#### June 06, 2012

### HSS - Random Walk III

Imagine Scott stood at zero on a life-sized number line. His friend flipped a coin $6$ times. When ...

#### June 06, 2012

### K - Shape Hunt Part 1

This game is a scavenger hunt. It can be played indoors or outdoors. In the play area, the teacher ...

#### June 05, 2012

### K - Shape Sequence Search

Find the row or column that contains each sequence. a. triangle-rectangle-rectangle-circle b. trian...

#### June 05, 2012

### HSG - Reflected Triangles

The triangle in the upper left of the figure below has been reflected across a line into the triang...

#### June 05, 2012

### HSF - Transforming the graph of a function

The figure shows the graph of a function $f$ whose domain is the interval $-2 \leq x \leq 2$. In (i...

#### May 27, 2012

### 4 - Explaining Fraction Equivalence with Pictures

The rectangle below has length 1. What fraction does the shaded part represent? The rectangle below...

#### May 21, 2012

### HSS - Random Walk IV

Imagine Scott stood at zero on a life-sized number line. His friend flipped a coin $100$ times. Whe...

#### May 21, 2012

### 6 - How many _______ are in. . . ?

Solve each problem using pictures and using a number sentence involving division. How many fives ar...

#### May 18, 2012

### 2 - Toll Bridge Puzzle

The picture shows islands connected by bridges. To cross a bridge, you must pay a toll in coins. If...

#### May 15, 2012

### 5 - Comparing Products

Leo and Silvia are looking at the following problem: How does the product of $60 \times 225$ compar...

#### May 13, 2012

### 8 - Riding by the Library

Nina rides her bike from her home to school passing by the library on the way, and traveling at a c...

#### May 05, 2012

### 7 - Fishing Adventures 2

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can ...

#### April 26, 2012

### 8 - Foxes and Rabbits

Given below is a table that gives the populations of foxes and rabbits in a national park over a 12...

#### April 26, 2012

### 6 - Log Ride

A theme park has a log ride that can hold 12 people. They also have a weight limit of 1500 lbs per ...

#### April 22, 2012

### HSA - Taxes and Sales

Judy is working at a retail store over summer break. A customer buys a \$50 shirt that is on sale f...

#### April 21, 2012

### 8 - Shipping Rolled Oats

Rolled oats (dry oatmeal) come in cylindrical containers with a diameter of 5 inches and a height o...

#### April 21, 2012

### HSF - Mathemafish Population

You are a marine biologist working for the Environmental Protection Agency (EPA). You are concerned...

#### April 19, 2012

### HSF - Flu on Campus

Suppose the swine flu, influenza H1N1, is spreading on a school campus. The following table shows t...

#### April 09, 2012

### 6 - Price per pound and pounds per dollar

The grocery store sells beans in bulk. The grocer's sign above the beans says, $$5 \text { pounds for }\$4.$$...

#### April 06, 2012

### 6 - Base and Height

Mrs. Lito asked her students to label a base $b$ and its corresponding height $h$ in the triangle s...

#### April 02, 2012

### 6 - Banana Bread

Leo's recipe for banana bread won't fit in his favorite pan. The batter fills the 8.5 inch by 11 in...

#### April 02, 2012

### 8 - Battery Charging

Sam wants to take his MP3 player and his video game player on a car trip. An hour before they plan ...

#### March 31, 2012

### 8 - Bike Race

Antonio and Juan are in a 4-mile bike race. The graph below shows the distance of each racer (in mi...

#### March 30, 2012

### 6 - Integers on the Number Line 1

Find and label the numbers $-3$ and $-5$ on the number line. For each of the following, state wheth...

#### March 29, 2012

### HSF - Telling a Story With Graphs

Each of the following graphs tells a story about some aspect of the weather: temperature (in degree...

#### March 29, 2012

### HSF - How is the Weather?

Given below are three graphs that show solar radiation, $S$, in watts per square meter, as a functi...

#### March 29, 2012

### 8 - Tides

The figure below gives the depth of the water at Montauk Point, New York, for a day in November. Ho...

#### March 29, 2012

### 5 - Video Game Scores

Eric is playing a video game. At a certain point in the game, he has 31500 points. Then the followi...

#### March 29, 2012

### HSF - Snail Invasion

In 1966, a Miami boy smuggled three Giant African Land Snails into the country. His grandmother eve...

#### March 29, 2012

### 8 - Distance

Below are two graphs that look the same. Note that the first graph shows the speed of a car as a fu...

#### March 29, 2012

### 6 - Finding Areas of Polygons

Find the area that is shaded in each figure in at least two different ways.

#### March 29, 2012

### 6 - Fishing Adventures 1

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can ...

#### March 29, 2012

### HSF - As the Wheel Turns

A wheel of radius 0.2 meters begins to move along a flat surface so that the center of the wheel mo...

#### March 28, 2012

### HSF - Graphs of Power Functions

1. Sketch the graphs of the functions described by $\displaystyle f(x)=x^2$ and $\displaystyle g(x)=x^4$...

#### March 28, 2012

### HSF - Which Function?

Which of the following could be the function of a real variable $x$ whose graph is shown below? Exp...

#### March 27, 2012

### HSF - Oakland Coliseum

Oakland Coliseum, home of the Oakland Raiders, is capable of seating 63,026 fans. For each game, th...

#### March 27, 2012

### HSF - Warming and Cooling

The figure shows the graph of $T$ , the temperature (in degrees Fahrenheit) over one particular 20-...

#### March 27, 2012

### HSN, HSA - Computations with Complex Numbers

Rewrite each of the following expressions involving complex numbers in the form $a+bi$ where $a$ an...

#### March 27, 2012

### HSG - Bank Shot

Pablo is practicing bank shots on a standard 4 ft.-by-8 ft. pool table that has a wall on each side...

#### March 27, 2012

### 7 - Estimating the Mean State Area

The table below gives the areas (in thousands of square miles) for each of the “lower 48” states. T...

#### March 27, 2012

### HSF - Interpreting the graph

Use the graph (for example, by marking specific points) to illustrate the statements in (a)–(d). If...

#### March 27, 2012

### 8 - Congruent Segments

Line segments AB and CD have the same length. Describe a sequence of reflections that exhibits a co...

#### March 27, 2012

### K - Rainbow Number Line

The teacher will need a package of regular sentence strips and a medium point black permanent marke...

#### March 27, 2012

### HSF - Compounding with a 100% Interest Rate

A man knows that money in an account where interest is compounded semi-annually will earn interest ...

#### March 27, 2012

### HSF - Domains

For the functions in (a)–(f), List the algebraic operations in order of evaluation. What restrictio...

#### March 26, 2012

### HSF - Points on a graph

Suppose $f$ is a function. If $10=f(-4)$, give the coordinates of a point on the graph of $f$. If $6$...

