Fractions

Lesson 11

Objective

Place any fraction on a number line with endpoints 0 and 1.

Common Core Standards

Core Standards

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

Foundational Standards

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  • 2.MD.B.6

Criteria for Success

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  1. Plot a given fraction on a number line by partitioning a whole on the number line into fractional units and counting by unit fractions to locate the relevant point (MP.5).
  2. Determine the value of a plotted point by determining the fractional unit and counting them from 0.
  3. Plot a given fraction or determine the value of a plotted point in special cases, including number lines where more intervals beyond one whole are shown (e.g., 6 intervals of 1 fourth are shown with 1 whole labeled) or the whole is already partitioned into related fractions (e.g., the number line is partitioned into halves and needs to be partitioned into fourths).
  4. Determine the distance between two points on a number line. (Optional)

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Anchor Tasks

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Problem 1

Mark and label a point for each fraction below on the number line to its right.

a. $$\frac{3}{4}$$
b. $$\frac{5}{6}$$

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 5 > Topic D > Lesson 15Concept Development

Grade 3 Mathematics > Module 5 > Topic D > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Determine the location of each of the following points.

a. 

b.

​​​

Guiding Questions

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Problem 3

Erin walked 1 mile from her house to the library. Along the way, she passed several places shown on the number line below.

  1. Which place is $$\frac{4}{8} $$mile from Erin’s house?
  2. Erin also passed the fire station, which is $$\frac{1}{8} $$ mile from Erin’s house. Plot the location of the fire station on the number line above.
  3. What is the distance, in miles, between the park and the market?

Guiding Questions

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References

EngageNY New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions June 2017Question #9

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions June 2017. Internet. Available from https://www.engageny.org/resource/released-2017-3-8-ela-and-mathematics-state-test-questions/file/150251; accessed Sept. 25, 2018, 4:32 p.m..

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • What is the distance from 0 to each of the fractions you plotted in #2? What is the distance from each of the fractions you plotted in #2 to 1? How are these pairs of fractions related to our work with shaded and unshaded portions of a whole?
  • How did you determine what fraction Point Q represented in #3? Why is it located at the same point as 1?
  • How did you determine what fraction Point B represented in #5?
  • What mistake did Shawn make in #6? How did you correct his mistake?
  • I think the Point P represents $$\frac{1}{6}$$ in #7. What mistake did I make?
  • How far does Barney live from the post office in #8? Is this the same or a different value than it would be if you were just labeled the value of that point? Why?
  • What made #9 more challenging than many of the previous problems?

Target Task

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Problem 1

  1. Identify the labeled points on the number line below.

 

A = ______

B = ______

 

  1. Explain how you figured out what fraction point B represents.

References

Achievement First Grade 3, Unit 5, Lesson 11Exit Ticket

Grade 3, Unit 5, Lesson 11 is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed March 8, 2019, 3:58 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Mary is running a marathon. The number line below represents the whole route. Mary stops after running $$\frac{1}{6}$$ mile to drink some water, and she stops after $$\frac{3}{6}$$ mile to tie her shoe. Place a W above where she stops to drink water and an S above where she stops to tie her shoe on the number line below.

References

Achievement First Grade 3, Unit 5, Lesson 11Exit Ticket

Grade 3, Unit 5, Lesson 11 is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed March 8, 2019, 3:58 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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