Section A: Practice Problems The Structure of the Number Line

Section Summary

Details

In this section, we learned about the number line. It is like a ruler because it shows numbers as different length units from 0. A number line can be used to represent numbers and show how close or how far they are from 0 and each other. Numbers can be represented by tick marks and points on the number line and increase in value when moving to the right. We used tick marks and counted by 5 and 10 to help us locate and label numbers. We also estimated numbers by thinking about how close they were to zero and other numbers.

Number line. Scale 0 to 12 by 1's. Evenly spaced tick marks. Point plotted at 4.
Ruler marked 0 to 12.

Problem 1 (Pre-Unit)

Write the number that makes each statement true.

Problem 2 (Pre-Unit)

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

  1. 91 19

  2. 84 87

  3. 52 36

Problem 3 (Pre-Unit)

  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.

Problem 4 (Pre-Unit)

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.

Problem 5 (Lesson 1)

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

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

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. 

Problem 6 (Lesson 2)

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.

Problem 7 (Lesson 3)

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

  2. Locate and label 78 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.

Problem 8 (Lesson 4)

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.

Problem 9 (Lesson 5)

What number could this be? Explain your reasoning.

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

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?

  3. Where do you think 83 is on the number line?

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

Problem 11 (Exploration)

  1. Here is a picture of a thermometer.

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

    Thermometer.

  2. Here is a picture of a rain gauge.

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

    Rain gauge.