Tell students that they are going to challenge each other to show fractions in five different ways. They will need their circle pieces and their Fraction Chart from Lesson 4.
Display a copy of the Show That Fraction Master. Demonstrate the challenge by dividing one whole fraction strip on the blank Master into fourths, labeling then shading in three-fourths. See Figure 1.
- How many wholes are shown on the drawing of the fraction strip and on the number line? How do you know? (There are two wholes. I know because the fraction strip shows a dark line in the middle showing two strips together and it says “one whole fraction strip” above each one. The number line is marked 0 to 2.)
- How did I divide the unit whole? How do you know? (You divided one whole into fourths because you showed 4 equal-size parts.)
- What fraction of the strip am I showing?
(three-fourths)
- How do you know that it is three-fourths? (3 of the 4 parts are shaded in.)
- How do you write three-fourths as a number? [Name a student], show us on the display.
- How do you write three-fourths in words? [Name a student], show us on the display.
While a student shows how to write the fraction as a number and in words, review the terms numerator and denominator.
- We showed three-fourths on the fraction strip and wrote it in words and as a number. Use your fraction pieces to show three-fourths of the red circle. (Students show three yellows covering their red circle.)
- Who can show three-fourths of the circle on the display? Tell us how you know that you have covered three-fourths of the circle. (I divided the circle into four parts like the yellow pieces and colored in 3 of the 4 parts.)
- Who can show a point three-fourths of the way from 0 to 1 on the number line. (See Figure 2.)
- How do you know the point is three-fourths of the way from 0 to 1? (Possible response: I divided the number line into four equal parts from 0 to 1. Then, I went to the end of the third part. That's where 3/4 is.)
The fraction strips and number lines shown in this lesson are not the same scale as the fraction strips folded and used to compare fractions in previous lessons in this unit. Students cannot measure or line-up their folded fraction along these representations but students can use their fraction strips and the Fraction Chart they created to compare fractions.
Demonstrate the challenge again using one and one-half. Both fraction strips should be divided into two equal parts labeling each part 1/2 on the Master. The number line should also be divided into two equal parts from 0 to 1 and 1 to 2.
Label the third mark from zero 11/2 . See Figure 3.
- How did I divide the unit whole? (into 2 equal-size parts)
- What fraction of the strip am I showing? (one and one-half)
- How do you know that it is one and one-half? (Three half parts are shaded in. Two halves make 1 and the third half makes 1/2 .)
- How is one and one-half shown on the number line? (Each whole is divided into two equal parts and there is a dot half way between the 1 and 2. It is one whole and one-half of the whole parts shown.)
- How do you write one and one-half as a number? [Name a student], show us on the display.
- How do you write one and one-half in words? [Name a student], show us on the display.
- Who can show one and one-half on the circle display? Tell us how you know that you have covered one and one-half. (I thought about one red fraction circle piece and the one-half pink piece. One whole circle is shown so I drew another half circle then colored in the whole circle and the half circle on the display.)
Ask a student to represent a different fraction on another display using one of the five representations and then challenge the rest of the class to show that fraction using the remaining four representations. Once a student has shown the challenge fraction to the class, choose (or have the student choose) four other students to represent the fraction using the remaining representations. Three students can work at the board to show the fraction on the number line, as a number, and in words while others are shown on the display using circle pieces and on the fraction strips. Students can represent the fraction in writing and with circle pieces at their seats.
Repeat the activity with other fractions. Be sure that during the activity students represent fractions with each of the denominators (halves, thirds, fourths, sixths and eighths), at least one fraction that is a whole ( 2/2 , 3/3 , 4/4 , 6/6 , or 8/8 ) and at least one that is greater than one. As students represent the fractions, briefly discuss them using prompts similar to those asked for 11/2 that ask students to explain their representations.
