ef student booklet

8/8/2019 EF Student Booklet

1/60

Student Booklet for Expressions and Formulas

EXPRESSIOAND FORMU

Students Name

Teachers Name

Math Section

School Name

These materials were developed by the Talent Development Middle Grades Program in the Ceof Schools at Johns Hopkins University in collaboration with Margaret King-Sears at George Mathe Expressions and FormulasUnit From Britannicas Math In Context. It is part of the NationaMiddle Grades Reform's Mathematics Improvement Toolkit, and was supported by The U.S. DeComprehensive School Reform Quality Initiative, grant # S332B060005.

math unitStudentBooklet


2/60


Unit Organizer

by using

Expressionsand

Formulas

is abouttools forsolving

problems

Formula

x _____

Arithmetic Trees

2 3

+5

Arrow Languaactionstarting number


3/60


Problem-Solving Strategy

Step 1 Identify whathe story proble

Step 2 Decide whictool to use.

Step 3 Use the stratorganize the

Step 4 Solve the pro

Step 5 Check my w


4/60

Student Booklet for Expressions and Formulas (CSOS Johns Hopkins University)

4

TABLE OF CONTENTS

Page

Section A Arrow Language 5

Section B Smart Calculations 20

Section C Formulas 36

Section D Reverse Operations 42

Section E Order of Operations1 49

1 This section is labeled E in the 2006 edition and F in the 2003 edition of the MIC unit Expressions andFormulas.


5/60


5

Section A Arrow Language


6/60


6

Vocabulary

Arrow Language

Arrow Language a method of writing a calculationby showing each operation with an arrow

+ 520 25

Arrow Stringa calculation that is written usingarrow language that uses more than one arrow

+ 5 - 420 25 21

Reverse String an arrow string that works throughcalculations backwards and is read from right to left

- 5 + 420 25 21


7/60


7

Arrow Language Independent Practice 1

Find the results of the following arrow strings.

+ 2 + 3 + 4

1. 8 ______ ______ ______

+ 11 - 9 + 102. 5 ______ ______ ______

- 4 - 5 + 63. 14 ______ ______ ______

+ 15 + 7 - 84. 22 ______ ______ ______

+ 12 + 32 + 28 - 25. 30 ______ ______ ______ ______

+ 45 - 18 + 36 + 96. 9 ______ ______ ______ ______


8/60


8

Arrow Language Independent Practice 2

Find the results of the following arrow strings.

-1.2 + 1.5 + 4.8

1. 1.6 ______ ______ ______

+ 33.2 +16 - 34.82. 13.8 ______ ______ ______

+ 28.1 +100 - 50.33. 7.8 ______ ______ ______

- 2.11 + 11.11 - 4.334. 4.33 ______ ______ ______

+ 23.25 + 62. 08 - 30.875. 47.23 ______ ______ ______

+ 21 + 88.1 - 33.25 + 146. .25 ______ ______ ______ ______


9/60


9

Arrow Language Word Problem A

Mr. Collins has an account with First American Bank. Use arrow language to show howmuch money Mr. Collins has in his account with each set of transactions.

1. Beginning balance in his account $2,452First withdrawal $769Second withdrawal $102

$2,452 _____ _____

2. Beginning balance in his account $625First withdrawal $79Second withdrawal $325

$625 _____ _____

3. Beginning balance in his account $1,734First withdrawal $290Second withdrawal $99

$1,734 _____ _____


10/60


10

Arrow Language Word Problem B

Mrs. Campbell grows tomatoes in her garden. She picks them as they ripen and putsthem on the kitchen windowsill until she needs them. On Monday she picked seventomatoes. For lunch she used one for a salad. For supper she used four to make soup.

The next time she went into her garden, she picked five more tomatoes. She gave 4tomatoes to her neighbor. The following day she picked 8 ripe tomatoes.

1. Use arrow language to show how many tomatoes are now on Mrs. Campbells kitchenwindowsill.

This table shows the number of tomatoes Mrs. Campbell picked and used over the nextseveral days.