#### March 26, 2012

### 3 - The Square Counting Shortcut

Imagine that each square in the picture measures one centimeter on each side. What is the area of e...

#### March 26, 2012

### HSA - Kitchen Floor Tiles

Fred has some colored kitchen floor tiles and wants to choose a pattern using them to make a border...

#### March 26, 2012

### HSF - Exponentials and Logarithms II

Let $f$ be the function defined by $f(x)=10^x$ and $g$ be the function defined by $g(x)=\log_{10}(x)$...

#### March 26, 2012

### 1 - Find the Missing Number

Find the missing number in each of the following equations: $$ 9 - 3 = \square \qquad \qquad 8 + \square = 15 \qquad \qquad 16 - \square = 5 $$...

#### March 26, 2012

### HSA - Fishing Adventures 3

Fishing Adventures rents small fishing boats to tourists for day long fishing trips. Each boat can ...

#### March 26, 2012

### HSF, HSA - Population and Food Supply

The population of a country is initially 2 million people and is increasing at 4% per year. The cou...

#### March 26, 2012

### HSN - Bus and Car

Julio went to Germany to watch an international soccer tournament. He first watched Argentina play ...

#### March 25, 2012

### 2 - Counting Dots in Arrays

Which of the following are equal to the number of dots in the picture below? (Choose all that apply...

#### March 25, 2012

### 6 - How Many Containers in One Cup / Cups in One Container?

If $\frac12$ cup of water fills $\frac23$ of a plastic container, how many containers will 1 cup fi...

#### March 25, 2012

### 1 - School Supplies

Pia takes some money to the store to buy school supplies. She buys some paper for \$3 and a pen for...

#### March 25, 2012

### 8 - Birds' Eggs

This scatter diagram shows the lengths and widths of the eggs of some American birds. A biologist m...

#### March 25, 2012

### 8 - Glasses

The diagram shows three glasses (not drawn to scale). The measurements are all in centimeters. The ...

#### March 25, 2012

### 8 - Downhill

A car is traveling down a long, steep hill. The elevation, $E$, above sea level (in feet) of the ca...

#### March 25, 2012

### 6 - Mile High

Denver, Colorado is called “The Mile High City” because its elevation is $5280$ feet above sea leve...

#### March 25, 2012

### 8 - Chicken and Steak, Variation 2

Consider the relationship between the number of pounds of chicken and the number of pounds of steak...

#### March 25, 2012

### HSF - Graphs of Compositions

For each function in this task, assume the domain is the largest set of real numbers for which the ...

#### March 25, 2012

### HSF - Influenza epidemic

An epidemic of influenza spreads through a city. The figure below is the graph of $I=f(w)$, where $I$...

#### March 25, 2012

### HSG - Two Wheels and a Belt

A certain machine is to contain two wheels, one of radius 3 centimeters and one of radius 5 centime...

#### March 25, 2012

### 6 - Same Base and Height, Variation 2

Which of the triangles, $\Delta ABC$, $\Delta ABD$, $\Delta ABE$ or $\Delta ABF$, has the largest a...

#### March 24, 2012

### 6 - Same Base and Height, Variation 1

Make the following triangles on a geoboard. Remember that the pegs are equally spaced in a square g...

#### March 24, 2012

### HSF - Yam in the Oven

You put a yam in the oven. After 45 minutes, you take it out. Let $f(t)$ be the temperature of the ...

#### March 24, 2012

### HSG - Are They Similar?

In the picture given below, line segments $AD$ and $BC$ intersect at $X$. Line segments $AB$ and $CD$...

#### March 24, 2012

### 8, HSF - The Customers

A certain business keeps a database of information about its customers. Let $C$ be the rule which a...

#### March 24, 2012

### HSG - Centerpiece

Janine is planning on creating a water-based centerpiece for each of the 30 tables at her wedding r...

#### March 23, 2012

### HSG - Are the Triangles Congruent?

In each of the following diagrams, two triangles are shaded. Based on the information given about e...

#### March 23, 2012

### 5 - Dividing by One-Half

Solve the four problems below. Which of the following problems can be solved by finding $3 \div \frac12$...

#### March 23, 2012

### HSF - The Parking Lot

A parking lot charges $\$0.50$ for each half hour or fraction thereof, up to a daily maximum of $\$10.00$...

#### March 23, 2012

### 7 - Stock Swaps, Variation 3

Microsoft Corp. has made an offer to acquire 1.5 million shares of Apple Corp. worth \$374 per shar...

#### March 22, 2012

### 7 - Stock Swaps, Variation 2

Microsoft Corp. wants to acquire 1.5 million shares of Apple Corp. that are worth \$374 per share a...

#### March 22, 2012

### HSG - Setting Up Sprinklers

Selina has a 9 meter by 12 meter lawn that she wants to water. She has two sprinklers, each of whic...

#### March 22, 2012

### HSG - Dilating a Line

Suppose we apply a dilation by a factor of 2, centered at the point P, to the figure below. In the ...

#### March 22, 2012

### HSG - A Midpoint Miracle

Draw a quadrilateral $ABCD$. Try to draw your quadrilateral so that no two sides are congruent, no ...

#### March 22, 2012

### HSG - Toilet Roll

Picture a roll of toilet paper; assume that the paper in the roll is very tightly rolled. Assuming ...

#### March 22, 2012

### 2 - Party Favors

Pia was having a party. She put 10 stickers in each party bag. On the first day she made 10 bags. H...

#### March 22, 2012

### HSF - Algae Blooms

Algalblooms routinely threaten the health of the Chesapeake Bay. Phosphate compounds supply a rich ...

#### March 22, 2012

### 4 - Comparing Growth, Variation 2

There are two snakes at the zoo, Jewel and Clyde. Jewel was six feet and Clyde was eight feet. A ye...

#### March 21, 2012

### 4 - Comparing Growth, Variation 1

There are two snakes at the zoo, Jewel and Clyde. Jewel was six feet and Clyde was eight feet. A ye...

#### March 21, 2012

### 2 - Red and Blue Tiles

Lin wants to put some red and blue tiles on a wall for decoration. She is thinking about several di...

#### March 21, 2012

### 4 - Double Plus One

The table below shows a list of numbers. For every number listed in the table, multiply it by 2 and...

#### March 21, 2012

### HSG - Locating Warehouse

You have been asked to place a warehouse so that it is an equal distance from the three roads indic...

#### March 21, 2012

### 2 - Three composing/decomposing problems

Some students are working with base-ten blocks. Nina has $3$ hundreds, $8$ tens, and $23$ ones. How...

#### March 20, 2012

### 2 - Counting Stamps

The post office packages stamps like this: 10 stamps in each strip. 10 strips of 10 in each sheet. ...

#### March 20, 2012

### HSA - Triangle Series

Consider the picture below, consisting of a nested sequence of five equilateral triangles, colored ...

