Lesson 5 | Fractions | 3rd Grade Mathematics

Objective

Draw the whole when given the unit fraction.

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.

Criteria for Success

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

Given a unit fraction, construct 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-sized pieces adjacent to one another). (Note: adjacent shapes is not completely necessary, since non-adjacent copies of the unit fraction can come to resemble a set model. However, since students will not work with set models in Grade 3, avoid discussing these representations as a whole group.)
Understand that there is more than one way to represent a whole given a unit fraction (and thus, wholes that are different shapes but the same size are equivalent).
Given a non-unit fraction, construct the whole by partitioning the given fraction into the appropriate number of equal-sized 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 part into 3 equal-sized pieces so that they each represent $$\frac{1}{5}$$, then make copies of that unit fraction so that there are 5 equal-sized pieces adjacent to one another). (Note: this Criteria for Success and its corresponding Anchor Task and problems on the Problem Set and Homework are optional.)

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson extends students’ understanding of the relationship between the part and the whole by having students iterate a unit fraction to represent the whole, which “helps children conceive of a whole as a multiple of a unit fraction, consisting of a certain number of copies of a same-size unit (Steffe and Olive, 2010) that draws their attention to the number of times a unit fraction fits within a whole” (Tzur and Hunt, “Iteration: Unit Fraction Knowledge and the French Fry Tasks,” Teaching Children Mathematics, Vol. 22 No. 3, October 2015). While the idea that a whole is a multiple of a unit fraction is not an explicit one, the idea of iteration and copies will certainly come in handy when students begin their work with number lines, which is constructed by iterating a whole (or a unit fraction) of equal length.
This lesson provides many opportunities for students to make sense of problems and persevere in solving them (MP.1). Each task pushes students to make sense of the meaning of unit fractions (and optionally non-unit fractions) and their numerators and denominators, and use that understanding to relate them to the whole.

Lesson Materials

Optional: Square inch tiles (at least 4 per student) — Students might not need these depending on their reliance on concrete materials. You could also provide square inches cut out from Template: Square Inch Grid if you do not have enough square inch tiles, which should be cut into pieces before the lesson.

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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

Mr. Strader brings in a chocolate bar and decides to share it with Mr. Silver, Mrs. Ingall, and Ms. Kosowsky. Below is what each of their equal-sized pieces looks like. How big was the chocolate bar before Mr. Strader broke it up?

Guiding Questions

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Problem 2

Each shape below represents a unit fraction of a whole. Draw a picture representing a possible whole.

Guiding Questions

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Problem 3

CHALLENGE: Each shape below represents a fraction of a whole. Draw a picture representing a possible whole.

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Which wholes had the most equal parts?
Which wholes had the least equal parts?
What did you notice about size of the whole when given a unit fraction with a larger denominator? What about with a smaller denominator?
Which fractions and/or shapes were the most difficult to create the whole for? Why?
What if all the wholes were the same size? What would happen to the equal parts?
Were there any unit fractions for which the wholes seemed to actually be the same? Which ones? How can you prove that their wholes are the same?
Why are both Aileen’s and Jack’s drawings correct? How many other possible unique drawings could there be?

Target Task

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

Each shape below represents a unit fraction of a whole. Draw a picture representing a possible whole.

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

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 4

Lesson 6

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

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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