88

Objective

Common Core State Standards

■ 4.NF.4a

7Number and Operations—Fractions

Multiples of Unit FractionsConcrete models help students understand the concept of multiplying a unit fraction by a whole number. The models help students see what the multiplication means. Then they can transfer that understanding to the formula a __

b = a × ( 1 __

b ). Real-world examples help students develop a better

grasp of multiplying unit fractions by whole numbers.

Talk About It ■ Write 7 × 1 __

6 on the board. Say: When we multiply a fraction by a whole

number, we multiply the numerator by the whole number. In the problem, we saw that 7 __

6 is 7 × 1 __

6 . Write 7 × 1 __

6 = 7 __

6 .

■ Ask: How many whole circles do you have? Write 1 on the board. Ask: How many additional sixths do you have? Write 1 __

6 . Say: Seven times 1 __

6 of a pizza

equals 7 __ 6 or 11 __

6 pizzas.

Solve ItWith students, reread the problem. Have students trace Fraction Circles divided into sixths and color the number of 1 __ 6 pieces needed. Have them write the equation 7 × 1 __ 6 = 7 __ 6 . Ask students how many slices of pizza were left over. Elicit that 7 slices were left.

More IdeasFor other ways to teach about multiples of unit fractions—

■ Have students use Fraction Squares to solve the problem. The procedure is the same, except that students build and draw squares.

■ Have students use Double Fraction Tower Number Lines (BLM 8) to solve the problem. Students can use Fraction Tower® Equivalency Cubes to mark off sixths intervals on a line. To perform the multiplication on the line, students trace and color a 1 __ 6 tower seven times nose to tail, starting at 0.

Formative AssessmentHave students try the following problem.

Keisha collects coins. Each page of her coin book holds 12 coins. If Keisha has 17 coins, how many pages of the book are filled?

A . 29 __ 12

B . 17 __ 12

C . 12 __ 17

D . 12 __ 29

Number and Operations—Fractions

89

Materials• Deluxe Rainbow Fraction® Circles

(1 set per group)• paper and pencils• colored pencils or crayons

Try It! 20 minutes | Groups of 3

Here is a problem about multiples of unit fractions.

Ana invited a few friends to her home for pizza. The three pizzas that Ana’s

parents ordered were each cut into six equal slices. When Ana and her

friends finished eating, 7 __ 6 of a pizza was left over. How many slices were left?

Introduce the problem. Then have students do the activity to solve the problem. Distribute Deluxe Rainbow Fraction Circles, paper, and pencils to students.

1. Say: Build a circle that shows sixths. Indicate the part of the model that represents one slice of pizza. Have students build the circle, then separate one sixths piece from the circle. Have students trace 2 whole circles onto a piece of paper, divide them into sixths, and color 1 __ 6 of the first circle.

3. Ask: How many sixths have we put together? How many sixths did Ana and her friends have left over? Elicit that another sixth is needed. Have students color one section of the second circle. Suggest to students that they built 7 __ 6 of a pizza by repeatedly adding sixths. Elicit that repeated addition is multiplication. Have students write 7 × 1 __ 6 = 7 __ 6 .

2. Say: Let’s continue putting the left over slices of pizza together. Ask: How many more sixths make 1 whole? Have students add pieces to the model to make a whole, and have them color the remaining sections of the first circle.

Watch for students who are hesitant to add the 7th sixth. Remind them that the extra sixth starts a new pizza.

Name Number and Operations—FractionsLesson

90

© E

TA hand

2mind

™

Hands-On Standards, Common Core Edition

7

Use Fraction Circles to model each number. Write the number as a fraction and as a mixed number.

1.

3 × 1 __ 2 =______ = ______

Using Fraction Circles, model each number. Sketch the model. Write the number as a fraction.

3. 1 1 __ 3 4 × 1 __ 3 = ______

4. 1 5 __ 8 13 × 1 __ 8 = ______

2.

8 × 1 __ 5 = ______ = ______

Write each product as an improper fraction.

5. 11 × 1 __ 4 = ______

8. 11 × 1 __ 2 = ______

6. 15 × 1 __ 8 = ______

9. 7 × 1 __ 3 = ______

7. 19 × 1 __ 5 = ______

10. 13 × 1 ___ 10 = ______

Write each product as a mixed number.

11. 12 × 1 __ 5 = ______

14. 63 × 1 ___ 10 = ______

12. 17 × 1 __ 8 = ______

15. 13 × 1 __ 2 = ______

13. 31 × 1 __ 6 = ______

16. 29 × 1 __ 4 = ______

Answer Key

Download student pages at hand2mind.com/hosstudent.

(Check students’ work.)

3 __ 2 1 1 __ 2 1 3 __ 5 8 __ 5

4 __ 3

13 ___ 8

11 ___ 4

11 ___ 2

2 2 __ 5

6 3 ___ 10

15 ___ 8

7 __ 3

2 1 __ 8

6 1 __ 2

19 ___ 5

13 ___ 10

5 1 __ 6

7 1 __ 4

(Check students’ models.)

91

Name

© E

TA hand

2mind

™

Hands-On Standards, Common Core Edition

Challenge! Write how to change a mixed number to an improper fraction. Why do the rules work?

Answer Key

Download student pages at hand2mind.com/hosstudent.

Challenge: (Sample) Multiply the whole number by the number in the denominator. Add the number in the numerator to that product. Write this number in the numerator of the improper fraction. Use the original denominator as the denominator of the improper fraction.

Name Number and Operations—FractionsLesson

90

© E

TA hand

2mind

™

Hands-On Standards, Common Core Edition

7

Use Fraction Circles to model each number. Write the number as a fraction and as a mixed number.

1.

3 × 1 __ 2 =______ = ______

Using Fraction Circles, model each number. Sketch the model. Write the number as a fraction.

3. 1 1 __ 3 4 × 1 __ 3 = ______

4. 1 5 __ 8 13 × 1 __ 8 = ______

2.

8 × 1 __ 5 = ______ = ______

Write each product as an improper fraction.

5. 11 × 1 __ 4 = ______

8. 11 × 1 __ 2 = ______

6. 15 × 1 __ 8 = ______

9. 7 × 1 __ 3 = ______

7. 19 × 1 __ 5 = ______

10. 13 × 1 ___ 10 = ______

Write each product as a mixed number.

11. 12 × 1 __ 5 = ______

14. 63 × 1 ___ 10 = ______

12. 17 × 1 __ 8 = ______

15. 13 × 1 __ 2 = ______

13. 31 × 1 __ 6 = ______

16. 29 × 1 __ 4 = ______

www.hand2mind.com

91

Name

© E

TA hand

2mind

™

Hands-On Standards, Common Core Editionwww.hand2mind.com

Challenge! Write how to change a mixed number to an improper fraction. Why do the rules work?