#### March 20, 2012

### HSA - Two Squares are Equal

Solve the quadratic equation $$ x^2 = (2x - 9)^2 $$ using as many different methods as...

#### March 20, 2012

### HSA - Trina's Triangles

Alice was having a conversation with her friend Trina, who had a discovery to share: “Pick any two ...

#### March 19, 2012

### HSA - How does the solution change?

In the equations (a)–(d), the solution $x$ to the equation depends on the constant $a$. Assuming $a$...

#### March 18, 2012

### HSA - Same solutions?

Which of the following equations have the same solution? Give reasons for your answer that do not d...

#### March 18, 2012

### HSA - Braking Distance

Thebraking distance, in feet, of a cartraveling at $v$ miles per houris given by $$ d= 2.2v+\frac{v^2}{20}. $$...

#### March 18, 2012

### HSA - Growing coffee

The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while Robusta yields ab...

#### March 18, 2012

### HSA - Writing constraints

In (a)–(d), (i) write a constraint equation, (ii) determine two solutions, and (iii) graph the equa...

#### March 18, 2012

### 6 - It's Warmer in Miami

One morning the temperature is -28$^\circ$ in Anchorage, Alaska, and 65$^\circ$ in Miami, Florida. ...

#### March 18, 2012

### 6 - Ratio of boys to girls

The ratio of the number of boys to the number of girls at school is 4:5. What fraction of the stude...

#### March 18, 2012

### 6 - Traffic Jam

You are stuck in a big traffic jam on the freeway and you are wondering how long it will take to ge...

#### March 18, 2012

### 6 - Running to School, Variation 3

Rosa ran $\frac13$ of the way from her home to school. She ran $\frac14$ mile. How far is it betwee...

#### March 18, 2012

### 6 - Christo’s Building

Christo and Jeanne Claude are artists who wrap large things – bridges, buildings, even islands. (Se...

#### March 18, 2012

### HSA - The Missing Coefficient

Consider the polynomial function $$ P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, $$ where $a$ is an unknown ...

#### March 18, 2012

### HSF - Do two points always determine an exponential function?

An exponential function is a function of the form $f(x) = a b^x$ where $a$ is a real number and $b$...

#### March 17, 2012

### HSF - Do two points always determine a linear function II?

Suppose $R_1 = (c,d)$ and $R_2 = (e,f)$ are two different points. Is there always a linear function...

#### March 17, 2012

### HSG - Placing a Fire Hydrant

You have been asked to place a fire hydrant so that it is an equal distance form three locations in...

#### March 17, 2012

### HSG - Why does SSS work?

In the picture below segment $AB$ is congruent to segment $DE$, segment $AC$ is congruent to segmen...

#### March 17, 2012

### 6 - Jayden’s Snacks

Jayden has \$20.56. He buys an apple for 79 cents and a granola bar for \$1.76. How much money did ...

#### March 17, 2012

### 2 - Comparisons 2

Use $\lt$, =, or $\gt$ to complete the following number sentences. $657$ ______ $457 + 100 + 100$ $926$...

#### March 17, 2012

### 6 - Buying Gas

Sophia’s dad paid $\$43.25$ for $12.5$ gallons of gas. What is the cost of one gallon of...

#### March 17, 2012

### 2 - Comparisons 1

Are these comparisons true or false? $2$ hundreds + $3$ ones $\gt 5$ tens + $9$ ones $9$ tens + $2$...

#### March 16, 2012

### 6 - Video Game Credits

It requires $\frac14$ of a credit to play a video game for one minute. Emma has $\frac78$ credits. ...

#### March 16, 2012

### HSF - The High School Gym

The school assembly is being held over the lunch hour in the school gym. All the teachers and stude...

#### March 16, 2012

### HSF - Do two points always determine a linear function?

Suppose $P_1 = (0,5)$ and $P_2 = (3,3)$. Sketch $P_1$ and $P_2$. For which real numbers $m$ and $b$...

#### March 16, 2012

### HSF - Compounding with a 5% Interest Rate

A man invests \$1000 in an account with a 5% annual interest rate. He knows that money in an accoun...

#### March 16, 2012

### 7 - Writing Expressions

Write an expression for the sequence of operations. Add 3 to $x$, subtract the result from 1, then ...

#### March 16, 2012

### HSF - In The Billions and Linear Modeling

The data in the table below was taken from Wikipedia. Year World Population (Estimate) 1804 1 1927 ...

#### March 16, 2012

### HSF - Illegal Fish

A ﬁsherman illegally introduces some ﬁsh into a lake, and they quickly propagate. The growth of the...

#### March 16, 2012

### HSF - In the Billions and Exponential Modeling

The data in the table below was taken from Wikipedia. Year World Population in Billions (Estimate) ...

#### March 16, 2012

### HSA - Paying the rent

A checking account is set up with an initial balance of \$4800, and \$400 is removed from the accou...

#### March 16, 2012

### HSA - Buying a Car

Suppose a friend tells you she paid a total of \$16,368 for a car, and you'd like to know the car's...

#### March 16, 2012

### HSA - A Linear and Quadratic System

The figure shows graphs of a linear and a quadratic function. What are the coordinates of the point...

#### March 16, 2012

### K - Which weighs more? Which weighs less?

Materials: Sheets of paper for each student that are folded in half with the words "Heavier" and "L...

#### March 14, 2012

### K - Size Shuffle

Materials * One pair of "taller" and "shorter" cards for each student Action * The students stand i...

#### March 14, 2012

### 1 - Valid Equalities?

Decide if the equations are true or false. Explain your answer. $2+5 = 6$ $3 + 4 = 2 + 5$ $8 = 4 + 4$...

#### March 14, 2012

### 2 - Ordering 3-digit numbers

1. Arrange the following numbers from least to greatest: $$ 476 \qquad \qquad 647 \qquad \qquad 74 \qquad \qquad 674 \qquad \qquad 467 $$...

#### March 14, 2012

### 8 - Ant and Elephant

An ant has a mass of approximately $4 \times 10^{3}$ grams and an elephant has a mass of approximat...

#### March 14, 2012

### 8 - Find the Angle

In triangle $\Delta ABC$, point $M$ is the point of intersection of the bisectors of angles $\angle BAC$...

#### March 14, 2012

### 7 - Distances on the Number Line 2

On the number line above, the numbers $a$ and $b$ are the same distance from $0$. What is $a+b$? Ex...

#### March 14, 2012

### 2 - Hand Span Measures

Hand span is a measure of distance from the tip of the thumb to the tip of the little finger with t...

#### March 14, 2012

### HSS - Musical Preferences

The 54 students in one of several middle school classrooms were asked two questions about musical p...

#### March 14, 2012

### HSN - How Much is a Penny Worth?

The price of copper fluctuates. Between 2002 and 2011, there were times when its price was lower th...

