Circle Pieces: Red, Pink, Yellow, Blue

Est. Class Sessions: 3

Developing the Lesson

Part 1. Exploring Circle Pieces

Use Circle Pieces to Show 3/4 . Distribute the sets of fraction circle pieces you prepared. See Materials Preparation. Ask students to remove the red, pink, yellow, and blue pieces from the sets. See Figure 3. Refer students to Question 5 on the Kid Fractions Homework page in Lesson 1 of the Student Guide. Reread Question 5 aloud as a class, and then ask students to share the drawings and fractions they wrote about objects around their homes with a partner.

The example in Question 5 describes four cans of soup — three tomato and one chicken noodle. We write 3/4 for the fraction of the cans that are tomato.

Display one blue circle piece and say:

This piece represents 1/4 of the 4 cans of soup. Use circle pieces to show 3/4 . (Students should find 4 blue pieces and indicate that 3 are of interest, possibly pointing to 3 or sliding 3 to the side. See Figure 4.)
What is the unit whole? (the pink piece)
How do you know? (You can cover one pink piece exactly with four blue pieces.)

Some students may place 3 blue pieces on their desks thinking this represents 3 fourth pieces, but in order to show the fraction 3/4 , the unit whole of 4 pieces must be shown and 3 of those pieces indicated.

Ask:

How do these three blue pieces show 3/4 ? (Possible response: There are 4 of the same-size pieces and I am looking at 3 of them in particular.)
How does knowing the denominator help you? (It helps me know how many total pieces to put down.)
How does knowing the numerator help you? (It helps me know how many in the group are special.)
Can we show fourths with a group of 2 blues and 2 yellows? Why or why not? (No, because all 4 parts need to be the same size.)
Show 3/4 another way. (See Figure 5 for another possible solution.)
What is the unit whole now? (two red circles)

Explore Size and Relationship Between Pieces. Direct students attention to the Circle Pieces: Red, Pink, Yellow, Blue pages in the Student Guide. Assign Questions 1–10 to student pairs. Give students time to answer the questions so that they become familiar with the size of each piece and the relationships among them.

Discuss Questions 6–10 by asking students to share their solutions with the class. Students can show their solutions with a display of the Red, Pink, Yellow, and Blue Pieces Master, with a display set of pieces, or sketch them on the board. Since there are multiple correct solutions for Question 8, ask more than one student to share.

Using the solutions in Figure 6 as examples, ask:

How are the solutions alike? (Possible response: The solutions follow the directions. They all use two colors and the pieces cover a whole circle.)
How are they different? (They use different colors and a different numbers of pieces.)
Are there other solutions? (Yes. See Content Note.)

How many solutions? To solve the problem in Question 8, students may arrange the pieces in the circle in a different order for Solutions D and E. See Figure 6. For example, for Solution E, instead of all the yellows and blues placed on the circle together, students may separate the two blues with a yellow piece. Decide as a class whether to count as one solution having the same number of pieces of each color regardless of arrangement, or to consider the different arrangements as different solutions.