Activity

Question

Valerie and Seth are measuring the outside walls of a house using two different instruments. They want to find the house’s perimeter. Valerie measured the north and east sides while Seth measured the west and south sides. Their results are listed in the table.

Valerie's Measurements Seth's Measurements
4 walls at
feet each 1 wall at
feet
3 walls at
feet each 2 walls at
feet each
1 wall at
feet 1 wall at
feet

Complete the steps below to help Valerie and Seth find the perimeter of the house.

Part A
Use decimal numbers to write an expression that represents the length of the walls that Valerie measured.

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Part B
Now use decimal numbers to write an expression that represents the length of the walls that Seth measured.

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Part C
Write an expression for the perimeter of the house. Use the work you completed in parts A and B to guide you.

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Part D
Simplify the expression from part C to find the perimeter of the house in feet.

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Part E
Suppose that you evaluate the expression for Valerie’s walls and the expression for Seth’s walls separately. Then you add the two expressions together. Will you get the same answer that you arrived at in part d? Why or why not? Show your work to prove your case.

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Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

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Answer 1

To help you find the perimeter of the house, let's go through each part step by step.

Part A:

Valerie's Measurements: Let's assume Valerie measured the following:

• 4 walls at 10 feet each
• 3 walls at 15 feet each
• 1 wall at 20 feet

The expression representing the total length of the walls that Valerie measured would be: \[ 4 \times 10 + 3 \times 15 + 20 \]

Part B:

Seth's Measurements: Let's assume Seth measured the following:

• 1 wall at 10 feet
• 2 walls at 5 feet each

The expression representing the total length of the walls that Seth measured would be: \[ 10 + 2 \times 5 \]

Part C:

Perimeter of the House: The perimeter of the house is the sum of the lengths of the walls measured by both Valerie and Seth. Combining both expressions from parts A and B: \[ (4 \times 10 + 3 \times 15 + 20) + (10 + 2 \times 5) \]

Part D:

Simplifying the Expression: Now let's simplify the expression:

1. Calculate Valerie's measurements:

   • \(4 \times 10 = 40\)
   • \(3 \times 15 = 45\)
   • Adding those together with the additional wall: \[ 40 + 45 + 20 = 105 \]

2. Calculate Seth's measurements:

   • \(10 + 2 \times 5 = 10 + 10 = 20\)

3. Now combine the two results: \[ 105 + 20 = 125 \]

So the perimeter of the house is 125 feet.

Part E:

To evaluate whether the perimeter calculated in part D matches the sum of the individual expressions:

• Valerie's total length: \[ 4 \times 10 + 3 \times 15 + 20 = 105 \]
• Seth's total length: \[ 10 + 2 \times 5 = 20 \]

Adding them together: \[ 105 + 20 = 125 \]

Thus, you will get the same answer (125 feet) as you arrived at in part D. This demonstrates the associative property of addition, which states that the way you group numbers when adding does not change the sum.

Self-Evaluation:

As for your self-evaluation:

• Rate your work on a scale of 1 to 5 based on clarity, accuracy, and thoroughness.
• You may note that you learned about using expressions to calculate perimeter and that clear organization helps in evaluating expressions accurately. Challenges may include remembering to follow arithmetic rules carefully to avoid mistakes.

Feel free to adjust any of the hypothetical measurements to reflect the actual measurements provided, and follow the same process to reach your answers.