#### March 14, 2012

### 7 - Operations on the number line

A number line is shown below. The numbers $0$ and $1$ are marked on the line, as are two other numb...

#### March 14, 2012

### 8 - Irrational Numbers on the Number Line

Without using your calculator, label approximate locations for the following numbers on the number ...

#### March 13, 2012

### 8 - Giantburgers

This headline appeared in a newspaper. Every day 7% of Americans eat at Giantburger restaurants Dec...

#### March 13, 2012

### 8 - Estimating Square Roots

Without using the square root button on your calculator, estimate $\sqrt{800}$ as accurately as pos...

#### March 13, 2012

### 8 - How Many Solutions?

Consider the equation $5x 2y = 3$. If possible, find a second linear equation to create a system o...

#### March 13, 2012

### 6 - Dan’s Division Strategy

Dan observes that $$\frac{6}{10}\div \frac{2}{10} = 6 \div 2$$ He says, I think that if we are divi...

#### March 13, 2012

### 7 - Comparing Freezing Points

Ocean water freezes at about $-2 \frac12 ^\circ C$. Fresh water freezes at $0 ^\circ C$. Antifreeze...

#### March 13, 2012

### 7 - Eight Circles

The figure below is composed of eight circles, seven small circles and one large circle containing ...

#### March 13, 2012

### 8 - Find the Missing Angle

In the picture below, lines $l$ and $m$ are parallel. The measure of angle $\angle PAX$ is $31^\circ$...

#### March 13, 2012

### HSG - Tennis Balls in a Can

The official diameter of a tennis ball, as defined by the International Tennis Federation, is at le...

#### March 13, 2012

### 6 - Equivalent Expressions

Which of the following expressions are equivalent? Why? If an expression has no match, write 2 equi...

#### March 13, 2012

### 8 - Kimi and Jordan

Kimi and Jordan are each working during the summer to earn money in addition to their weekly allowa...

#### March 13, 2012

### 2 - The Longest Walk

Pick two points on the outside borders of the United States map (excluding Hawaii and Alaska) so th...

#### March 12, 2012

### 8 - Comparing Rational and Irrational Numbers

For each pair of numbers, decide which is greater without using a calculator. Explain your choices....

#### March 12, 2012

### 6 - The Djinni’s Offer

After opening an ancient bottle you find on the beach, a Djinni appears. In payment for his freedom...

#### March 12, 2012

### 8 - Chicken and Steak, Variation 1

You have \$100 to spend on a barbeque where you want to serve chicken and steak. Chicken costs \$1....

#### March 12, 2012

### HSA - Mixing Candies

A candy shop sells a box of chocolates for \$30. It has \$29 worth of chocolates plus \$1 for the b...

#### March 12, 2012

### HSF - The Canoe Trip, Variation 2

Mike likes to canoe. He can paddle 150 feet per minute. He is planning a river trip that will take ...

#### March 12, 2012

### HSF - The Canoe Trip, Variation 1

Mike likes to canoe. He can paddle 150 feet per minute. He is planning a river trip that will take ...

#### March 12, 2012

### 7 - Discounted Books

Katie and Margarita have \$20.00 each to spend at Students' Choice book store, where all students r...

#### March 11, 2012

### 7 - Miles to Kilometers

The students in Mr. Sanchez's class are converting distances measured in miles to kilometers. To es...

#### March 11, 2012

### 6 - Making Hot Cocoa, Variation 2

A recipe for hot chocolate calls for 3 cups of milk. What fraction of the recipe can Nelli make wit...

#### March 11, 2012

### 6 - Making Hot Cocoa, Variation 1

One thermos of hot chocolate uses $\frac23$ cup of cocoa powder. How many thermoses can Nelli make ...

#### March 11, 2012

### 6 - Jumping Flea

A flea is jumping around on the number line. If he starts at 1 and jumps 3 units to the right, then...

#### March 11, 2012

### 6 - Computing Volume Progression 4

A rectangular tank is $24\text{ cm}$ wide, and $30\text{ cm}$ long. It contains a stone and is fill...

#### March 11, 2012

### 6 - Computing Volume Progression 3

A rectangular tank is $50\text{ cm}$ wide and $60\text{ cm}$ long. It can hold up to $126$ $\ell$ o...

#### March 11, 2012

### 6 - Computing Volume Progression 2

Amy has a fish tank shaped like a rectangular prism that is 20 cm by 20 cm by 16 cm. What is the vo...

#### March 11, 2012

### 6 - Computing Volume Progression 1

Amy wants to build a cube with $3$ $cm$ sides using $1$ $cm$ cubes. How many cubes does she need? H...

#### March 11, 2012

### 3 - Ordering Fractions

Arrange the fractions in order from least to greatest. Explain your answer with a picture. $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $...

#### March 11, 2012

### HSF - Lake Algae

On June 1, a fast growing species of algae is accidentally introduced into a lake in a city park. I...

#### March 11, 2012

### 7 - Floor Plan

Mariko has an $80 : 1$ scale-drawing of the floor plan of her house. On the floor plan, the dimensi...

#### March 10, 2012

### 8 - Comparing Snow Cones

Pablo's Icy Treat Stand sells home-made frozen juice treats as well as snow-cones. Originally, Pabl...

#### March 10, 2012

### 6 - Jim and Jesse's Money

Jim and Jesse each had the same amount of money. Jim spent $\$58$ to fill the car up with gas for a...

#### March 10, 2012

### 5 - Watch Out for Parentheses 1

Evaluate the following numerical expressions. $2\times5+3\times2+4$ $2\times(5+3\times2+4)$ $2\times5+3\times(2+4)$...

#### March 10, 2012

### 2 - A Pencil and a Sticker

A pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost...

#### March 10, 2012

### 8 - Two Lines

Consider the graph below showing two lines, $L1$ and $L2$. Find the two corresponding linear equati...

#### March 10, 2012

### 6 - Interpreting a Division Computation

Use the computation shown below to find the products. $189\times 16$ $80\times 16$ $9 \times 16$

#### March 09, 2012

### HSF - Carbon 14 Dating, Variation 2

Carbon 14 is a common form of carbon which decays exponentially over time. The half-life of Carbon ...

#### March 09, 2012

### HSF - Finding Parabolas through Two Points

Find all quadratic functions described by the equation $y = ax^2 + bx + c$ whose graph contains the...

#### March 09, 2012

### 6 - Running to School, Variation 2

The distance between Rosa’s house and her school is $\frac34$ mile. She ran $\frac14$ mile. What fr...

#### March 08, 2012

### 6 - Drinking Juice, Variation 3

Alisa had some juice in a bottle. Then she drank $\frac38$ liters of juice. If this was $\frac34$ o...

#### March 08, 2012

### 8 - Fixing the Furnace

Ivan’s furnace has quit working during the coldest part of the year, and he is eager to get it fixe...

