Fractions in Number Stories



Objective To provide experiences with solving number stories involving fractions.

www.everydaymathonline.com

ePresentations

eToolkit

Algorithms Practice

EM Facts Workshop Game™

Teaching the Lesson

Family Letters

Assessment Management

Common Core State Standards

Ongoing Learning & Practice

Key Concepts and Skills

Reviewing the Line Plot Routine

• Use pennies, counters, or pictures to solve fraction number stories. 

Student Reference Book, pp. 79–81 stick-on notes Children describe landmarks on a line plot and compare chances for two different events.

[Number and Numeration Goal 2]

• Describe solution strategies for solving fraction number stories.  [Number and Numeration Goal 2]

• Use Fraction Cards to compare fractions.  [Number and Numeration Goal 6]

• Measure and draw a line segment to the nearest _14 inch.  [Measurement and Reference Frames Goal 1]

Key Activities The teacher and children make up and solve number stories involving fractions. Children practice solving fraction number stories independently.

Curriculum Focal Points

Math Boxes 8 8 

Math Journal 2, p. 202 Children practice and maintain skills through Math Box problems.

Interactive Teacher’s Lesson Guide

Differentiation Options ENRICHMENT

Solving Math Curse Number Stories Math Curse  paper Children solve and write fraction number stories based on those found in the book Math Curse. EXTRA PRACTICE

Minute Math + Minute Math®+, pp. 86, 90, 92, and 155 Children solve number stories with fractions.

Home Link 8 8 

Math Masters, p. 262 Children practice and maintain skills through Home Link activities.

Ongoing Assessment: Informing Instruction See page 689. Ongoing Assessment: Recognizing Student Achievement Use journal page 201.  [Number and Numeration Goal 2]

Materials Math Journal 2, pp. 200 and 201 Home Link 8 7 inch ruler  pennies or counters (optional)  Fraction Cards (optional)  tool-kit clock (optional)  slate

Advance Preparation Prepare the line plot (pictured on page 692) for Part 2. For the optional Enrichment activity in Part 3, obtain a copy of the book Math Curse by Jon Scieszka and Lane Smith (Viking, 1995).

Teacher’s Reference Manual, Grades 1– 3 pp. 225–227

688

Unit 8

Fractions

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Getting Started Mental Math and Reflexes

Math Message

Pose problems like the following as children write the answers on slates. They may use tool-kit clocks as needed.

Using your ruler, draw a line segment 3

1 minute = ____ seconds 60

1 _ hour = ____ minutes 20

1 hour = ____ minutes 60

1 _ hour = ____ minutes 5

1 _ hour = ____ minutes 30

3

2

12 1 _ hour = 6

inches long on your slate. that is 1_ 4

____ minutes 10

PROBLEM PR PRO P RO R OB BLE BL L LE LEM EM SOLVING SO S OL O L LV VIN V ING

1 Divide the line segment into _ -inch 4

1 -inch segments are there? segments. How many _ 4

Home Link 8 7 Follow-Up 

Go over the answer to Problem 5. The

1 _ hour = ____ minutes 15

diagram shows 2 wholes and _ (or _ ) 12 3 4

4 2 _ hour = ____ minutes 30 4 3 _ hour = ____ minutes 45 4

1

of a whole. The corresponding mixed number, then, is (or 2_ ). You may want to have children write 2_ 12 3 4

1

number models for Problems 1–3. For example: Problem 1: _ +_ +_ +_ +_ +_ =_ , or 1_ , or 1_ 4 4 4 4 4 4 4 4 2 1

1

1

1

1

1

6

1 4

1 4

1 4

1 4

1 4

1 4

2

1

1 Teaching the Lesson

 Math Message Follow-Up

WHOLE-CLASS DISCUSSION

If an overhead projector is available, use it to go over the solution. Lead children to the conclusion that since there are seven _14 -inch segments, the line segment is _74 inches long. _74 inches is another name for 1_34 inches.

 Writing and Solving Fraction Number Stories

PROBLEM PRO P RO R OB BLE BL L LE LEM EM SOLVING SO S OL O LV L VIN V IIN NG

3

1

14

Math Message solution

WHOLE-CLASS ACTIVITY

You and the children make up stories involving fractions of sets. Children solve the problems in any way they can—using pennies or counters, drawing pictures or doodles, and so on. You might want to begin with stories such as the following: ●

0

1 4

Adjusting the Activity Extend the line segment _14 inch. Think of the line segment as part of a number line from 0 to 2. With children, label the points that are _14 inch apart. AUDITORY



KINESTHETIC



TACTILE



VISUAL

Andy bought 24 stamps for his stamp collection. _34 of the stamps were from the United States. How many stamps were from the United States? 18 stamps

Possible solution strategy: Take 24 coins or counters and divide them into 4 equal sets. Each set consists of 6 counters and is 1 _ of the total, so _14 of 24 = 6. Three sets consist of 18 counters and 4 are _34 of the total, so _34 of 24 = 18.

