Multiplication and Division of Fractions

Lesson 24

Math

Unit 5

5th Grade

Lesson 24 of 25

Objective


Create line plots.

Common Core Standards


Core Standards

  • 5.MD.B.2 — Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Foundational Standards

  • 4.MD.B.4

Criteria for Success


  1. Construct a line plot by:
    1. Determining the starting and ending value for the line plot by finding the largest and the smallest value in the data set,
    2. Determining the interval for the line plot by determining the smallest fractional unit that is represented in the data, 
    3. Plotting X’s above the corresponding value for each value in the data set, 
    4. Creating a label for the number line that describes the unit that is represented by the data, and 
    5. Creating a title for the line plot that explains what the data set as a whole represents. 
  2. Understand the purpose of a line plot as a way to represent a data set to be able to see trends and analyze it more easily. 
  3. Make observations and inferences of the data represented in a line plot (namely, that don’t involve computing with the data values themselves—e.g., “What is the most common value?” rather than “What is the difference between the largest and the smallest value in the data set?”) (MP.7).

Tips for Teachers


  • Students will need the line plot from today’s Target Task for Lesson 25, so make sure to hold on to it.

Lesson Materials

  • Fraction Cards (1 per pair of students) — This material should be cut into pieces before the lesson.
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Anchor Tasks


Problem 1

a.   Label the line plot below with $${{1\over8}}$$s. Cut out and divide the cards from Template 2 evenly between the two players, laying them facedown. Each partner will choose one of their facedown cards and turn it over. The team will then add their fractions together. For each turn, each team will record their sum on the line plot.

Each team should have 12 data points marked on their line plot.

b.   Look at the line plot. Which values came up the most? Which values did not come up?

c.   The tick marks on the number line correspond to eighths. Which of the eighths will never come up as a sum of two of these cards? Why?

d.   You want to improve the game so that it is possible for two fractions to sum to $${{{{7\over8}}}}$$. Name one fraction card that you could add to the deck and explain why your new card would now make it possible to have $${{{{7\over8}}}}$$ as a sum of two cards.

Guiding Questions

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References

Illustrative Mathematics Fractions on a Line Plot

Fractions on a Line Plot, accessed on April 26, 2018, 10:07 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

Mr. Pernell has the fifth graders take a physical fitness test. Part of the physical fitness test was a sit-and-reach test, where students sit and stretch their fingers forward, with this distance measured in inches. The data from the girls is listed below:

$${{{2{5\over8}}}}$$ $${3{3\over8}}$$ $${{{{3{1\over8}}}}}$$ $${{2{7\over8}}}$$ $${{{{3{1\over8}}}}}$$ $${{{2{5\over8}}}}$$ $${2{3\over4}}$$ $${{{{3{1\over8}}}}}$$ $${{3{1\over2}}}$$ $${{{2{5\over8}}}}$$
$${{4{1\over4}}}$$ $${3{1\over4}}$$ $${{2{7\over8}}}$$ $${{3{7\over8}}}$$ $${{{{3{1\over8}}}}}$$ $${{3{7\over8}}}$$ $${{4{1\over4}}}$$ $${1{7\over8}}$$ $${{3{1\over2}}}$$ $$3$$

a.   Create a line plot that represents this data.

b.   What is the shortest sit-and-reach length?

c.   What is the longest sit-and-reach length?

d.   What is the most common sit-and-reach length?

e.   If girls in the fifth grade are supposed to have a sit-and-reach distance of 3 inches, do you think Mr. Pernell should feel good about how his fifth-grade girls are doing? Why or why not?

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1. What advice would you give to the person who made the line plot on the right in order to improve it?
  • Look at #3. How did you determine what the typical amount of growth for a student of the same age was? What evidence can you use to support your answer?
  • Look at #4. Was there more snowfall in the first week of January or the first week of February? How do you know? 

Target Task


Irene is training to run a marathon. The list below shows the number of miles she ran each day for 2 weeks.

$$8\frac{1}{4}, \ 7, \ 7\frac{1}{2}, \ 7\frac{3}{4}, \ 8\frac{3}{4}, \ 8, \ 7\frac{3}{4}, \ 8\frac{1}{4}, \ 7\frac{2}{4}, \ 7\frac{3}{4}, \ 8\frac{1}{4}, \ 8, \ 8\frac{1}{2}, \ 8\frac{3}{4}$$

Make a line plot of the data below. Include a title and the correct labels.

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

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Lesson 23

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Lesson 25

Lesson Map

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

Topic A: Fractions as Division

Topic B: Multiplying a Fraction by a Whole Number

Topic C: Multiplying a Fraction by a Fraction

Topic D: Multiplying with Mixed Numbers

Topic E: Dividing with Fractions

Topic F: Fraction Expressions and Real-World Problems

Topic G: Line Plots

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