Lesson 4 | Fractions | 3rd Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Number and Operations—Fractions

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Foundational Standards

The foundational standards covered in this lesson

2.G.A.3

Geometry

2.G.A.3 — Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Criteria for Success

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

Partition a whole into fractional units in more than one way.
Understand that equal shares of identical wholes need not have the same shape.
Determine the fraction that parts of a whole represent when those pieces are not equal in shape or size by partitioning them further to identify their equal parts.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Too often, when students are asked questions about what fraction is shaded, they are shown regions that are portioned into pieces of the same size and shape. The result is that students think that equal shares need to be the same shape, which is not the case. On the other hand, sometimes visuals do not show all of the partitions” (Van de Walle, Teaching Student-Centered Mathematics, Grades 3–5, vol.2, p. 211). Thus, this lesson tries to address both of these potential misconceptions and deepen students’ conceptual understanding of fractions. Having students explain what it meant by “equal parts” also provides opportunities for students to attend to precision (MP.6) (NF Progression, p. 7).

Lesson Materials

Square-sized paper (1 piece per student)

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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

Using a square sheet of paper, make folds as explained in each part below to construct a new shape. Explain how you know the shape you constructed has the specified area.

a. Construct a square with exactly $$\frac{1}{4}$$ the area of the original square. Convince yourself and then your partner that it is a square and has $$\frac{1}{4}$$ of the area.

b. Construct a triangle with exactly $$\frac{1}{4}$$ of the area of the original square. Convince yourself and then your partner that it has $$\frac{1}{4}$$ of the area.

c. Construct another triangle, also with $$\frac{1}{4}$$ the area, that is not the same shape as the first one you constructed. Convince yourself and then your partner that it has $$\frac{1}{4}$$ of the area.

d. Construct a square with exactly $$\frac{1}{2}$$ the area of the original square. Convince yourself and then your partner that it is a square and has $$\frac{1}{2}$$ of the area.

Guiding Questions

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References

youcubed Paper Folding

Paper Folding is made available by youcubed under the CC BY 4.0 license. Accessed March 29, 2019, 12:31 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Below is an image of a tangram set. Determine what fraction of the overall set each shape is.

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Which circles have $$\frac{1}{2}$$ shaded? How do you know?
How did you determine the fractional part of each square in #2? In Part (f), did you need to make every single piece the same size or were you able to determine the fractional part of some pieces without breaking the whole into the smallest possible shape that could tile the whole square?
What shape did you draw for #3? How do you know the shaded part represents $$\frac{3}{8}$$ of the whole?
What made finding the fraction of each whole that each color represents in #4 different from the fraction of each whole that each region represents in #2? Was it easier or more difficult to do that?
How did you solve #5?

Target Task

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

Problem 1

Are each of the fractional pieces below $$\frac{1}{2}$$ of the whole square? Explain why or why not.

Problem 2

Determine the fraction of the whole square each piece represents.

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 3

Lesson 5

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

Geometry

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

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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