Lesson 11 | Fractions | 3rd Grade Mathematics

Objective

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

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.
3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Number and Operations—Fractions

3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Criteria for Success

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

Given a unit fraction on a number line, plot the whole by making a certain number of copies of the unit fraction adjacent to one another (e.g., to create the whole given $$ \frac{1}{5}$$, make copies of the unit fraction so that there are 5 equal pieces adjacent to one another).
Given a non-unit fraction on a number line, construct the whole by partitioning the given fraction into the appropriate number of equal pieces so that they represent the unit fraction, and then add copies of the unit fraction so that they make a whole (e.g., to create the whole given $$ \frac{3}{5}$$, partition the given interval into 3 equal pieces so that they each represent $$ \frac{1}{5}$$, then make copies of that unit fraction so that there are 5 equal intervals adjacent to one another).
Given a fraction greater than 1 on a number line, construct the whole by partitioning the given fraction into the appropriate number of equal pieces so that they represent the unit fraction, and then count the number of unit fractions that make a whole (e.g., to create the whole given $$\frac{5}{3}$$, partition the given interval into 5 equal pieces so that they each represent $$\frac{1}{3}$$, then plot a point at $$\frac{3}{3}$$ by counting up 3 intervals).
Given a fraction on a number line, plot another fraction of the same whole by using any of the strategies above to find the whole, then partition the whole into the relevant fractional pieces (e.g., to plot $$\frac{2}{3}$$ given $$\frac{3}{4}$$, partition the interval into three equal pieces, then make a fourth copy of it to construct a whole; then partition that whole into thirds and plot a point at $$\frac{2}{3}$$ by counting up 2 intervals).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson provides many opportunities for students make sense of problems and persevere in solving them (MP.1). Each task pushes students to make sense of the meaning of fractions and their numerators and denominators and use that understanding to relate them to the whole as well as other fractions of the same whole.

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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

Iskra is running a race as shown on the number line below. Iskra is $$\frac{1}{3}$$ of the way from the starting line to the finish line. Where is the finish line? Locate and label it on the number line below.

Guiding Questions

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Problem 2

Locate 1 on each number line below. Label the point. Be as exact as possible.

Guiding Questions

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References

Illustrative Mathematics Find 1 — Part b

Find 1, accessed on March 19, 2019, 9:45 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 3

Locate $$\frac{5}{6}$$ on the number line. Label the point. Be as exact as possible.

Guiding Questions

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References

Illustrative Mathematics Find 2/3

Find 2/3, accessed on March 25, 2019, 12:08 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 Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #1. How can you tell just by looking at the numerator and denominator that $$\frac{3}{2} $$ would be to the right of 1?
Look at #4. Did anyone solve it without locating where 1 was? How did you know to do that?
Look at #6. What number corresponds with the point Anna mislabeled?
Look at #3 and #7. What do you notice about these number lines? What do you wonder?
How did you decide to create 5 fractions in #8? How did you know how to place fractions in relation to one another on the number line? Where would you place a fraction with 1 as the denominator, such as $$\frac{5}{1}$$? Where would you place the fraction $$\frac{4}{2} $$ on the number line? Why?

Target Task

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

Problem 1

The number line below shows two numbers, 0 and $$\frac{6}{5}$$.

Where is 1 on this number line?

Problem 2

The number line below shows two numbers, 0 and $$\frac{1}{2}$$.

Where is $$2\over 3$$ on this number line?

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

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Lesson 10

Lesson 12

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

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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