Show Fractions With Words, Numbers, Models, and Number Lines. The Circles, Fraction Strips, and Number Lines pages in the Student Guide depict a class discussion about different representations of fractions including circle pieces, fraction strips, number lines, and a set of objects.
Use the discussion questions to facilitate a similar discussion with your students. Have students discuss the questions for each representation with partners before discussing them as a whole class. Assign Questions 1–14 to student pairs.
Questions 1–4 refer to Jason's drawing using circle pieces.
Questions 5–6 refer to Natasha's use of a fraction strip.
Question 7–8 refer to Sam's use of a number line.
Questions 9–14 refer to Kathy's drawing of a fractional part of a set.
Students who are using their Fraction Charts to answer Question 13 will notice that 2/8 is equivalent to the other possible responses. However, in this context, 2/8 of the pack does not make sense. Help students understand that they need to keep the context of the problem in mind. In this case, 1/8 of the pack of 12 cards is 11/2 cards and 2/8 is 3 cards. A trade would be made only with whole cards.
Make connections between the representations by asking:
- What is the unit whole for each way the students used to show 1/3 ? (The red circle, one fraction strip, from 0 to 1 on the number line, and a whole pack of trading cards.)
- How is the denominator shown for the circle pieces, fraction strip, and number line? (Possible responses: For the circle pieces, three orange pieces cover the whole. The fraction strip is divided into three equal parts. The number line between zero and 1 is divided into three equal parts.)
- If I covered the red circle with one pink and two yellows, would that show thirds? Why or why not? (No. There are three pieces, but they are not equal pieces.)
- How did Jason, Natasha, Sam, and Kathy show the numerator in the way they showed 1/3 ? (Jason shaded one of the three parts of the circle. Natasha shaded in one of the parts of the fraction strip. Sam put a point 1/3 of the way from 0 to 1 on the number line. Kathy divided the cards into 3 piles of 4 cards and circled one of the piles.
Many Ways to Show a Fraction. Have students complete the Many Ways to Show a Fraction pages in the Student Activity Book. The problems are similar to the Show That Fraction activity. Have students complete the missing representations for each problem using a Fraction Chart, fraction circle pieces, fraction strips, and the Writing Numbers in Words page in the Student Guide Reference section as they work.
In Question 8 students should draw a set of objects and represent the fraction indicated. The focus is on the representation of the fraction rather than the drawing, so encourage children to use simple objects in their drawing such as dots, stars, or balls.
Use Questions 1–8 on the Many Ways to Show a Fraction pages in the Student Activity Book to assess students' abilities toward the Expectations that follow:
- Represent fractions using circle pieces, fraction strips, number lines, and drawings [E1].
- Represent fractions using words and numbers [E2].
- Recognize that fractional parts a unit whole may be different shapes but must be the same size [E3].
- Partition circles by a given unit fraction [E6].
- Make connections among representations of fractions including symbols, words, drawings, fraction strips, and number lines [E8].