2. Fill in the missing numbers in the table.

Tomatoes used Tomatoes pickedChange in number of

tomatoes

5 11 6 more

8 10

7 7

6 2

10 4

3 fewer

3. Look at the last row in the chart. What can you say about the numbers of tomatoespicked and used when you know there are 3 fewer tomatoes?


11/60


11

Arrow Language Word Problem C

Lydia and Mia started a new business named Read It Again, in which they ask fordonations of used books that they can resell. Their school principal gave them a spacenext to the school store to display and sell their books. The money they made went to the

class activity fund.

The month before opening their business the girls began to ask for donations of usedbooks. By opening day they had 158 books.

The table below shows the amount of business Read It Again had in itsfirst 4 weeks.

Books donated Books soldFirst Week 158 54

Second week 35 26

Third week 87 40Fourth week 56 62

1. a. Use arrow language to find how many books Lydia and Mia had in theirstock at the end of the first week.

b. Continue the arrow string above to find how many books were in stock atthe end of the second week. Write your answer here.

c. Continue the arrow string above to find how many books were in stock atthe end of the third week. Write your answer here.

2. At the end of the fourth week, did the girls have more or fewer books than they had

when they started their business? Show your work.


12/60


12

The table below shows the number of books donated and sold in a later week.

3. Fill in the missing numbers in the shaded parts of the table.

Day Books sold Books donated Change in numberof books

Monday 10 20 10 more

Tuesday 9 31

Wednesday 27 11

Thursday 19 13

Friday 11 fewer

4. Look at the last row in the chart. What can you say about the numbers of booksdonated and sold when you know there were 11 fewer books?


13/60


13

Arrow Language Word Problems D,E

D. The Blue Mountain Summer Art Camp has weekly sessions. Campers may signup for one, two, or three weeks. On July 31, the camp had 24 campers.

This table shows how many campers came or left each week in August.

August 1 7 6 campers came

August 8 14 7 campers left

August 15 21 4 campers came

August 22 28 5 campers left

How many campers did Blue Mountain Summer Art Camp have the lastweek of August? Show your work.

E. Mayor Weed employs a public relations company to conduct a survey every twomonths to find out if the citizens of Grassland approve of how he is running thetown. He started the year with an approval rating of 64.6%.

This table shows the results of the survey over one year.

March Rating up 6.2%

June Rating down 13.9%

August Rating down 9.4%

November Rating up 5.7%

What is Mayor Weeds approval rating in November? Show your

work.


14/60


14

Arrow Language Word Problem F

Mr. Hares sixth grade class at Butler Middle School volunteered to plant a gardenaround the flag pole in front of the school. The class planted 24 marigolds on Friday.

1. When the students went outside to water the plants on Monday, only 11plants remained. Rabbits had eaten the rest of the marigolds. Use arrowlanguage to show how many plants the rabbits had eaten over the weekend.

2. By Wednesday, the rabbits had eaten 6 more plants. Continue the arrow string toshow how many plants were left in the garden.

3. The garden looked very empty, So Mr. Hare bought 24 more marigolds, and thestudents planted them on Thursday. Use an arrow string to show how manymarigolds were in the garden on Thursday when the students had finished theirplanting.

4. To keep the rabbits from feasting on the plants, Mr. Hare bought some wire fencing

and brought it to school on Friday. Too late! The rabbits had eaten 8 more plants.Use arrow language to find how many marigolds were left on Friday.

5. The students put the wire fence around the garden to protect the remaining plants.Now the rabbits would have to find something else to eat. On what day did the

garden have the most plants? If you need to, write the days of the week over eachnumber of plants that were in the garden on each day.


15/60


15

Arrow Language Word Problem G

On Sunday, Lucy celebrated her fourteenth birthday. She received a gift of $20 fromher grandparents. Her Aunt Susan gave her $10. On Monday, she earned $15 froma babysitting job for the Lewis family. Because she baby-sits for the family often and

does a good job, Mr. and Mrs. Lewis gave Lucy a $5 birthday bonus.

