Review Concepts and Misconceptions.
To review fraction concepts, ask:
- Tell about a time when you used a fraction at home or at the store. What fraction did you use? What was the unit whole? (Possible responses: I read for a 1/2 hour or 30 minutes. The unit whole was 1 hour or 60 minutes. Or, I ate 3/4 of a sandwich. The unit whole was the sandwich.)
Display the Agree or Disagree? Master. It highlights several of Moe and Joe Smart's misconceptions about fractions. Direct students' attention to the first scenario.
Read it aloud, and then ask:
- Do you agree with Joe or Moe? Is the pie cut into thirds? Why or why not? (I agree with Joe. The pie is not cut into thirds because the three parts of the whole must be equal size.)
Read the second scenario aloud. Joe thinks the shape does not show 1/2 because the halves are not symmetrical.
- Do you agree with Joe? Must the halves be symmetrical? (No)
- Use circle pieces to show that each part of Moe's shape is a half. (Students can use two orange pieces to show that each half of Moe's shape is the same size. 1 of 2 of the parts shows 1/2.)
- Do parts have to be the same shape in order to be equal in size? (No)
In the same scenario, Joe thinks the rectangle does not show 1/2 because the unit whole is divided into more than 2 parts, and because it is not symmetrical.
- Does Moe's rectangle show 1/2? Show or tell how you know. (Possible response: The rectangle shows 1/2 because it is divided into 8 equal parts and 4 of the parts are shaded. I think of 4 squares making 1 part, and 1 of the 2 parts of the rectangle is shaded. That shows 1/2.)
Read the last scenario aloud and ask:
- Moe thinks Joe poured much more than a 1/2 glass of juice. Do you agree or disagree? (I disagree with Moe. Joe poured 1/2 glass of juice.)
- Why does Joe have more juice than Moe? (Joe's glass, his unit whole, is larger so his half will be larger, too.)
Joe and Moe Smart's statements discussed on the Agree or Disagree? Master came directly from student and classroom observations. Students need to grapple with their prior knowledge and prior conceptions as they further develop their understanding.
Explore Size and Relationship Between Pieces. Direct students' attention to the Circle Pieces: Red, Pink, Orange, Aqua pages in the Student Guide. Assign Questions 1–10 to student pairs to continue exploration of the circle pieces.
These questions give students the opportunity to develop visual images of the pieces and their relationships to one another before being asked to use fraction language and notation to describe them.
Discuss Questions 5–10 by asking students to share their solutions with the class. Students can show their solutions with a display set or sketch them using a display of the Red, Pink, Orange, and Aqua Pieces Master. Since there are multiple correct solutions for Question 8, ask more than one student to share.
Using the solutions in Figure 1 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 different numbers of pieces.)
