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Standards-based assessment and Instruction

# Instructional Task: Grade 4

## Dog Years

### Task

It is said that dogs age seven years for every "people year." Mason's dog, Shep, was born on Mason's eighth birthday. When Mason was nine years old, Shep was seven dog years old. In dog years, how old will Shep be on Mason's twelfth birthday? Show all your mathematical thinking.

### Alternative Versions of Task

#### More Accessible Version

It is said that dogs age seven years for every "people year." Mason's dog, Shep, was born on Mason's eighth birthday. When Mason was nine years old, Shep was seven dog years old. In dog years, how old will Shep be on Mason's tenth birthday? Show all your mathematical thinking.

#### More Challenging Version

It is said that dogs age seven years for every "people year." Mason’s dog, Shep, was born on Mason's eighth birthday. When Mason was nine years old, Shep was seven dog years old. If Shep is fifty-six dog years old, how old is Mason? Show all your mathematical thinking.

### Common Core Content Standards and Evidence

#### 4.OA Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

2.   Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

### Exemplars Task-Specific Evidence

This task requires students to use multiplication in comparison situations.

### GO Math! Alignments

• Chapter 2, Lesson: 2.2

### Common Core Standards of Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.

### Underlying Mathematical Concepts

• Multiplicative comparison
• Number sense to 28

### Possible Problem-Solving Strategies

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

### Possible Mathematical Vocabulary/Symbolic Representation

• Model
• Diagram/Key
• Table
• Number line
• Pictograph
• Pattern
• Multiple
• Odd/Even
• Per
• Year, month, day
• Ordinal numbers: 8th, 9th, 10th ...
• Total/Sum
• Dozen

### Possible Solutions

In dog years, Shep will be 28 years old on Mason's 12th birthday.

#### More Accessible Version Solution

In dog years, Shep will be 14 years old on Mason's 10th birthday.

#### More Challenging Version Solution

Mason is 16 years old.

### Possible Connections

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

• Patterns: Mason's age +1, Shep's age in dog years +7.
• Continue to find Mason and Shep's ages after Mason's 12th birthday.
• Rule for Shep: 7 · "people years" = dog years, 7 · p = d.
• If a dog is a dozen people years old, the dog is 84 years old. Dogs don't tend to live as long as people.
• Relate to a similar task and state a math link.
• Solve more than one way to verify the answer.

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