1. Use arrow language to find the total amount of money Lucy has.

2. On Wednesday, Lucy saw a toy stuffed lion in a store window that she really liked for$35. Write an arrow string to find how much money she had left after she bought the

lion.

3. The day after she bought the toy lion, her father gave Lucy her weekly allowance of$10. On Saturday, she had another babysitting job with the Lewis family and earned$20. Write an arrow string to find how much money Lucy had on Saturday.

4. On which day of the week did Lucy have the most money? How much money did shehave? If you need to, write the days of the week over each amount that she had that

day.


16/60


16

Arrow Language Word Problem H

The Archer family keeps a money jar in the kitchen. When a family member needs somecash, he or she may borrow some money from the jar. Every Friday, each member of thefamily puts $3.00 in the money jar. If someone has extra change, he or she may put it in

the money jar. On a Monday morning, the jar contains $12.31.

This table shows the borrowing/contributing activity with the money jar for a week.

Day Money Added Money Borrowed

Monday$3.60

(Ben buys some comicbooks)

Tuesday$ 1.91

(Dad has extra change)

Wednesday$5.00

(Mom gives Ben moneyfor a field trip)

Thursday$2.75

(Clara pays back moneyshe borrowed last week)

Friday

$12.00(Dad, Mom, Ben, andClara each contribute

$3.00

1. How much cash is in the money jar on Wednesday evening?

2. a. On Friday evening, does the money jar have more or less cash than it had onMonday morning?

b. Explain or show how you got your answer to part a.


17/60


17

Arrow Language Word Problem I

Kentas favorite hobby is Kumihimo, which he learned from his grandfather. Kumihimo isthe Japanese art of braiding stings into interesting patterns. During spring vacationin March, Kenta made several braids. Altogether, he braided a total of 1.2 meters.

This table shows Kentas Kumihumo output and how much of his braiding he used fromMarch to June.

Length Of Braid Made Length Of Braid Used

March 1.2 meters20 cm

for a key chain for hisgrandfather

April 40 cm

May 30 cm 1 meterfor a belt for his mother

June 1.3 meters

1. How many cm of braid does Kenta have at the end of April? Remember to convertmeters to centimeters when necessary.

2. a . At the end of June, does Kunta have more or less braid than he had at thebeginning of March?

b. Explain or show how you got your answer to part a.


18/60


18

Arrow Language Word Problem J

The Christmas Bird Count, begun by Frank Chapman in 1900, has continued for over100 years. On December 25th, thousands of volunteers count the species andnumber of birds that they see. In Maryland, observers reported seeing 398 Eastern

Bluebirds in 1951. In 1961, they counted 345 fewer Eastern Bluebirds than they hadseen a decade earlier. By 1971, the number of Eastern Bluebirds observed hadincreased by 102. Five years later, in 1976, the Eastern Bluebird count increased by807.

1. Write an arrow string to show the changes in the number of EasternBluebirds and how many were seen each Christmas.

2. What is the total change in the number of Eastern Bluebirds from 1951to 1976?

3. Describe the total change by using one arrow.

4. How did you decide what number to place over the arrow?


19/60


19

Arrow Language Word Problem K

In Oklahoma, volunteers for the Christmas Bird Count reported seeing 663 NorthernCardinals in 1961. In 1971, they spotted 717 more Northern Cardinals than they hadseen 10 years earlier. By 1981, the number of Northern Cardinals observed had

increased by 870 since 1971. Four years later, in 1985, the observers reported seeing320 fewer Northern Cardinals than they had counted in 1981.

1. Write an arrow string to show the changes in the number of NorthernCardinals from 1971 to 1985.

2. What is the total number of Northern Cardinals in 1985?

3. Describe the total change by using one arrow.

4. How did you decide what number to place over the arrow?


20/60


20

Section B Smart Calculations


21/60


21

Smart Calculations Independent Practice 1Making Change

Use arrow language to show how you would make change.

