Circle Pieces: Red, Pink, Yellow, Blue

Est. Class Sessions: 3

Developing the Lesson

Part 2. Fractions of a Unit Whole

Equal-Size Parts. Once students have developed an understanding of the relative size of the circle pieces, continue with a class discussion. Focus on the important concept that in order to name fractional parts, the unit whole must be divided into equal-size parts.

Ask:

What do you know about halves? (Possible response: One-half of something means that it is divided into two equal parts and we are interested in one of the parts.)

Use the Red, Pink, Yellow, and Blue Pieces Master and divide two or three of the shapes into unequal parts. See Figure 7 for examples.

Ask:

Is the circle divided into halves? Why or why not? (Possible response: No, halves have to be the same size.)
Is the semicircle divided into halves? Why or why not? (Possible response: No, because the two parts are not equal.)

Agree as a class that the unit whole has to be divided into equal-size parts to show fractional parts. Discuss sharing a pizza among friends. For the pizza to be shared fairly, each person must get the same amount of pizza.

Name Fractional Parts. Have students place a pink piece on their red circles.

Ask:

What part of the circle is covered with the pink piece? (one-half)

Write one-half in words and as a number ( 1/2 ). Point out to students that one-half means that one out of two equal parts of the whole circle are covered. The 2 in the fraction means that the whole is divided into two equal parts and the 1 means that we are interested in one of the parts.

Have students place three yellow pieces on their red circles.

Ask:

What part of the circle is covered with the yellow pieces? (three-fourths)
How do you know? (The circle is divided into four equal parts and three of them are covered with yellow.)
Write that as a fraction. ( 3/4 )
What does the 4 tell you? (The whole circle is divided into 4 equal parts.)
What does the 3 tell you? (Three of the parts are shown with the yellow pieces.)
Which number is the numerator? (3)
Which number is the denominator? (4)

Show Halves. Continue the class discussion to emphasize the important idea that the size of fractional parts depends on the size of the unit whole. For example, one-half of a red circle is not the same size as one-half of a pink piece.

Have students place two blue pieces on a pink piece.

Ask:

The pink piece is the unit whole. What part of the pink piece is covered with the blue pieces? (two-fourths)
How do you know? (Four blue pieces divide the pink piece into equal parts, so one blue piece is one-fourth.)
Write that as a fraction. ( 2/4 )
What does the 4 tell you? (The pink piece is divided into 4 equal parts.)
What does the 2 tell you? (Two of the parts are shown with the blue pieces.)
Is there another name for this fraction? ( 1/2 )

Ask students to choose from the red, pink, yellow, and blue pieces. For each prompt, ask them to first work with a partner to find an answer and then be ready to explain their thinking to others.

Ask a student volunteer:

Choose a fraction piece to show one whole. (The student may pick a red, pink, or yellow piece to represent the whole.)
We call that the unit or the unit whole. Now show me that piece divided into halves. (Possible responses are in Figure 8.)
Choose another fraction piece to be the unit whole. What does that piece look like divided into halves?

Continue the discussion until students find all the possibilities as shown in Figure 8. Refer students to the Fraction Names Chart you prepared. See Materials Preparation. Start to complete this table with the fraction names by asking students what words are used to describe a unit whole divided into 2 equal parts. See Figure 9. Place the chart in the room where it can remain throughout the unit.

Show Fourths, Eighths, and Fifths. Use these ideas to discuss fourths and eighths.

Ask:

If the red circle is the unit whole, use other pieces to show fourths. (See Figure 10.)
Use the pink piece for the unit whole and show fourths with it. (See Figure 11.)
Explain how you know that you have divided the unit whole into fourths. (The pink piece covered with four blue pieces shows fourths because it is divided into four equal parts.)
How can both the yellow piece and the blue piece be a called a fourth? (The yellow piece covers one-fourth of the red circle. The blue piece covers one-fourth of the pink piece.)
If the red circle is the unit whole, what piece shows the unit whole divided into eighths? (Blue. See Figure 12.)

Ask students to write names for a whole divided into four parts and eight parts. Record their responses on the Fraction Names chart. See Figure 9.

Show students the shape at the bottom of the Red, Pink, Yellow, and Blue Pieces Master. This is the shape in Question 9 in the Student Guide. See Figure 13.

Ask:

If this shape is the unit whole, what pieces can you use to divide it into equal parts? (blue pieces)
How many pieces did you use? What is the name for these parts of the unit whole? (5 pieces, fifths)
We have called this blue piece a fourth, an eighth, and a fifth. Show or tell us why its name changes. (The unit whole changes, so the fractional part the blue piece represents changes. The blue piece was a fourth when the whole was a pink piece. The blue piece was an eighth when the whole was a red circle. The blue piece was one-fifth of the shape in Question 9.)

Ask students to write names for the whole divided into five parts and record their responses on the chart. See Figure 9.

Assign Questions 11–15 in the Naming Fractions section of the Student Guide to student pairs to practice exploring and naming fourths, eighths, and fifths.

As students work, ask them to justify their solutions using the fraction pieces. For example, students can use their pieces to show how they know that three blues are more than, less than, or equal to one-half of the circle (Question 12D).

When students have completed the problems, ask them to share their thinking for some questions with the rest of the class using circle pieces and a display of the Red, Pink, Yellow, and Blue Pieces Master. Encourage the class to ask the presenters clarifying questions.

Assign the Fourths Homework page in the Student Activity Book. As stated in the directions on the page, students may cut out the shapes to help decide if they show fourths or not. Encourage students to fold or cut apart each shape to help them decide.

Student Guide: 251

Answers