Lesson 1

Tape Diagrams and Equations

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Problem 1

Here is an equation: \(x + 4 = 17\)

  1. Draw a tape diagram to represent the equation.
  2. Which part of the diagram shows the quantity \(x\)? What about 4? What about 17?
  3. How does the diagram show that \(x+4\) has the same value as 17?

Solution

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Problem 2

Diego is trying to find the value of \(x\) in \(5 \boldcdot x = 35\). He draws this diagram but is not certain how to proceed.

Tape diagram. 5 equal parts labeled x, x, x, x, x. 

 

  1. Complete the tape diagram so it represents the equation \(5 \boldcdot x = 35\).
  2. Find the value of \(x\).

Solution

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Problem 3

Match each equation to one of the two tape diagrams.

  1. \(x + 3 = 9\)
  2. \(3 \boldcdot x = 9\)
  3. \(9=3 \boldcdot x\)
  4. \(3+x=9\)
  5. \(x = 9 - 3\)
  6. \(x = 9 \div 3\)
  7. \(x + x+ x = 9\)
Two tape diagrams, A and B. A, 3 equal parts labeled, x. Total, 9. B, 2 parts labeled x and 3. Total, 9.

Solution

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Problem 4

For each equation, draw a tape diagram and find the unknown value.

  1. \(x+9=16\)

  2. \(4 \boldcdot x = 28\)

Solution

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Problem 5

A shopper paid $2.52 for 4.5 pounds of potatoes, $7.75 for 2.5 pounds of broccoli, and $2.45 for 2.5 pounds of pears. What is the unit price of each item she bought? Show your reasoning.

Solution

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(From Unit 5, Lesson 13.)

Problem 6

A sports drink bottle contains 16.9 fluid ounces. Andre drank 80% of the bottle. How many fluid ounces did Andre drink? Show your reasoning.

Solution

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(From Unit 3, Lesson 14.)

Problem 7

The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of milk has 25% of the recommended daily allowance of calcium. How many milligrams of calcium are in a cup of milk? If you get stuck, consider using the double number line.

A double number line.

Solution

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(From Unit 3, Lesson 11.)