0

1 4

2 4

3 4

1

2

3

1 14 14 14 2

Extending the line segment

Ongoing Assessment: Informing Instruction Watch for children who are having difficulty solving problems with fractions of sets. Remind them that the denominator (the bottom number in a fraction) tells the total number of equal groups, and the numerator (the top number in a fraction) tells the number of equal groups being considered. Children count the objects in the number of groups given by the numerator to solve the problem. Have children use manipulatives to act out each problem.

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●

Ruthann read 12 books in the last 4 months. Three were 3 nonfiction. What fraction of the books were nonfiction? _ or _14 12 of the books On average, how many books did she read per month? 3 books Possible solution strategy: Three out of 12 books is equivalent 3 to _ of the total. Take 12 counters and divide them into 4 sets 12 of 3. Each set is _14 of the total. To find the average number read per month, divide 12 by 4.

●

Kiko has done _35 of the math problems. What fraction of the math problems does she still have to do? _25 of the problems Possible solution strategy: Suppose Kiko has 5 problems to solve. She solved _35 of the problems—3 problems. This leaves 2 problems still to be solved. Two out of 5 problems is _25 of the problems.

●

Which would you rather have— _23 of a can of lemonade or _56 of a can of lemonade? Assuming you like lemonade, _56 of a can Possible solution strategy: Use Fraction Cards to compare the fractions, or reason as follows: _23 is equivalent to _46 , which is less than _56 . Therefore, _56 is more than _23 .

●

Jim has $8. If he shares his money equally with 8 people, each person gets $8 ÷ 8 = $__88 = $1; if he shares it equally with 4 people, each person gets $8 ÷ 4 = $__84 = $2. If Jim doesn’t share his money, how much money does he have? $8 Write a fraction to show how much money Jim has. $__81 Possible solution strategy: The denominator names the number of people among whom Jim’s $8 is divided. Since the money was not divided or shared with anyone but Jim, the denominator is 1. Since there are $8, 8 is the number in the numerator. $__81 = $8 ÷ 1 = $8

●

Possible solution strategy: The denominator tells how many parts the whole is divided into. For __13 , the whole is divided into 3 parts and __13 is one of those parts. For __31 , the whole is divided into 1 part and there are 3 wholes. __31 = 3 × __11 = 3 So, __31 is more than __13 .

Adjusting the Activity Make up additional fraction number stories as appropriate before children solve problems independently. Use similar number stories in future Minute Math+ sessions. AUDITORY

690



KINESTHETIC



TACTILE



VISUAL

3 __ Which is the larger fraction, __13 or __ ?3 1 1

●

It took Nathan 1_14 hours to do his homework. How many minutes did he spend on homework? 75 minutes Possible solution strategy: 1 hour = 60 minutes, _14 hour = _14 of 60 minutes, or 15 minutes. Therefore, 1_14 hours = 60 minutes + 15 minutes = 75 minutes.

Unit 8 Fractions

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●

Tamekka had 20 books to put into her bookcase. She put _12 of the books on the top shelf and _12 of the remaining books on the second shelf. How many books did she still need to put into the bookcase? 5 books What fraction of the total number of books is that? _14 of the total Possible solution strategy: _12 of 20 = 10, so she put 10 books on the top shelf, which left 10 books to be shelved. She put _12 of the remaining 10 books on the second shelf—that’s 5 books. She put a total of 10 books + 5 books, or 15 books, into the bookcase which left 5 books to be shelved.

After working through a few examples, ask volunteers to make up stories for the class to solve.

 Solving Fraction Stories

PARTNER ACTIVITY

(Math Journal 2, pp. 200 and 201)

PROBLEM PR PRO P RO R OBL BLE B L LE LEM EM SO S SOLVING OL O LV L VIIIN VIN V NG N G

NOTE For practice with adding

Children work with a partner or independently to complete journal pages 200 and 201.

Ongoing Assessment: Recognizing Student Achievement

and subtracting fractions, go to www.everydaymathonline.com.