1. $2.75 $3.00 $10.00 $20.00

2. $8.65 $8.75 $9.00 $10.00 $20.00

3. $2.87 $2.90 $3.00 $5.00

4. $29.60 $29.70 $29.75 $30.00 $50.00

5. $66.95 $67.00 $70.00 $80.00 $100.00

6. $114.50 $115.00 $120.00 $130.00 $150.00


22/60


22

Smart Calculations Independent Practice 2Making Change

Write an arrow string to show how you would make change using the small coins and billsmethod. You do not need to use all the spaces and arrows.

Example: Make change for a $5.49 purchase from $10.00.

+ $0.01 + $0.50 + $4.00$5.49 $5.50 $6.00 $10.00 _____

1. Make change for an $18.65 purchase from $20.00.

$18.65 _______ _______ _______ _____

2. Make change for a $53.00 purchase from $60.00.

$53.00 ______ ______ _______ ______


$67.50 ______ _______ ______ ______

4. Make change for a $101.85 purchase from $110.00

$101.85 ______ ______ _______ ______


$32.48 ______ ______ _______ ______


23/60


23

Smart Calculations Independent Practice 3Making Change Naming Coins and Bills


Example: Make change for a $3.28 purchase from $4.00. Then name the coins andcurrency you would use.

2 pennies 2 dimes 2 quarters

+ $0.02 + $0.20 + $0.50$3.28 $3.30 $3.50 $4.00


__________ __________ __________ __________

$11.50 ________ _______ _______ _______


__________ __________ __________ ___________

$67.00 ________ ________ ________ _______


__________ __________ __________ __________

$16.10 ________ ________ ________ _______


__________ __________ __________ __________

$399.89 ________ ________ _______ ________


24/60


24

Smart Calculations Independent Practice 4Making Change Naming Coins and Bills


Example: Make change for a $49.90 purchase from $100.00. Then name the coins andcurrency you would use.

1 dime 1 fifty dollar bill _____

+ $0.10 + $50.00$49.90 $50.00 $100.00 _____


_________ __________ _________ _________

$68.05 ________ ________ ________ _________


_________ __________ _________ _________

$27.00 ________ ________ _______ _______


__________ __________ _________ ___________

$243.80 ________ ________ ________ ________


__________ _________ __________ __________ __________

$611.99 _______ ________ ________ ________ ________


25/60


25

Smart Calculations Independent Practice 5

Shorten the following arrow strings so that each has only one arrow.

Example

+ 23 + 92 + 115102 125 217 is the same as 102 217_

+ 56 + 251. 19 __ ___ is the same as 19 ___

+ 11 +3012. 74 ___ ___ is the same as 74 ____

+ 54 +207

3. 10 ___ ___ is the same as 10 ____

+ 5 + 180

4. 232 ___ ____ is the same as 232 ____

+ 63 + 6215. 63 ____ ___ is the same as 63 ____


26/60


26


Shorten the following arrow strings so that each has only one arrow.

Example

- 88 + 98 + 1091 3 101 is the same as 91 101_

- 37 + 3261. 837 ___ _____ is the same as 837 _____

- 14 + 3892. 25 ____ _____ is the same as 25 ____

- 21 +271

3. 54 ___ ___ is the same as 54 ____

- 14 + 8104. 99 ____ ____ is the same as 99 ____

- 43 + 9155. 128 ___ _____ is the same as 128 _____


27/60


27


For each of the arrow strings below, make a longer string that is easier. Then use the newarrow string to find the result.

Example

+ 39 + 30 + 946 _____ rewrite as 46 76 85

+ 1051. 28 ____ rewrite as ______ ______ ______

+ 3112. 22 _____ rewrite as _____ ______ _____

+ 193. 145 _____ rewrite as _____ _____ _____

+ 1204. 874 _____ rewrite as _____ ______ _____

+ 8035. 67 _____ rewrite as _____ _____ _____


28/60


28


For each of the arrow strings below, make a longer string that is easier. Then use the newarrow string to find the result..

Example

- 42 - 40 - 2654 ___ rewrite as 654 614 612

- 691. 387 _____ rewrite as _____ _____ _____

- 4832. 555 _____ rewrite as _____ _____ _____ ______

- 8033. 1,264 _____ rewrite as _____ _____ _____

- 5284. 3,602 _____ rewrite as _____ _____ _____ _____

- 3915. 461 _____ rewrite as _____ _____ _____ _____


29/60


29


For each of the arrow strings below make two longer strings. Then use both arrow strings to finabout the result?