#### March 08, 2012

### 7 - Shrinking

When working on a report for class, Catrina read that a woman over the age of 40 can lose approxima...

#### March 08, 2012

### 1 - Daisies in vases

Jasmine has eight daisies and three vases - one large, one medium-sized and one small. She puts 5 d...

#### March 08, 2012

### 7 - Waiting Times

Suppose each box of a popular brand of cereal contains a pen as a prize. The pens come in four colo...

#### March 07, 2012

### 8 - Extending the Definitions of Exponents, Variation 1

Marco and Seth are lab partners studying bacterial growth. They were surprised to find that the pop...

#### March 07, 2012

### HSS - Why Randomize?

For the 100 rectangles shown, the small squares that compose them have area 1, so the area of the r...

#### March 07, 2012

### K - Assessing Writing Numbers

In a small group or whole group setting, give each student a piece of paper. It may be useful to us...

#### March 07, 2012

### K - Five by Two

Materials The students will need a deck of playing cards including some of the face cards. It is a ...

#### March 07, 2012

### K - Teen Go Fish

Materials One deck of cards with the teen numbers (11-19), 4 of each number. Play The students play...

#### March 07, 2012

### 7 - Election Poll, Variation 2

Members of the seventh grade math group have nominated a member of their group for class president....

#### March 06, 2012

### 7 - Election Poll, Variation 3

Members of the seventh grade math group have nominated a member of their group for class president....

#### March 06, 2012

### 7 - Election Poll, Variation 1

Members of the seventh grade math group have nominated a member of their group to be class presiden...

#### March 06, 2012

### 7 - Sale!

Four different stores are having a sale. The signs below show the discounts available at each of th...

#### March 06, 2012

### 8 - Converting Decimal Representations of Rational Numbers to Fraction Representations

Represent each of the following rational numbers in fraction form. $0.33\overline{3}$ $0.3\overline{17}$...

#### March 06, 2012

### 8 - Solving Equations

In elementary school, students often draw pictures of the arithmetic they do. For instance, they mi...

#### March 06, 2012

### 6 - Voting for Two, Variation 4

John and Will ran for 6th grade class president. John got two votes for every vote Will got. It was...

#### March 06, 2012

### 6 - Voting for Two, Variation 3

John and Will ran for 6th grade class president. There were 36 students voting. John got two votes ...

#### March 06, 2012

### 6 - Voting for Two, Variation 2

John and Will ran for 6th grade class president. There were 36 students voting. John got two votes ...

#### March 06, 2012

### 6 - Voting for Two, Variation 1

John and Will ran for 6th grade class president. There were 36 students voting. John got two votes ...

#### March 06, 2012

### 6 - Painting a Barn

Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn i...

#### March 06, 2012

### K - Biggest Number Wins

Materials Students play in pairs. Each student has a deck of 44 cards, 4 identical cards for each o...

#### March 06, 2012

### HSF - Average Cost

John makes DVDs of his friend’s shows. He has realized that, because of his fixed costs, his averag...

#### March 05, 2012

### 6 - Firefighter Allocation

A town's total allocation for firefighter's wages and beneﬁts in a new budget is \$600,000. If wage...

#### March 05, 2012

### K - Race to the Top

The teacher will need a sheet of 1 inch graph paper turned sideways (horizontally) with the numbers...

#### March 04, 2012

### K - Alike or Different Game

Materials: This game uses the 16 cards below. Actions: Students in pairs take turns drawing two car...

#### March 04, 2012

### 6 - Rectangle Perimeter 2

The students in Mr. Nolan's class are writing expressions for the perimeter of a rectangle of side ...

#### March 04, 2012

### 6 - Triangular Tables

A classroom has triangular tables. There is enough space at each side of a table to seat one child....

#### March 04, 2012

### 8 - Flower Vases

My sister’s birthday is in a few weeks and I would like to buy her a new vase to keep fresh flowers...

#### March 02, 2012

### HSS - Block Scheduling

A random sample of 100 students from a specific high school resulted in 45% of them favoring a plan...

#### February 28, 2012

### HSG - Doctor's Appointment

Jared is scheduled for some tests at his doctor’s office tomorrow. His doctor has instructed him to...

#### February 28, 2012

### HSA - Delivery Trucks

A company uses two different-sized trucks to deliver sand. The first truck can transport $x$ cubic ...

#### February 28, 2012

### HSG - Use Cavalieri’s Principle to Compare Aquarium Volumes

The management of an ocean life museum will choose to include either Aquarium A or Aquarium B in a ...

#### February 27, 2012

### HSN - Runners' World

According to an article in Runners' World magazine: On average the human body is more than 50 perce...

#### February 25, 2012

### HSG - Satellite

A satellite orbiting the earth uses radar to communicate with two control stations on the earth's s...

#### February 25, 2012

### HSG - Ice Cream Cone

You have been hired by the owner of a local ice cream parlor to assist in his company’s new venture...

#### February 25, 2012

### HSN - Selling Fuel Oil at a Loss

A fuel oil dealer buys 20,000 gallons of heating oil at \$2.65 per gallon and another 14,000 gallon...

#### February 24, 2012

### HSG - The Lighthouse Problem

Suppose that even in perfect visibility conditions, the lamp at the top of a lighthouse is visible ...

#### February 24, 2012

### HSF - Linear Functions

The figure below shows the graphs of the functions represented by $f(x)=4x-a$ and $g(x)=2x+b$ for s...

#### February 24, 2012

### HSF - U.S. Population 1790-1860

U.S. Population 1790 - 1860 Year Population (in thousands) Change in Population (in thousands) Succ...

#### February 19, 2012

### 8 - Find the Change

The table below shows two coordinate pairs $(x, y)$ that satisfy the equation $y=mx+b$ for some num...

#### February 12, 2012

### HSA - Throwing a Ball

A ball thrown vertically upward at a speed of $v$ ft/sec rises a distance $d$ feet in $t$ seconds, ...

#### February 12, 2012

### HSF - Equal Differences over Equal Intervals 2

Complete the table below. Is $\Delta x$ constant? What constant is it? What do you notice about the...

#### February 08, 2012

### 7 - Cooking with the Whole Cup

Travis was attempting to make muffins to take to a neighbor that had just moved in down the street....

#### February 08, 2012

### 2 - Growing Bean Plants

Students in pairs grow bean plants from seed. In a small glass jar, put a roll of paper towel insid...

#### February 05, 2012

### HSA - Profit of a company

The proﬁt that a company makes selling an item (in thousands of dollars) depends on the price of th...

#### February 03, 2012

### HSA - The Circle and The Line

Sketch the circle with equation $x^2 + y^2 = 1$ and the line with equation $y = 2x -1$ on the same ...

