Grade 8
- Approximating pi
- Calculating and Rounding Numbers
- Calculating the square root of 2
- Estimating Square Roots
8.NS. Grade 8 - The Number System
8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
8.NS.A.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., $\pi^2$). For example, by truncating the decimal expansion of $\sqrt{2}$, show that $\sqrt{2}$ is between $1$ and $2$, then between $1.4$ and $1.5$, and explain how to continue on to get better approximations.
- No tasks yet illustrate this standard.
- Different Areas?
- DVD Profits, Variation 1
- Equations of Lines
- Find the Change
- Folding a Square into Thirds
- Proportional relationships, lines, and linear equations
- Stuffing Envelopes
- Coupon versus discount
- Sammy's Chipmunk and Squirrel Observations
- Solving Equations
- The Sign of Solutions
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- No tasks yet illustrate this standard.
- Cell Phone Plans
- Fixing the Furnace
- Folding a Square into Thirds
- How Many Solutions?
- Kimi and Jordan
- No tasks yet illustrate this standard.
8.EE. Grade 8 - Expressions and Equations
8.EE.A. Work with radicals and integer exponents.
8.EE.A.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, $3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27$.
8.EE.A.2. Use square root and cube root symbols to represent solutions to equations of the form $x^2 = p$ and $x^3 = p$, where $p$ is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that $\sqrt{2}$ is irrational.
8.EE.A.3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as $3 \times 10^8$ and the population of the world as $7 \times 10^9$, and determine that the world population is more than $20$ times larger.
8.EE.A.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
8.EE.B. Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.EE.B.6. Use similar triangles to explain why the slope $m$ is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation $y = mx$ for a line through the origin and the equation $y = mx + b$ for a line intercepting the vertical axis at $b$.
8.EE.C. Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7. Solve linear equations in one variable.
8.EE.C.7.a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form $x = a$, $a = a$, or $a = b$ results (where $a$ and $b$ are different numbers).
8.EE.C.7.b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.EE.C.8. Analyze and solve pairs of simultaneous linear equations.
8.EE.C.8.a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.C.8.b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, $3x + 2y = 5$ and $3x + 2y = 6$ have no solution because $3x + 2y$ cannot simultaneously be $5$ and $6$.
8.EE.C.8.c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
8.F. Grade 8 - Functions
8.F.A. Define, evaluate, and compare functions.
8.F.A.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.Function notation is not required in Grade 8.
8.F.A.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
8.F.A.3. Interpret the equation $y = mx + b$ as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function $A = s^2$ giving the area of a square as a function of its side length is not linear because its graph contains the points $(1,1)$, $(2,4)$ and $(3,9)$, which are not on a straight line.
8.F.B. Use functions to model relationships between quantities.
8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two $(x, y)$ values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.B.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
- A scaled curve
- Is this a rectangle?
- Partitioning a hexagon
- Reflecting a rectangle over a diagonal
- Same Size, Same Shape?
- Scaling angles and polygons
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- No tasks yet illustrate this standard.
- No tasks yet illustrate this standard.
- Applying the Pythagorean Theorem in a mathematical context
- A rectangle in the coordinate plane
- Bird and Dog Race
- Is this a rectangle?
- Sizing up Squares