2.4 Addition and Subtraction on the Number Line

Unit Goals

  • Students learn about the structure of a number line and use it to represent numbers within 100. They also relate addition and subtraction to length and represent the operations on the number line.

Section A Goals

  • Represent whole numbers within 100 as lengths from 0 on a number line.
  • Understand the structure of the number line.

Section B Goals

  • Represent sums and differences on a number line.
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Section A: The Structure of the Number Line

Problem 1

Pre-unit

Practicing Standards:  1.OA.D.8

Write the number that makes each statement true.

  1. \(9 + 7 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(15 - \boxed{\phantom{\frac{aaai}{aaai}}} = 8\)
  3. \(\boxed{\phantom{\frac{aaai}{aaai}}} - 11 = 8\)

Solution

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Problem 2

Pre-unit

Practicing Standards:  1.NBT.B.3

Put a < or > in each box to make each statement true.

  1. \(91\phantom{a} \boxed{\phantom{\frac{aaai}{aaai}}} \phantom{a}19 \)
  2. \(84\phantom{a} \boxed{\phantom{\frac{aaai}{aaai}}} \phantom{a}87 \)
  3. \(52\phantom{a} \boxed{\phantom{\frac{aaai}{aaai}}} \phantom{a}36 \)

Solution

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Problem 3

Pre-unit

Practicing Standards:  2.NBT.B.5

  1. Write an equation that matches the tape diagram.
    Diagram. One rectangle split into 2 parts. Total length, 41. 1 part, total length, 13. Other part, total length, question mark.

  2. Find the unknown value.

Solution

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Problem 4

Pre-unit

Practicing Standards:  2.OA.A.1

There are 37 frogs in the pond. There are 16 more goldfish than frogs in the pond.

  1. Complete the diagram to match the story problem.

    Diagram. Two rectangles of equal length. Top rectangle labeled blank, split into two parts. First part, shaded, total length, blank. Second part has a dashed outline, total length, blank. Bottom rectangle, shaded, labeled blank, total length, blank.
  2. How many goldfish are there in the pond? Explain or show your reasoning.

Solution

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Problem 5

  1. Label each tick mark with the number it represents.

    Number line. Scale 0 to 10. Evenly spaced tick marks. First tick mark, 0. Second tick mark, 1. Next 8 tick marks labeled with blank. Last tick mark, 10. 

  2. Locate 7 on the number line. Mark it with a point.

Solution

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Problem 6

Here is Mai's number line. How should she revise her number line?

Number line. Scale 10 to 0 by 1's. Evenly spaced tick marks. First tick mark, 10. Last tick mark, 0.

Solution

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Problem 7

  1. Count by 10 starting at 50 and ending at 100. Label each of the numbers in your count on the number line.

    Number line. Scale 50 to 100 by 10's. Evenly spaced tick marks. First tick mark labeled 50, last tick mark labeled 100. 4 tick marks not labeled.

  2. Locate and label 78 on the number line.

Solution

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Problem 8

Locate and label each pair of numbers on the number line. Then use \(<\) or \(>\) to compare the numbers.

  1. 23 and 27

    Number line. Scale 15 to 35, by 5's. 

  2. 34 and 43

    Number line. Scale 25 to 50 by 5's.

Solution

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Problem 9

What number could this be? Explain your reasoning.

Number line. Scale 30 to 70. No tick marks. Point plotted between 30 and 70.

Solution

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Problem 10

Exploration

  1. Locate and label where you think 35 could be on the number line. Explain or show your reasoning.

    Number line. Scale 0 to 100, no tick marks.

  2. Elena and Han located where they think 83 is.

    Why do you think they put their points at different locations on the number line?

    Where do you think 83 is on the number line?

    Number line. Scale 0 to 100, no tick marks.

Solution

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Problem 11

Exploration

  1. Here is a picture of a thermometer.

    Thermometer.

    How is the thermometer the same as a number line? How is it different?

  2. Here is a picture of a rain gauge.

    Rain gauge.

    How is the rain gauge the same as a number line? How is it different?

Solution

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Section B: Add and Subtract on a Number Line

Problem 1

Which equation does the number line represent? Explain your reasoning.

  1. \(7 + 6 = 13\)
  2. \(13 - 6 = 7\)

Number line. Scale 0 to 15 by 1's. Evenly spaced tick marks. Arrow starts at 7, ends at 13.

Solution

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Problem 2

Here is a number line.

Number line. Scale 20 to 40 by 1's. Evenly spaced tick marks. Arrow from 35 to 27.

  1. Write an equation that the number line represents.

  2. Explain how your equation matches the number line.

Solution

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Problem 3

  1. Explain or show how each number line represents the value of \(47 - 41\).

    Number line. Scale 0 to 50 by 5's. Evenly spaced tick marks. Arrow starts at 41, ends at 47.

    Number line. Scale 0 to 50 by 5's. Evenly spaced tick marks. Arrow starts at 47, ends at 6.

  2. Which method do you prefer to calculate \(47 - 41\)?

Solution

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Problem 4

Find the value of \(32 + 26\). Represent your thinking on the number line.

Number line. Scale 10 to 70, by 5's. Evenly spaced tick marks.

Solution

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Problem 5

Find the value of \(65 - 58\) in two different ways. Show your thinking on the number lines.

  1. Method 1:

    Number line. Scale 0 to 70 by 5's. Evenly spaced tick marks.

  2. Method 2:

    Number line. Scale 0 to 70, by 5's. Evenly spaced tick marks.

Solution

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Problem 6

I started at a number on the number line and jumped back 37. I landed at 26. Where did I start?

  1. Write an equation with a ? for the unknown.

  2. Find the number that makes the equation true.

  3. Represent your thinking on the number line.

    Number line. Scale 10 to 70 by 5's. Evenly spaced tick marks.

Solution

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Problem 7

There are 18 students in the classroom. Then 13 more students join them.

  1. Label the tape diagram to match the story.

    Diagram. One rectangle split into 2 parts. Total length, question mark. 1 part, labeled blank, total length, blank. Other part, labeled blank, total length, blank.

  2. Label the number line to match the story.

    Number line. Scale 0 to 40 by 5's. Evenly spaced tick marks.

  3. How are the tape diagram and number lines the same? How are they different?

  4. How many students are in the classroom now?

Solution

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Problem 8

Exploration

  1. Using addition or subtraction, how many equations can you make with these three numbers: 20, 13, 7?

  2. Draw number lines to match each of the equations you wrote.

  3. How are the number lines the same? How are they different?

Solution

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Problem 9

Exploration

 
  1. Write a story problem that can be solved with this number line.

  2. Explain how the number line solves your story.

Solution

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