#### February 03, 2012

### HSF - Newton's Law of Cooling

A cup of hot coffee will, over time, cool down to room temperature. The principle of physics govern...

#### February 02, 2012

### 6 - Cup of Rice

Tonya and Chrissy are trying to understand the following story problem for $1 \div \frac23$: One se...

#### February 01, 2012

### K - Assessing Reading Numbers

Materials: numbercards 1–10 and 10–20. One-on-one with a student, the teacher shows the numbers 1–1...

#### January 29, 2012

### 6 - Fractions on the Number Line

Find and label the numbers $\frac43$, $\frac 54$, $-\frac23$, and $-\frac34$ on the number line. Fo...

#### January 27, 2012

### HSG - When Does SSA Work to Determine Triangle Congruence?

Josh is told that two triangles $ABC$ and $DEF$ share two sets of congruent sides and one pair of c...

#### January 26, 2012

### HSG - Why Does ASA Work?

In triangles $ABC$ and $ABD$ below, we are given that angle $BAC$ is congruent to angle $BAD$ and a...

#### January 26, 2012

### K - Find The Numbers 0-5 or 5-10

The teacher will need to create 2-3 sets of six number cards (0,1,2,3,4,5) and a matching number di...

#### January 26, 2012

### K - Assessing Counting Sequences Part II

This activity is designed to determine the appropriate instructional level for a student in a one-o...

#### January 26, 2012

### 1 - “Crossing the Decade” Concentration

This game is a version of the traditional memory or concentration game. You will need to create a s...

#### January 26, 2012

### HSG - Why does SAS work?

In the two triangles below, angle $A$ is congruent to angle $D$, side $AC$ is congruent to side $DF$...

#### January 26, 2012

### K - Assessing Counting Sequences Part I

This activity is designed to determine the appropriate instructional level for a student in a one-o...

#### January 26, 2012

### 8 - Identifying Rational Numbers

Decide whether each of the following numbers is rational or irrational. If it is rational, explain ...

#### January 21, 2012

### HSF, HSA - Graphs of Quadratic Functions

Graph these equations on your graphing calculator at the same time. What happens? Why? $$ \begin{align} y_1 &= (x – 3)(x + 1) \\ y_2 &= x^2 – 2x – 3 \\ y_3 &= (x – 1)^2 – 4 \\ y_4 &= x^2 – 2x + 1 \end{align} $$...

#### January 20, 2012

### HSA - Equations and Formulas

Use inverse operations to solve the equations for the unknown variable, or for the designated varia...

#### January 19, 2012

### HSF, HSN - Extending the Definitions of Exponents, Variation 2

A biology student is studying bacterial growth. She was surprised to find that the population of th...

#### January 18, 2012

### 8 - High School Graduation

The SLV High School graduation started at 1:00PM. After some speeches, the principal started readin...

#### January 17, 2012

### 6 - Games at Recess

The students in Mr. Hill’s class played games at recess. $\hskip30pt$6 boys played soccer $\hskip30pt$...

#### January 16, 2012

### HSF, HSA - Springboard Dive

Suppose $h(t) = -5t^2 + 10t + 3$ isthe height of a diver above the water (in meters), $t$ seconds a...

#### January 16, 2012

### 3 - Two Interpretations of Division

Maria cuts 12 feet of ribbon into 3 equal pieces so she can share it with her two sisters. How long...

#### January 10, 2012

### 3 - Analyzing Word Problems Involving Multiplication

Many problems can be solved in different ways. Decide if the following word problems can be solved ...

#### January 02, 2012

### HSN - Traffic Jam

Last Sunday an accident caused a traffic jam 12 miles long on a straight stretch of a two lane free...

#### January 02, 2012

### HSF - Exponential growth versus linear growth I

Mr. Wiggins gives his daughter Celia two choices of payment for raking leaves: Two dollars for each...

#### January 02, 2012

### HSF - Exponential growth versus polynomial growth

The table below shows the values of $2^x$ and $2x^3 + 1$ for some whole number values of $x$: $x$$2^x$$2x^3+1$...

#### January 02, 2012

### HSF - Exponential growth versus linear growth II

Using a scientific calculator, Alex makes the following table listing values of $(1.001)^x$ and $2x$...

#### January 02, 2012

### HSF - Skeleton Tower

How many cubes are needed to build this tower? How many cubes are needed to build a tower like this...

#### January 01, 2012

### HSF - Rumors

Susanna heard some exciting news about a well-known celebrity. Within a day she told 4 friends who ...

#### January 01, 2012

### HSF - A Sum of Functions

Using the graphs below, sketch a graph of the function $s(x) = f(x) + g(x)$.

#### January 01, 2012

### HSF - Sandia Aerial Tram

Albuquerque boasts one of the longest aerial trams in the world. The tram transports people up to S...

#### January 01, 2012

### HSF - Kimi and Jordan

Kimi and Jordan are each working during the summer to earn money in addition to their weekly allowa...

#### January 01, 2012

### HSA - Equivalent Expressions

Find a value for $a$, a value for $k$, and and a value for $n$ so that $$(3x + 2) (2x - 5) = ax^2 + kx + n.$$...

#### January 01, 2012

### HSF - US Households

The table below shows the number of households in the U.S. in the years 1998-2004 [data source: www...

#### January 01, 2012

### HSF - Interesting Interest Rates

City Bank pays a simple interest rate of 3% per year, meaning that each year the balance increases ...

#### January 01, 2012

### 8 - Equations of Lines

The figure below shows two lines. One is described by the equation $4x-y=c$ and the other by equati...

#### January 01, 2012

### 6 - Reasoning about Multiplication and Division and Place Value, Part 2

Place a decimal on the right side of the equal sign to make the equation true. Explain your reasoni...

#### December 31, 2011

### 6 - Gifts from Grandma, Variation 3

Juanita spent \$24.50 on each of her 6 grandchildren at the fair. How much money did Juanita spend?...

#### December 31, 2011

### K - Number After Bingo 1-15

Each student will need a different Number After Game Board (a 5x5 grid with numbers from 2 through ...

#### December 31, 2011

### K - Start-Stop Counting

Have students form a circle and sit facing in toward each other. The teacher selects a range of the...

#### December 31, 2011

### K - Counting Circles

Have students stand and form a circle facing in toward each other. Select a counting sequence to be...

#### December 31, 2011

### K - Choral Counting

The teacher will need a 100 chart or large number line and a pointer. As a whole group, have studen...

#### December 31, 2011

### 7 - Sharing Prize Money

The three seventh grade classes at Sunview Middle School collected the most boxtops for a school fu...

#### December 31, 2011

### 4 - Comparing Money Raised

Helen raised \$12 for the food bank last year and she raised 6 times as much money this year. How m...

#### December 31, 2011

### 3 - Gifts from Grandma, Variation 1

Juanita spent \$9 on each of her 6 grandchildren at the fair. How much money did she spend? Nita bo...

