Circle Pieces: Red, Pink, Orange, Aqua

Est. Class Sessions: 2–3

Developing the Lesson

Part 3. Parts and Wholes

Introduce Equivalence with Pieces. Assign Questions 11–15 in the Parts and Wholes section of the Student Guide to give students more experiences representing fractions with circle pieces, words, and numbers. Ask students to work together in pairs to solve the problems and represent the fractions using the pieces. As they work, ask them to justify their answers using the pieces.

Question 12 introduces the idea of equivalent fractions—that two different numbers can name the same fractional part of a unit whole. Using the red circle as the unit whole, three aqua pieces are 3/6 (Question 12A). Answering Question 12B correctly will show that three aquas is the same as one-half of the circle. See Figure 8.

Ask:

Use pieces to show how you know that three aquas is the same as one-half. (Students can show that three aquas cover one pink.)
What fraction can we write for three aquas? (3/6)
What fraction can we write for one pink? (1/2)

Point out to students that three-sixths (3/6) and one-half (1/2) represent the same fractional part of the circle. Have a similar discussion about two-sixths and one-third using Questions 12C and 12D. See Figure 8.

Name the Unit Whole. Tell students that Moe and Joe Smart are disagreeing again.

Display 1 red circle piece and say:

Moe thinks that the red circle is always the unit whole. Joe disagrees. What do you think? Use your red, pink, orange, and aqua pieces to explain. (Possible response: I agree with Joe. Other pieces can be the unit whole. A pink piece could be the unit whole. I can fit 3 aqua pieces on it. Each aqua piece would be 1/3.)
Use pieces to show an example of another unit whole other than the red circle. (The orange piece could be the unit whole. 2 aquas divide it into halves.)
Could the aqua piece be the unit whole? (Yes, but we don't have a piece in our set to divide it evenly.)
Use pieces to find the unit whole if the orange piece is 1/3. Show how you know. (Students show the fraction 1/3 with one orange piece and then put down 2 more to show that the red circle is the whole.)
Find the unit whole if the aqua piece is 1/3. Explain how you know. (Possible response: The unit whole is the pink piece. I look at the denominator to know that there are 3 parts to the unit whole. The aqua piece is 1 of the 3 parts. I need 2 more aqua pieces to make the unit whole and that shape is the pink piece.)

Assign Questions 16–19 in the Name the Unit Whole section of the Student Guide to student pairs. The questions ask students to name the unit whole when a fraction is given. Encourage students to first use the circle pieces to show the fraction and then the unit whole.

Upon completion, ask student volunteers to use circle pieces to share their answers to some of the problems.

Student Guide: 254 255 256

Answers