Section B: Practice Problems Add and Subtract on a Number Line

Section Summary

Details

In this unit, we have solved all types of problems and represented them in different ways. We represented addition and subtraction on the number line and made connections to equations and strategies. When adding and subtracting within 100, we can use diagrams, base-ten blocks, number lines, and equations to make sense of stories and situations and to show our thinking. They are all connected.

Number line. Scale 0 to 10 by 1's. Arrow from 5 to 9, labeled 4.
Diagram. One rectangle split into 2 parts. Total length, 9. 1 part, total length, 5. Other part, total length, 4. 
Two base ten diagrams. Top diagram, 3 tens, 3 ones. Bottom diagram, 4 tens, 5 ones.
Number Line. Scale 0 to 100 by 5’s. Arrow from 33 to 43, labeled 10. Arrow from 43 to 53, labeled 10. Arrow from 53 to 63, labeled 10. Arrow from 63 to 73, labeled 10. Arrow from 73 to 78, labeled 5. 

Problem 1 (Lesson 7)

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

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

Problem 2 (Lesson 8)

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.

Problem 3 (Lesson 9)

  1. Explain or show how each number line represents the value of .

    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 ?

Problem 4 (Lesson 10)

Find the value of . Represent your thinking on the number line.

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

Problem 5 (Lesson 11)

Find the value of 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.

Problem 6 (Lesson 12)

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.

Problem 7 (Lesson 13)

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?

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?

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.