Standards-based assessment and Instruction

## Pairs of Shoes

Evan has six pairs of shoes! Evan's shoes are all over his bedroom floor. Evan counts his shoes. First, Evan counts seven shoes. Next, Evan counts four shoes. Evan says he must find one more shoe. How does Evan know he must find one more shoe? Show your math thinking.

#### More Accessible Version

Evan has three pairs of shoes! Evan's shoes are all over his bedroom floor. Evan counts his shoes. First, Evan counts three shoes. Next, Evan finds two more shoes. Evan says he has one more shoe left to find. How does Evan know he must find one more shoe? Show all your math thinking.

#### More Challenging Version

Evan has twelve pairs of shoes! Evan's shoes are all over his bedroom floor. Evan counts his shoes. First, Evan counts eight shoes. Next, Evan counts fourteen shoes. Evan says he must find one more pair of shoes. How does Evan know he must find one more pair of shoes? Show all your math thinking.

### Strategies for Addition and Subtraction Unit

The Strategies for Addition and Subtraction Unit involves understanding the processes of addition and subtraction in order to solve problems and answer questions such as –

• If we know all of the parts, how can we find the whole?
• If we know the whole and one of the parts, how can we find the missing part?
• Given an equation, can you create an addition or subtraction situation to match it? How can you prove it matches the equation?

### Math Concepts and Skills Covered

The student solves problems by developing and using strategies for addition and subtraction. The student:

• Finds the sum of a multiple of 10 and a one-digit number (up to 99) in problem situations.
• Develops, applies and explains strategies used to add and subtract within 20, such as making 10 and decomposing a number leading to a 10.
• Creates problem situations when given a number sentence involving addition or subtraction of numbers within 20; solves the problems created.
• Represents word problems involving addition and subtraction of numbers up to 20.
• Applies properties of operations to add and subtract two or three numbers-if 4 + 3 = 7 is known, then 3 + 4 = 7 is also known.

This task requires students to solve addition and subtraction problems in which the difference and the sum are unknown. Students also need to know that there are 2 objects in a pair as well as to have number sense to 12.

### Underlying Mathematical Concepts

• Number sense to 12
• Comparison
• 2 is a pair

### Possible Problem-Solving Strategies

• Model (manipulatives)
• Diagram/Key
• Number line
• Tally chart
• Table

### Formal Mathematical Language and Symbolic Notation

• Model
• Diagram/Key
• Number line
• Tally chart
• Table
• Total/Sum
• More than (>)/Greater than (>)/Less than (<)
• Equivalent/Equal to
• Dozen
• Halves, half of
• Pair
• 1st, 2nd, ...6th
• First, next, last
• Odd/Even

### Possible Solutions

Evan needs to find 12 shoes to make 6 pairs. Evan finds 11 shoes, so he needs to find one more shoe.

#### More Accessible Version Solution

Evan needs to find 6 shoes to make 3 pairs. Evan finds 5 shoes, so he needs to find 1 more.

#### More Challenging Version Solution

Evan needs to find 24 shoes to make 12 pairs. Evan finds 22 shoes, so he needs to find two more or 1 pair.

### Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

• 6 pairs are 12 shoes-a dozen.
• Pairs are 2-an even number, so you can not have an odd number of shoes.
• Evan found 3 more shoes first than next.
• Odd + Even = Odd, so a shoe is missing.
• Solve more than one way to verify the answer.
• Evan should find 6 shoes first and next to find an equal number each time.
• Evan finds an odd number of shoes first.
• Evan finds 2 pairs of shoes next.
• Evan found 3 less shoes next than first.
• Evan found an even number of shoes next.
• Evan found 3 pairs and 1 extra shoe first.
• 6 shoes or 3 pairs is a half dozen shoes.

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## Here's What People Are Saying

The Exemplars program is designed to assess students' problem-solving and mathematical-communication skills. It also supports higher-level thinking and extension of mathematical reasoning.

S. Dement
Teacher

Converse, TX

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