Standards-based assessment and Instruction

## View Spanish Translation     Cars on a Ramp

Sabrina and Joel are measuring how far their cars roll down a ramp. Sabrina's car rolls forty-eight inches. Joel's car rolls seventy-two inches. Sabrina says her car rolls four times as far as one foot. Joel says his car rolls two times as far as one yard. Who is correct, Sabrina or Joel? 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.

This task requires students to use multiplication in comparison situations. The students also need to know that one foot is 12 inches and one yard is 36 inches.

### Common Core Standards of Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
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

• Multiplicative comparison
• Linear measurement: 12" = 1', 36" = 1 yard
• Number sense to 72

### Possible Problem-Solving Strategies

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

### Formal Mathematical Language and Symbolic Notation

• Model
• Diagram/Key
• Chart
• Number line
• Inch, in.,"
• Foot, ft. '
• Yard, yd.
• Total/Sum
• Amount
• Greater than (>)/Less than (<)
• Most/Least
• Distance
• Per
• Angle
• Degrees

### Possible Solutions

Sabrina and Joel are both correct.

### Possible Connections

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

• The cars roll a total of 120 inches or 10 feet.
• Joel's car travels the most, 2 more feet than Sabrina's car.
• Sabrina's car travels 1 1/3 yards or 1 yard and 12 inches.
• Solve more than one way to verify the answer.
• Using the same ramp makes the distance traveled per car fair as the slope is the same.
• If you raise the ramp, the cars could go faster.
• Angle/ramp/degrees are discussed.

### Scoring Rationales and Corresponding Anchor Papers

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## Here's What People Are Saying

"In 1999, only 28% of our 8th grade students met or exceeded state standards." After the introduction of Exemplars, "In 2001, 56% of our 8th grade students met or exceeded the standards. In other words, we doubled the number of students passing the state test in the two-year time period."

R. Cox

Principal