Lesson 8 | Fractions | 3rd Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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

Number and Operations—Fractions

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

Foundational Standards

The foundational standards covered in this lesson

2.MD.B.6

Measurement and Data

2.MD.B.6 — Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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).
Determine the value of a plotted point by determining the fractional unit and counting them from 0.
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).
Determine the distance between two points on a number line. (Optional)

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Here is a neat Desmos activity you can use to supplement today’s lesson, essentially in place of Anchor Task 1. It’s a nice visualization to help students see the magnitude of fractions on fraction strips and then translates that to number lines.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

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

$$\frac{1}{3}$$

$$\frac{5}{6}$$

$$\frac{3}{8}$$

Guiding Questions

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Problem 2

Determine the location of each of the following points.

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.

a. Which place is $$\frac{4}{8} $$ mile from Erin’s house?

b. 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.

c. 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 2017 — Question #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 Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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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

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

a. Identify the fractions represented by each point on the number line below.

b. Explain how you determined the location of point B.

Student Response

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Problem 2

Jermaine is making a beaded necklace. The number line below represents the whole length of necklace. Jermaine uses red beads for the first $$1\over 8$$ of the necklace. After the red beads, he switches to yellow beads for the next $$5\over 8$$ of the necklace. Label the point where Jermaine switches from red to yellow beads with the letter R and label the point where Jermaine finishes the yellow beads with the letter Y on the number line below.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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

Lesson 7

Lesson 9

Lesson Map

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

Partition a whole into equal parts using area models, identifying fractional units.

3.G.A.2 3.NF.A.1

Partition a whole into equal parts using tape diagrams (i.e., fraction strips), identifying and writing unit fractions in fraction notation.

3.G.A.2 3.NF.A.1

Partition a whole into equal parts using area models and tape diagrams, identifying and writing non-unit fractions in fraction notation.

3.NF.A.1

Identify fractions of a whole that is not partitioned into equal parts.

3.NF.A.1

Draw the whole when given the unit fraction.

3.NF.A.1

Identify a shaded fractional part in different ways, depending on the designation of the whole.

3.NF.A.1

Topic B: Fractions on a Number Line

Partition a number line from 0 to 1 into fractional units.

3.NF.A.2

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

3.NF.A.2

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

3.NF.A.2

Place any fraction on a number line with endpoints greater than 0.

3.NF.A.2 3.NF.A.3.C

Place various fractions on a number line where the given interval is not a whole.

3.NF.A.2 3.NF.A.3.D

Topic C: Equivalent Fractions

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

3.NF.A.3.A 3.NF.A.3.B

Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. Use this understanding to generate simple equivalent fractions.

3.NF.A.3.A 3.NF.A.3.B

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

3.NF.A.3.C

Explain equivalence by manipulating units and reasoning about their size.

3.NF.A.3.A 3.NF.A.3.B 3.NF.A.3.C

Topic D: Comparing Fractions

Compare unit fractions (a unique case of fractions with the same numerators) by reasoning about the size of their units. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <.

3.NF.A.3.D

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

3.NF.A.3.D

Compare fractions with the same denominators by reasoning about their number of units. Record the results of comparisons with the symbols >, =, or <.

3.NF.A.3.D

Compare and order fractions using various methods.

3.NF.A.3

Understand fractions as numbers.

3.NF.A

Topic E: Line Plots

Measure lengths to the nearest half inch.

3.MD.B.4

Measure lengths to the nearest quarter inch.

3.MD.B.4

Generate measurement data and represent it in a line plot.

3.MD.B.4

Create line plots (dot plots).

3.MD.B.4

Fractions

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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