Reasoning about Contexts with Tape Diagrams

Red and Yellow Apples

5 min

Problem

Here is a story: Lin bought 4 bags of apples. Each bag had the same number of apples. After eating 1 apple from each bag, she had 28 apples left.

  1. Which diagram best represents the story? Explain why the diagram represents it.

    A
    Tape diagram A with 4 equal parts labeled, x + 1, total 28.

    B
    Tape diagram B with 1 small part labeled 1, four equal parts labeled x, total 28.

    C
    Tape diagram C with four equal parts labeled, x minus 1, total 28.

  2. Describe how you would find the unknown amount in the story.

Answer

  1. C. Sample reasoning: When she ate 1 apple from each bag, there were x−1x-1 apples left in each bag. 
  2. Each of the 4 pieces of the diagram represents 7 apples, because 28÷4=7.28 \div 4 = 7. If x−1=7x-1=7, then xx is 8.

Sample Response

  1. C. Sample reasoning: When she ate 1 apple from each bag, there were x−1x-1 apples left in each bag. 
  2. Each of the 4 pieces of the diagram represents 7 apples, because 28÷4=7.28 \div 4 = 7. If x−1=7x-1=7, then xx is 8.
Responding to Student Thinking
More Chancesmore_chances

Response: Students will have more opportunities to understand the mathematical ideas addressed here. There is no need to slow down or add additional work to the next lessons.

Standards
Addressing
  • 7.EE.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. <em>For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.</em>
  • 7.EE.B.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Building Toward
  • 7.EE.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
  • 7.EE.B.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.