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# Hitting The Target Number

## Task

#### Materials

- Number cards labeled 1-10 (attached as a PDF)

#### Actions

Begin by playing the game as a whole class to demonstrate the rules and for students to illustrate the range of possible strategies.

Have a student pick 5 number cards from the cards labeled 1 through 10. Then, have another student pick a “Target Number” between 10 through 20. Students must add and/or subtract 2 or more of the 5 number cards to arrive at the “target” number.

As students present the different number combinations for the “target” number, write their expressions on the board and have them explain how they were able to mentally come up with the solution.

As students explain their reasoning, name the strategies they used. For example, look for students making fives (e.g. 6 + 8 = 5 + 1 + 5 +3= 10 + 4 = 14) and tens (9 + 8 = 10 + 7), and using known facts (e.g. 8 + 8 is 16 so 8 + 7 is one less than 16) to encourage flexible thinking about the relationship among the facts.

When students understand how the game works, they can play in pairs, checking each other's solutions.

## IM Commentary

The purpose of this task is to help students develop flexible strategies for adding and subtracting within 20. "Computational fluency refers to having efficient, accurate, generalizable methods (algorithms) for computing numbers that are based on well-understood properties and number relationships" (NCTM, 2000). Therefore, the focus in developing fluency should be more than the internalization of facts but on supporting students natural development of number sense so that they are able to solve computations flexibly and efficiently using their understanding of place value and relationships between numbers.

Children’s natural development of numbers progress from the concrete to the abstract, from counting all (e.g. physically making four counters and then making twelve and counting all the counters to get sixteen), to counting on (e.g., counting four more starting at twelve to get to sixteen), to using part-whole (e.g. splitting apart the twelve to ten and two, and adding the two to four, then adding the ten) and relational thinking (knowing that 4 + 10 is 14 so 4 + 9 would be just one less). As this activity requires students to add or subtract two or more numbers mentally, students are pushed to develop more efficient strategies.

Once you have modeled the game as a whole class, this activity can be played by individual pairs of students. The number of cards and the target number can be modified to meet the needs of your students and your instructional intent.

Reference

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

## Solution

Suppose the five number cards selected are 5, 3, 8, 1, and 9 and a target number is 16.

- 5 + 3 + 8. 5 and 3 is 8 and doubles 8 is 16.

Another strategy:

- Break apart the 8 into 5 and 3. Add the two 5s to make 10 and the two 3s to make 6. Then add 10 and 6 to make 16.

## Hitting The Target Number

#### Materials

- Number cards labeled 1-10 (attached as a PDF)

#### Actions

Begin by playing the game as a whole class to demonstrate the rules and for students to illustrate the range of possible strategies.

Have a student pick 5 number cards from the cards labeled 1 through 10. Then, have another student pick a “Target Number” between 10 through 20. Students must add and/or subtract 2 or more of the 5 number cards to arrive at the “target” number.

As students present the different number combinations for the “target” number, write their expressions on the board and have them explain how they were able to mentally come up with the solution.

As students explain their reasoning, name the strategies they used. For example, look for students making fives (e.g. 6 + 8 = 5 + 1 + 5 +3= 10 + 4 = 14) and tens (9 + 8 = 10 + 7), and using known facts (e.g. 8 + 8 is 16 so 8 + 7 is one less than 16) to encourage flexible thinking about the relationship among the facts.

When students understand how the game works, they can play in pairs, checking each other's solutions.

## Comments

Log in to comment## Dev Sinha says:

over 4 yearsGreat question. I see this as an instructional task which provides an opportunity for differentiated instruction. Meeting the standard means fluency (that's the first word), which to me would mean not needing fingers or other objects. But some students who are counting on or who rely on manipulatives can very productively engage in the task, and be working towards the number sense which the standard prescribes, side-by-side with students who are further along.

## Claire says:

almost 5 yearsWhat behaviors does the teacher not want to see the student do? Can a student use their fingers/objects to count?