#### December 31, 2011

### 6 - Multiples and Common Multiples

List all the multiples of 8 that are less than or equal to 100. List all the multiples of 12 that a...

#### December 29, 2011

### 6 - The Florist Shop

The florist can order roses in bunches of one dozen and lilies in bunches of 8. Last month she orde...

#### December 29, 2011

### HSF - Equal Differences over Equal Intervals 1

Complete the table. In the third column, show your work as demonstrated. What do you notice about t...

#### December 28, 2011

### HSF - Equal Factors over Equal Intervals

Complete the table below. Is $\Delta x$ a constant? If so, what constant is it? What do you notice ...

#### December 28, 2011

### HSF - Identifying Functions

The following tables show the values of linear, quadratic, and exponential functions at various val...

#### December 28, 2011

### HSF - US Population 1982-1988

The below table provides some U.S. Population data from 1982 to 1988: U.S. Population 1982 – 1988 Y...

#### December 28, 2011

### HSF - Two Points Determine an Exponential Function I

The graph of a function of the form $f(x)=ab^x$ is shown below. Find the values of $a$ and $b$.

#### December 28, 2011

### HSF - Two Points Determine an Exponential Function II

The graph of a function of the form $f(x)=ab^x$ is shown below. Find the values of $a$ and $b$.

#### December 28, 2011

### HSF - Basketball Rebounds

According to Wikipedia, the International Basketball Federation (FIBA) requires that a basketball b...

#### December 28, 2011

### HSF, HSA - Taxi!

Lauren keeps records of the distances she travels in a taxi and what she pays: Distance, $d$, in mi...

#### December 28, 2011

### HSG - Midpoints of the Sides of a Paralellogram

Suppose that $ABCD$ is a parallelogram, and that $M$ and $N$ are the midpoints of $\overline{AB}$ a...

#### December 28, 2011

### HSA - Mixing Fertilizer

A landscaping company prepares two mixtures of fertilizer. Mixture A contains 5 liters of liquid fe...

#### December 27, 2011

### 6 - Adding Multiples

Nina was finding multiples of 6. She said, 18 and 42 are both multiples of 6, and when I add them, ...

#### December 27, 2011

### HSF - Crude Oil and Gas Mileage

According to the U.S. Energy Information Administration, a barrel of crude oil produces approximate...

#### December 21, 2011

### HSF - Susita's Account

At the beginning of January, Susita had some money in her checking account. At the end of each mont...

#### December 21, 2011

### 5 - Making Cookies

A recipe for chocolate chip cookies makes 4 dozen cookies and calls for the following ingredients: ...

#### December 20, 2011

### HSF - Comparing Exponentials

Lincoln deposits money in a Certificate of Deposit account. The balance (in dollars) in his account...

#### December 17, 2011

### 6 - Factors and Common Factors

List all the factors of 48. List all the factors of 64. What are the common factors of 48 and 64? W...

#### December 15, 2011

### 7 - Sand Under the Swing Set

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartne...

#### December 14, 2011

### 7 - Comparing Years

Historically, different people have defined a year in different ways. For example, an Egyptian year...

#### December 14, 2011

### 5 - Half of a Recipe

Kendra is making $\frac{1}{2}$ of a recipe. The full recipe calls for $3\frac{1}{4}$ cup of flour. ...

#### December 13, 2011

### 5 - Drinking Juice

Alisa had $\frac{1}{2}$ a liter of juice in a bottle. She drank $\frac{3}{4}$ of the juice that was...

#### December 13, 2011

### 5 - Running to School

The distance between Rosa’s house and her school is $\frac{3}{4}$ mile. She ran $\frac{1}{3}$ of th...

#### December 13, 2011

### 7 - Chess Club

There were 24 boys and 20 girls in a chess club last year. This year the number of boys increased b...

#### December 12, 2011

### HSN - Weed killer

A liquid weed-killer comes in four different bottles, all with the same active ingredient. The acco...

#### December 12, 2011

### 6 - Bake Sale

Lindy is having a bake sale. She has 48 chocolate chip cookies to put in bags. How many bags can sh...

#### December 12, 2011

### 5 - Converting Fractions of a Unit into a Smaller Unit

Five brothers are going to take turns watching their family's new puppy. How much time will each br...

#### December 12, 2011

### 7 - Tax and Tip

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and that the ...

#### December 08, 2011

### 7 - Selling Computers

The sales team at an electronics store sold 48 computers last month. The manager at the store wants...

#### December 08, 2011

### 7 - Buying Protein Bars and Magazines

Tom wants to buy some protein bars and magazines for a trip. He has decided to buy three times as m...

#### December 08, 2011

### 7 - Friends Meeting on Bikes

Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each...

#### December 05, 2011

### HSA - Throwing Horseshoes

The height (in feet) of a thrown horseshoe $t$ seconds into flight can be described by the expressi...

#### December 05, 2011

### K - What’s Missing?

Show the student 6 counters (small, flat objects). Ask the student to close his/her eyes. Hide some...

#### November 27, 2011

### HSS - SAT Scores

Suppose that SAT mathematics scores for a particular year are approximately normally distributed wi...

#### November 26, 2011

### 7 - Music Companies, Variation 2

BeatStreet, TunesTown, and MusicMind are music companies. BeatStreet and MusicMind are teaming up t...

#### November 26, 2011

### 1 - Finding a Chair

There are 8 children and 6 chairs. A child sits in each chair. How many children won’t have a chair...

#### November 09, 2011

### 1 - Sharing Markers

Char had 10 markers. She gave 3 to a friend. How many did she have left? Char had 10 markers. She g...

#### November 09, 2011

### 1 - The Pet Snake

The class had a pet snake. It was 14 inches long. It grew 3 more inches. How long is it now? The cl...

#### November 09, 2011

### 1 - Maria’s Marbles

Ali had 9 marbles. Maria had 5 marbles. How many more marbles did Ali have than Maria? Ali had 9 ma...

#### November 09, 2011

### 1 - Boys and Girls, Variation 2

9 children were in the class. How many boys and how many girls could have been in the class? Solve ...

#### November 09, 2011

### 1 - At the Park

There were 7 children at the park. Then 4 more showed up. How many children were at the park all to...

#### November 09, 2011

### 1 - Boys and Girls, Variation 1

9 boys and 8 girls were in the class. How many children were in the class in all? 17 children were ...

#### November 09, 2011

### 3 - Which is Closer to 1?

Which is closer to 1 on the number line, $\frac45$ or $\frac54$? Explain....

#### November 05, 2011

### 3 - Find 2/3

Label the point where $\frac23$ belongs on the number line. Be as exact as possible.

#### November 05, 2011

### 3 - Find 1

Locate 1 on the number line. Label the point. Be as exact as possible. Locate 1 on the number line....

