Standards-based assessment and Instruction

## Three Fish Limit

Some friends are camping near the shore. One friend suggests that they go fishing. Six boats are available at the campsite. Each boat holds two people and the friends are excited because that is exactly how many they need. The rule on this lake is that each person can catch only three fish. How many fish did the friends catch that day if each friend caught the limit? Show all your mathematical thinking.

### Common Core Content Standards and Evidence

#### 3.OA Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

3.   Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

This task requires students to use repeated addition or multiplication to find the number of people who are camping and the number of fish they catch.

### GO Math! Alignments

• Chapter 3, Lessons: 3.3, 3.5
• Chapter 4, Lessons: 4.1, 4.2, 4.3
• Chapter 6, Lessons: 6.1, 6.5, 6.6

### 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.5
Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.

### Underlying Mathematical Concepts

• Two to one
• Three to one
• Multiplication within 100
• Number sense to 36
• Combining

### Possible Problem-Solving Strategies

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

### Possible Mathematical Vocabulary/Symbolic Representation

• Model
• Diagram/Key
• Table
• Tally chart
• Number line
• Pattern
• Multiples
• Per
• Odd/Even
• More/Less than
• 1/2
• Rule
• 2 · b = p (b + b = p), 6 · b = f
• Variables
• Per
• Total/Sum
• Product
• Dozen
• Pair
• Input/Output
• Array
• Graph
• Axis
• Sets
• Groups

### Possible Solutions

The friends caught 36 fish.

### Possible Connections

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

• Patterns: Boat +1, People +2, Fish +6.
• The people and amount of fish caught are even numbers.
• 1 person = 1/2 boat.
• 2 people is a pair.
• There are 4 more fish than people.
• Rules: 2 · b = p, 6 · b = f.
• Solve more than one way to verify the answer.
• Multiples of 2 and 6 are even numbers.
• Graph input/outputs on graph paper.

### Scoring Rationales and Corresponding Anchor Papers

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## Here's What People Are Saying

The Southwest Vermont Supervisory Union (SVSU) in Bennington was trying to help its local community gain a better understanding of what students need to demonstrate in order to be successful on their math assessments. One of the most difficult sections of the exam is problem solving. Here, students are not only expected to determine the correct strategy, but also to explain their answers in writing, using math language and representation. For four years SVSU has used Exemplars as a curriculum tool in teaching its students how to solve these types of problems...

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