Lesson 10 Place Value and the Number Line

    • Let’s compare methods using the number line.

Warm-up Notice and Wonder: Base-ten and the Number Line

What do you notice? What do you wonder?

Number line. Scale, 0 to 45, by 5's. Arrows from 0 to 28, labeled 28. From 28 to 38, labeled 10. From 38 to 43, labeled 5. Base 10 pieces between each arrow.

Activity 1 Compare Representations

Clare subtracted and represented her work with a base-ten diagram.

  1. Write an equation to represent Clare’s work.

  2. Represent Clare’s method on the number line.

    Number line. Scale 0 to 50 by 5's. Evenly spaced tick marks.

  3. Find the value of .

    Show your thinking using a base-ten diagram.

  4. Represent how you found the value of on the number line.

    Number line. Scale, 0 to 60, by 5's.

Activity 2 On the Number Line

Diego is finding the value of . He says he can count on by tens, then by ones. He used a number line to show what he means.

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. 

  1. Write an equation to show the sum for Diego’s work.

  2. Find the value of .

    Represent your thinking on the number line.

    Number line. Scale 0 to 60 by 5's. 

  3. Find the value of .

    Represent your thinking on the number line.

    Number line. Scale 0 to 60 by 5's.

  4. Find the value of .

    Represent your thinking on the number line.

    Number line. Scale, 0 to 60, by 5's.

Practice Problem

Problem 1

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

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