#### November 05, 2011

### 3 - Closest to 1/2

Which number is closest to $\frac12$? $\frac18$ $\frac38$ $\frac78$ $\frac98$

#### November 05, 2011

### 3 - Locating Fractions Greater than One on the Number Line

Mark and label points on the number line for $\frac12$, $\frac22$, $\frac32$, $\frac42$, $\frac52$,...

#### November 05, 2011

### 3 - Locating Fractions Less than One on the Number Line

Mark and label the points $\frac14$, $\frac24$, $\frac34$, and $\frac44$ on the number line. Be as ...

#### November 05, 2011

### 5 - Running a Mile

Curt and Ian both ran a mile. Curt's time was $ \frac89$ Ian's time. Who ran faster? Explain and dr...

#### November 05, 2011

### 5 - Grass Seedlings

The students in Raul’s class were growing grass seedlings in different conditions for a science pro...

#### November 05, 2011

### 5 - Fundraising

Cai, Mark, and Jen were raising money for a school trip. Cai collected $ 2 \frac12 $ times as much ...

#### November 05, 2011

### 5 - Calculator Trouble

Luke had a calculator that will only display numbers less than or equal to 999,999,999. Which of th...

#### November 05, 2011

### 8 - Sore Throats, Variation 2

Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water. $\hskip30pt$...

#### November 02, 2011

### 8 - Peaches and Plums

The graphs below show the cost $y$ of buying $x$ pounds of fruit. One graph shows the cost of buyin...

#### November 02, 2011

### 8 - Comparing Speeds in Graphs and Equations

The graphs below show the distance two cars have traveled along the freeway over a period of severa...

#### November 02, 2011

### 8 - Coffee by the Pound

Lena paid \$18.96 for 3 pounds of coffee. What is the cost per pound for this coffee? How many poun...

#### November 02, 2011

### 8 - Who Has the Best Job?

Kell works at an after-school program at an elementary school. The table below shows how much money...

#### November 02, 2011

### 7 - Music Companies, Variation 1

BeatStreet, TunesTown, and MusicMind are music companies. BeatStreet offers to buy 1.5 million shar...

#### November 02, 2011

### 7 - Art Class, Variation 2

The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixt...

#### November 02, 2011

### 7 - Art Class, Variation 1

The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixt...

#### November 02, 2011

### 7 - Buying Coffee

Coffee costs \$18.96 for 3 pounds. What is the cost for one pound of coffee? At this store, the pri...

#### November 02, 2011

### 7 - Robot Races

Carli’s class built some solar-powered robots. They raced the robots in the parking lot of the scho...

#### November 02, 2011

### 2 - Boxes and Cartons of Pencils

Pencils are packed 10 in a box. A classroom carton has 10 boxes. Jem has 1 carton and 4 boxes. How ...

#### November 02, 2011

### K - Pick Two

For each set of numbers below, pick two numbers that add to make six. Write an equation that shows ...

#### November 02, 2011

### K - Make 9

Make 9 in as many ways as you can by adding two numbers between 0 and...

#### November 02, 2011

### K - Christina's Candies

This task is meant to be presented as a sequence of questions posed by the teacher to the students....

#### November 02, 2011

### 2 - Regrouping

What number represents the same amount as 2 tens + 7 ones? What number represents the same amount a...

#### November 02, 2011

### 2 - Ten \$10s make \$100

How many ten-dollar bills equal a hundred-dollar bill? Jem had 20 ten-dollar bills. How many hundre...

#### November 02, 2011

### 2 - Largest Number Game

Dona had cards with the numbers 0 to 9 written on them. She flipped over three of them. Her teacher...

#### October 29, 2011

### 2 - Bundling and Unbundling

Make true equations. Write one number in every space. Draw a picture if it helps. 1 hundred + 4 ten...

#### October 29, 2011

### 2 - Making 124

Lamar and Siri had some base-ten blocks. Lamar said, "I can make 124 using 1 hundred, 2 tens, and 4...

#### October 29, 2011

### 4 - Adding Tenths and Hundredths

Find the sums. $\displaystyle \frac{9}{10} + \frac{8}{100}$ $\displaystyle \frac{7}{100} + \frac{3}{10}$...

#### October 28, 2011

### 4 - Fraction Equivalence

Explain why $\frac{6}{10} = \frac{60}{100}$. Draw a picture to illustrate your...

#### October 28, 2011

### 4 - Expanded Fractions and Decimals

Complete the table. Fraction Expanded Fraction Form Expanded Decimal Form Decimal $43 \frac{65}{100}$...

#### October 28, 2011

### 4 - Dimes and Pennies

A dime is $\frac{1}{10}$ of a dollar and a penny is $\frac{1}{100}$ of a dollar. What fraction of a...

#### October 28, 2011

### 6 - Security Camera

A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling o...

#### October 22, 2011

### 6 - Mixing Concrete

A mixture of concrete is made up of sand and cement in a ratio of 5 : 3. How many cubic feet of eac...

#### October 22, 2011

### 6 - Converting Square Units

Jada has a rectangular board that is 60 inches long and 48 inches wide. How long is the board measu...

#### October 22, 2011

### 6 - Voting for Three, Variation 3

John, Marie, and Will all ran for 6th grade class president. The ratio of votes for John to votes f...

#### October 22, 2011

### 6 - Voting for Three, Variation 2

John, Marie, and Will all ran for 6th grade class president. Of the 36 students voting, the ratio o...

#### October 22, 2011

### 6 - Voting for Three, Variation 1

John, Marie, and Will all ran for 6th grade class president. Of the 36 students, 16 voted for John,...

#### October 22, 2011

### 6 - Kendall's Vase - Tax

Kendall bought a vase that was priced at \$450. In addition, she had to pay 3% sales tax. How much ...

#### October 22, 2011

### 6 - Dana's House

The lot that Dana is buying for her new one story house is 35 yards by 50 yards. Dana’s house plans...

#### October 22, 2011

### 8 - Applying the Pythagorean Theorem in a mathematical context

Three right triangles surround a shaded triangle; together they form a rectangle measuring 12 units...

#### September 14, 2011

### 2 - One, Ten, and One Hundred More and Less

What number is 1 more than 99? What number is 1 less than 600? What number is 10 more than 90? What...

#### September 14, 2011

### HSN - Ice Cream Van

You are considering driving an ice cream van during the summer vacation. Your friend, who “knows ev...

#### September 14, 2011

### HSF - Summer Intern

You have been hired for a summer internship at a marine life aquarium. Part of your job is diluting...

#### September 14, 2011

### 6 - Baking Cookies

Alice, Raul, and Maria are baking cookies together. They need $\frac34$ cup of flour and $\frac13$ ...

#### September 02, 2011

### 6 - Shirt Sale

Selina bought a shirt on sale that was 20% less than the original price. The original price was $\$ $...