Fractions

Lesson 1

Math

Unit 6

3rd Grade

Lesson 1 of 24

Objective


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

Common Core Standards


Core Standards

  • 3.G.A.2 — Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
  • 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

  • 2.G.A.3

Criteria for Success


  1. Determine whether an area model is partitioned into equal parts. 
  2. Describe the shares of a whole when it is partitioned into two, three, or four equal parts as halves, thirds, fourth/quarters, respectively. (Students are familiar with these fractional units from Grade 2 (2.G.3).) 
  3. Understand that the fractional unit when a whole is partitioned into 6 equal parts is sixths. (This fractional unit is new to Grade 3.)
  4. Understand that the fractional unit when a whole is partitioned into 8 equal parts is eighths. (This fractional unit is new to Grade 3.)

Tips for Teachers


  • Using counting routines throughout the unit may be very useful for your students. Counting fractions just like you’d count whole numbers can help students see fractions as numbers, and that non-unit fractions are built from unit fractions. Further, “in whole-number learning, counting precedes and helps students compare the size of numbers and later to add and subtract. This is also true with fractions. Counting fractional parts, initially unit fractions, to see how multiple parts compare to the whole helps students understand the relationship between the parts (the numerator) and the whole (the denominator)” (Van de Walle, Teaching Student-Centered Mathematics, Grades 3–5, vol. 2, p. 213). For even more information on the usefulness and implementation of choral counting by fractions, see this Achieve the Core blogpost

    Fractions can be counted in a variety of ways, including without regard to whole numbers (e.g., 1 third, 2 thirds, 3 thirds, 4 thirds, etc.) or by replacing fractions equivalent to whole numbers with the whole numbers themselves (e.g., 1 third, 2 thirds, 1, 4 thirds, etc. Note: you could also have students say “1 whole” so that students are always saying the unit involved.). Eventually, students could even count by whole numbers (e.g., 2 halves, 4 halves, 6 halves, etc.). At the beginning of the unit, you can use the same routines as you did for skip-counting in Units 2 and 3, which are:

    • Choral Counting: Choral counting is simply counting out loud as a whole class. You can involve movement, as well, by having students count on their fingers, do jumping jacks with every count, etc. You can ask some basic questions about the count sequence, but because this routine really just helps introduce students to new sequences or ones that they struggle with, more rigorous questions can be saved for the other routines (which are in bullets below).
    • Count around the Circle: Have one child start with the first number in the counting sequence, and go around the circle having each child say one number. You could decide to write the numbers on the board as students say them, either as a scaffold for them or to encourage a discussion of patterns afterward. Some questions you can ask before/during/after this routine to encourage sense-making include:
      • If we count by halves around the circle starting with Student A, what number do you think Student Z will say? If you didn’t count to figure that out, how did you solve?
      • Why did you choose ____ as an estimate?
      • If we count around the circle by fourths, what student will say the whole number 3?
      • How did you know what comes next?
      • (After a child gets stuck but figures it out): What did you do to figure it out?
      • (If you’ve written the numbers on the board as students counted): What do you notice? What do you wonder?

Source for these routines: Jessica Shumway, Number Sense Routines: Building Numerical Literacy Every Day in Grades K–3, pp. 55–67, 2011.

Lesson Materials

  • Optional: Template: Fair Shares (1 per student)
  • Rectangular Pieces of Paper (5 per student) — These can be any size but must be the same size for all students. You could use a quarter piece of paper or an unlined index card for each.
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Anchor Tasks


Problem 1

A group of friends go to a bakery. They buy lots of sweets to share equally so that they can try various things.

a.   Two friends share a cookie. They split the cookie in the following way:

Is this a fair share of the cookie? Why or why not?

b.   Three friends share a slice of banana bread. They split the banana bread in the following way:

Is this a fair share of the banana bread? Why or why not?

c.   Four friends share a cake. They split the cake in the following way:

Is this a fair share of the cake? Why or why not?

Guiding Questions

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Problem 2

Your teacher will give you some paper rectangles. Each rectangle represents 1. Fold each rectangle into the following number of equal parts:

a.   Two

b.   Three

c.   Four

d.   Six

e.   Eight

Guiding Questions

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Problem 3

Kai says that the shape below is partitioned into halves. Do you agree or disagree? Explain your thinking.

Guiding Questions

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References

Inside Mathematics Problems of the Month Part and Whole

Part and Whole from the Problems of the Month made available by Inside Mathematics under the CC BY-NC-ND 3.0 license. © Noyce Foundation. Accessed Feb. 20, 2018, 10:46 p.m..

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • How did you determine which shapes were partitioned into equal parts in #1? For those shapes that are split into equal parts, what word can you use to describe those equal parts? 
  • In #3, did you use your rectangle partitioned into halves to help you draw your rectangle partitioned into fourths? In what way? 
  • What did you notice in #3? What do you wonder? 

Target Task


Partition the rectangle below into sixths.

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

Answer Keys

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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.

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Lesson 2

Lesson Map

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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

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