Journal page 201 Problems 10–13



Use journal page 201, Problems 10–13 to assess children’s progress toward solving problems involving fractional parts of a collection. Children are making adequate progress if they are able to successfully complete Problems 10–13. Some children may successfully complete Problems 14–16. [Number and Numeration Goal 2]

Student Page Date

Student Page

Time

LESSON

Date

Fraction Number Stories

8 8 䉬

8 8 䉬

Solve these number stories. Use pennies, counters, or draw pictures to help you. 1.

There are 8 apples in the package. Glenn did not eat any. What fraction of the package did Glenn eat?

Anik bought a dozen eggs at the supermarket. When he got home, he 1 found that ᎏᎏ of the eggs were cracked. 6 How many eggs were cracked?

4.

I had 2 whole cookies. I gave you ᎏᎏ 4 of 1 cookie. How many cookies did I have left?

3.

2 2 ᎏᎏ 3

Chante used of a package of ribbon to wrap presents. Did she use 3 more or less than ᎏᎏ of the package?

5.

There are 10 quarters. You have 3. I have 2. What fraction of the quarters do you have?

1ᎏ34ᎏ 6.

3 ᎏᎏ 10

2 ᎏᎏ 10

or

7.

or

cookies

1 ᎏᎏ 3

1

Neither;

1ᎏ12ᎏ

⫽

1ᎏ24ᎏ

Math Journal 2, p. 200

夹 夹

10. 6 ᎏᎏ 12

12. ᎏ3ᎏ 12

夹 夹

14. 3 ᎏᎏ 4

1 ᎏᎏ 2

Dorothy walks 1ᎏᎏ miles to school. 2 2 Jaime walks 1ᎏᎏ miles to school. 4 Who walks the longer distance?

8.

Sample answers:

7 ᎏᎏ 12

1

One day, Edwin read ᎏᎏ of a book. 3 1 The next day, he read another ᎏᎏ of 3 the book. What fraction of the book had he read after 2 days?

What fraction of the quarters do we have together?

5 ᎏᎏ 10

Draw eggs in each carton to show the fraction. Example:

What fraction of the book did he have left to read?

1 ᎏᎏ 5

continued

Sample answer: Jerome gave 2 new pens to his little sister. If the package had 10 pens in it, what fraction of the pens did he keep for 8 himself? ᎏ10ᎏ of the pens

eggs

2 ᎏᎏ 3

What fraction of the quarters do I have?

Fraction Number Stories

Write a fraction story. Ask your partner to solve it.

1

4

less

9.

2.

0 ᎏᎏ 8

Time

LESSON

Twelve children shared 2 medium-size pizzas equally. What fraction of 1 whole pizza did each child eat?

ᎏ1ᎏ 6

or

ᎏ2ᎏ 12

1 16. Julie drank ᎏᎏ of a glass of juice. 4

Draw an empty glass. Shade in the glass to show how much juice is left. Write the fraction.

11. ᎏ4ᎏ 12

13. ᎏ1ᎏ 2

15. 1 ᎏᎏ 3

3 – 4

of the

glass of juice is left.

Math Journal 2, p. 201

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2 Ongoing Learning & Practice

 Reviewing the Line Plot

WHOLE-CLASS ACTIVITY

Routine (Student Reference Book, pp. 79–81)

Use pages 79–81 in the Student Reference Book to review data landmarks. On the board, prepare a line plot with stick-on notes using this data: 42, 42, 43, 45, 45, 46, 46, 46, 46, 47, 47, 48, 48, 48, 48, 48, 50, 51, 53. To provide a context for children, suggest that the line plot shows the arm span measures in inches of a class of third graders. Number of Children

42 43 44 45 46 47 48 49 50 51 52 53 Number of Inches Line plot of 3rd grade arm spans

Ask children to identify the maximum arm span 53 inches, the minimum arm span 42 inches, the mode 48 inches, and the range 11 inches from the line-plot data. Next, ask children to think of another way to find the median without removing the stick-on notes from the line plot. If no one suggests it, have volunteers cross out the first and last stick-on note from each end of the line plot over and over until one remains—this is the median arm span. 47 inches Number of Children

42 43 44 45 46 47 48 49 50 51 52 53 Number of Inches The median arm span is 47 inches.

Have children imagine that you will put all the stick-on notes in a container and draw one out at random without looking. To practice comparing chances for two different events, pose the following: ●

692

Compare the chance of drawing a note that says 42 with the chance of getting a note that says 50. There is a greater chance of drawing 42 than 50. Explain how you figured it out. There are two 42s and only one 50.

Unit 8 Fractions

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Student Page ●

Compare the chances of drawing 42 and 47. The chances are equal because there are two 42s and two 47s.

Date

●

䉬

2 3.

