Curriculum  /  Math  /  3rd Grade  /  Unit 6: Fractions  /  Lesson 5

Fractions

Lesson 5

Math

Unit 6

3rd Grade

Lesson 5 of 24

Objective

Draw the whole when given the unit fraction.

Common Core Standards

Core Standards

  • 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

  1. 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.)
  2. 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).
  3. 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 Extra Practice Problems are optional.)

Tips for Teachers

  • 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 Square Inch Grid Template if you do not have enough square inch tiles, which should be cut into pieces before the lesson.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

25-30 minutes

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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

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

a.   

b.   

c.   

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 3

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

a.   

b.   

c.   

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem Set

15-20 minutes

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

5-10 minutes

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

a.   

b.   

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

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

Next

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

Lesson 6
icon/arrow/right/large

Lesson Map

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

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

Topic B: Fractions on a Number Line

Topic C: Equivalent Fractions

Topic D: Comparing Fractions

Topic E: Line Plots

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free