Parts are Equal Size and Depend on the Whole. Use the prompts to lead a class discussion that extends the following important ideas developed in Lesson 2 about fractions to thirds and sixths:
- The unit whole must be divided into equal-size parts. The parts can be given a fraction name. For example, one-third of a red circle means that the red circle is divided into three equal parts and we are interested in one of the parts.
- The fractional parts depend on the unit whole. One-third of a red circle is not the same size as one-third of a pink piece.
Ask students to use the red, pink, orange, and aqua pieces and to work with a partner to answer the following questions:
- Show me what halves look like using these pieces. Find two ways. (Possible responses are shown in Figure 2.)
- What is the unit whole? (a red or orange piece)
- What color pieces divide the whole into halves? (If red is the unit, pink pieces divide it into halves. If orange is the unit, aqua pieces divide it into halves.)
Direct students' attention to the Fraction Names chart displayed from Lesson 2. Review the row for halves.
Ask students to cover a pink piece with an orange and an aqua piece as shown in Figure 3.
- Is the pink piece divided into halves? Why or why not? (No. It is divided into two parts, but they are not the same size.)
Introduce Thirds. Continue the discussion by introducing thirds.
- Show me what thirds look like using these pieces. Find two ways. (Solutions are shown in Figure 4.)
- For each way that you showed thirds, tell me what is the unit whole and what pieces show thirds. (If the red circle is the unit, orange pieces divide it into thirds. If a pink piece is the unit, aqua pieces divide it into thirds.)
Ask students to cover a red circle with a pink, an orange, and an aqua piece as shown in Figure 5.
- Is the circle divided into thirds? Why or why not? (No. It is divided into three parts, but they are not the same size.)
Direct students' attention to the Fraction Names chart. Ask a student to complete a row of the chart for thirds. See Figure 6.
- What piece shows one-third of the red piece? (an orange)
- Show me how to write that as a fraction. (1/3)
- Use your pieces to show two-thirds of a red circle. Show how to write two-thirds as a number. (2/3)
- What does the 3 in the denominator of the fraction tell you? (The circle is divided into three equal parts.)
- What does the two in the numerator of the fraction tell you? (That we covered two out of three pieces of the whole.)
- What piece shows one-third of the pink piece? (an aqua)
- Cover two-thirds of a pink piece. Find more than one way. (Two aqua pieces or one orange piece both cover two-thirds of a pink.)
Introduce Sixths. Discuss sixths by asking students to use pieces to divide a circle into sixths and complete a row for sixths on the Fraction Names chart. See Figures 6 and 7. Ask questions similar to those you posed when discussing thirds.
Assign the Naming Wholes and Parts Homework page in the Student Activity Book.
Use the Naming Wholes and Parts Homework page in the Student Activity Book to assess students' progress toward the following Expectations:
- Representing fractions using drawings [E1].
- Recognizing that fractional parts of a unit whole must be equal in size [E3].
- Partition shapes by a given unit fraction [E6].
- Identify the unit whole when given a fractional part of a whole [E7].
