Fractions

Lesson 9

Math

Unit 6

3rd Grade

Lesson 9 of 24

Objective


Place any fraction on a number line with endpoints 0 and another whole number greater than 1.

Common Core Standards


Core Standards

  • 3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Foundational Standards

  • 2.MD.B.6

Criteria for Success


  1. Plot a given fraction on a number line that starts at 0 and counts by 1 by:
    1. Partitioning each whole on the number line into fractional units and counting by unit fractions from 0 to locate the relevant point, or
    2. Determining the two wholes that the fraction is in between and partitioning that whole into fractional units and plotting it (MP.5).
  2. Plot a given fraction on a number line that starts at 0 but does not have whole number partitions by first partitioning the number line into wholes and then using one of the two above strategies (MP.5).
  3. Look for and express regularity in repeated reasoning to generalize when a fraction is greater than or less than 1 based on the relationship between its numerator and denominator (MP.8).
  4. Look for and express regularity in repeated reasoning to generalize when a fraction will be located at the same point as a whole number on a number line (previewed in this Lesson but solidified in Lesson 10) (MP.8).

Tips for Teachers


  • Lessons 9 and 10 nicely prepare students for a more extensive discussion of the equivalence of fractions and whole numbers to come in Lesson 14.
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Anchor Tasks


Problem 1

Three students are partitioning a number line into fourths. Their work is shown.

Chadwick’s number line:

Allan's number line:

Dobrilla's number line:

Whose partitioning makes the most sense to you? Explain your reasoning.

Guiding Questions

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References

Illustrative Mathematics Illustrative Math Grade 3 Unit 5 Lesson 6 Activity 1

Locating Fractions Greater than One on the Number Line, accessed on March 19, 2019, 10:57 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

a.    

Locate and label $$\frac{3}{4}$$ and $$\frac{6}{4}$$

b.    

Locate and label $$\frac{7}{8}$$ and $$\frac{12}{8}$$

c.    

Locate and label $$\frac{2}{3}$$ and $$\frac{4}{3}$$.

d.    

Locate and label $$\frac{2}{6}$$ and $$\frac{7}{6}$$.

e.   How did you partition the number line when you were locating the numbers $$\frac{7}{8}$$ and $$\frac{12}{8}$$? Explain your reasoning.

f.   What patterns did you notice in the fractions you located?

Guiding Questions

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References

Illustrative Mathematics Illustrative Math Grade 3 Unit 5 Lesson 7 Activity 2

Illustrative Math Grade 3 Unit 5 Lesson 7 Activity 2, accessed on Jan. 20, 2023, 1:14 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Locate and label a point on the number line for $$\frac{7}{3}$$. Be as exact as possible.

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • In #2, what fractions are at the exact same point as 2 on the number line? What do you notice about those fractions? What do you wonder?
  • What number is at the exact same point as 12 fourths in #2?
  • Look at the fractions you boxed in #2e. What pattern do you notice? What is the connection between multiplication and fractions equal to whole numbers? How do you think that strategy might help you find other whole number fractions?
  • Look at #5. Why is labeling points important?

Target Task


Problem 1

Determine the location of the points on the number line below. 

Problem 2

Mark and label the following points on the number line. Be as exact as possible.

  1. $$3\over 4$$
  2. $$6\over 4$$

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

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Lesson 8

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Lesson 10

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Unit Fractions and Building Non-Unit Fractions

Topic B: Fractions on a Number Line

Topic C: Equivalent Fractions

Topic D: Comparing Fractions

Topic E: Line Plots

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