Draw two ways to show ᎏᎏ

Compare the chances of drawing 46 and 48. There is a greater chance of drawing 48 because there are five 48s and four 46s. Compare the chances of drawing 48 or a number larger than 48. There is a greater chance of drawing 48 because there are five 48s and only three numbers larger than 48.

Math Boxes

8 8 1.

●

Time

LESSON

2.

6 feet ⫽

2

yards

1

1ᎏ2ᎏ

Sample answers:

1 3 1 1ᎏᎏ 2

feet ⫽ 18 inches

1ᎏᎏ yards ⫽ yards ⫽

4 54

feet inches

246

22–24

3.

Use simple drawings to show all of the possible ways you can take 2 blocks from the bag.

4.

4

Tara frosted ᎏᎏ of the cupcakes. 5 What fraction of the cupcakes

1 ᎏᎏ 5

is not frosted?

1

 Math Boxes 8 8 

Did she frost more or less than ᎏᎏ 2 of the cupcakes?

more

INDEPENDENT ACTIVITY

If there were 20 cupcakes in all, how many did she frost?

16 cupcakes

(Math Journal 2, p. 202) 5.

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-6. The skill in Problem 6 previews Unit 9 content.

Show two ways a team can score 37 points in a football game.

6.

Sample answer: 7 points

6 points

3 points

2 points

3 2

1 3

2 1

2 1

Will, Wes, Sam, and Ameer want to share $25 equally. How much money will each person get? Answer:

Write a number model:

Writing/Reasoning Have children draw or write an answer to the following: In Problem 4, is __15 more or less than _12 ? Use >, __15 or __15 < __12 How do you know? Sample answer: __15 is less than _12 because 1 of 5 equal parts is less than 1 of 2 equal parts.

 Home Link 8 8 

(Math Masters, p. 262)

Use your calculator. Pretend the division key is broken. Solve this problem.

(3 ⫻ 7) ⫹ 6 ⫹ (2 ⫻ 3) ⫹ (2 ⫻ 2) ⫽ 37; (2 ⫻ 7) ⫹ (3 ⫻ 6) ⫹ 3 ⫹ 2 ⫽ 37

$6.25

16 17

Math Journal 2, p. 202

INDEPENDENT ACTIVITY PROBLEM PR PRO P RO R OBL BLE B L LE LEM EM SO S SOLVING OL O LV VIIIN VIN NG N G

Home Connection Children solve fraction number stories like those in the lesson. They solve multidigit addition and subtraction problems.

3 Differentiation Options

Home Link Master Name HOME LINK

88 

ENRICHMENT

 Solving Math Curse

SMALL-GROUP ACTIVITY 15–30 Min

Number Stories

Family Note

Date

Time

Fraction Number Stories In class we have been solving many kinds of fraction number stories. If some of these Home Link problems seem difficult, encourage your child to model them with pennies or draw pictures to help solve them. 22–24

Please return this Home Link to school tomorrow.

Solve these fraction stories. Use pennies, counters, or pictures to help. 1. Elizabeth bought a dozen eggs. She dropped her bag on the

To apply children’s understanding of fraction concepts, read Math Curse and identify and solve the fraction problems in the story. Have children write their own fraction number stories based on daily activities, like those in Math Curse. The class can then discuss and solve these stories. Consider assembling the stories into a class book.

8

2 way home, and _3 of the eggs broke. How many eggs broke? eggs 3 _ 1 2. Katie mowed 4 of the lawn before lunch. What fraction of the lawn did she have to finish after lunch? 4 of the lawn

_

1 _

3. Donnie lives 1 mile from school. One day he walked 2 of the way to school

when he remembered he had to return home to get a book. When he finally made it to school, how far did he walk in all?

2

classmates. She took _4 of a tray of cookies to her teacher. How many trays of cookies did Sheridan have left? 3

1 _14

EXTRA PRACTICE

 Minute Math+

in the refrigerator, how much did he use? (Hint: 1 gallon = 4 quarts, and 1 quart = 2 pints)

_1 4

gallon

7. 6,714 - 3,806 = 8. 4,762 + 4,762 =

To offer children more experience with fractions, see the following pages in Minute Math+: pp. 86, 90, 92, and 155.

Unit

Write these problems on the back of this page. Solve and show your work. 6. 2,083 + 4,678 =

5–15 Min

trays

5. Jackson needed 2 pints of milk for his recipe. If he had one gallon of milk

Practice

SMALL-GROUP ACTIVITY

miles

4. Sheridan made 4 trays of cookies. She took 2 trays to school for her

6,761 2,908 9,524

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