Example Arrow String 1 Arrow Strin

+ 98 + 90 + 8 + 100 348 _____ 348 438 446 348 448

+ 691. 45 _____ 45 _____ _____

+ 192. 162 _____ 162 172 181 162 182

+ 173. 248 _____ 248 ______ _____ 248


30/60


31/60


31


Change each of the following calculations into an arrow string with one arrow. Then make a louse.

Example

Calculation One Arrow String Longer Arrow String

+ 714 + 700 + 10 243 + 714 243 _____ 243 943 953

1. 184 + 822 _____ ______ _____ _____ _____

2. 5,738 + 3,125 _____ _____ _____ _____

3. 494 + 1,396 _____ _____ _____ _____ _____


32/60


32


For each of the arrow strings below, either write a new string that will make the computation eaexplain why the string is already the easiest it can be.

+ 3181. 562 _____

+202. 820 _____

+ 1753. 308 _____

- 364. 400 _____


33/60


33


For each of the arrow strings below, either write a new string that will make the computation eaexplain why the string is already the easiest it can be.

+ 935 - 1101. 175 _____ _____

+46 - 2002. 279 _____ _____

+ 1,000 - 203. 1,027 _____

+ 500 - 684. 568 _____


34/60


35/60


35

Smart Calculations Word Problems D, E, F

Directions: Write an arrow string for each of these problems, showing the change using the small-coins-and-bills first method. Then write another arrow string with only one arrow to show the totalchange.

D Arlene buys a biking helmet for $27.75. She gives the cashier $40.00.

E Parker buys plastic cups, plates, and napkins for his familys picnic. The total cost forhis purchase is $12.23. He gives the cashier $15.00.

F Freddie buys two guppies, an angel fish, and a catfish for his aquarium. His totalpurchase is $11.66. He gives the cashier a twenty dollar bill.


36/60


36

Section C Formula


37/60


37

Expressions and FormulasVocabulary

Formula

A Formula tells how to do a specific type of calculation inthe form of

an Arrow Stringa calculation that is written using arrowlanguage that uses more than one arrow;

+ 15 - 410 25 21

an Arithmetic Tree amathematical map that shows theorder for performing calculations;

10 5

+15

a Word Formula a formula written in words.

x number of poundscost of apples total cost

(per pound)


38/60


38

Formulas Independent Practice 1Complete these tables by calculating the prices of different weights of produce.

Example

Weight Apples $1.00 Pears $1.50 Apricots $3.50

0.5 pounds $0.50 $0.75 $1.75

1 pound $1.00 $1.50 $3.50

2 pounds $2.00 $3.00 $7.00

1.

Weight Oranges $1.25 Grapefruit $2.50 Avocadoes $4.00

1 pound

4 pounds

6 pounds

2.

Weight Potatoes $0.50 Onions $1.00 Carrots $0.90

3 pounds

5 pounds

10 pounds


39/60


39

Formulas Word Problems A, BTaxi Fares

Use arrow strings to solve these problems.

The ABC Taxi company charges the following rates:

Starting amount (base price): $3.00Price per mile: $2.00

A. What would it cost for a ride from the train station to the zoo (6 miles)?

B. What would it cost for a ride from the zoo to the mall (11 miles)?


40/60


41/60


41

Formulas Word Problems E, FTaxi Fares

Use arrow strings to solve these problems

The Albany Airport Taxi Service takes passengers to or from the Albany International Airport inNew York to surrounding destinations within 50 miles of the airport.

Starting amount (base price): $10.00Price per mile: $3.00

E. Mr. Garcia wants the airport taxi to pick him up at his hotel in downtownAlbany and take him to the airport. The distance is 8.3 miles. How much willMr. Garcia pay for the ride?

F. Mrs. Allenwood is visiting her grandchildren. She flies into the Albany airport,and takes the airport taxi to Saratoga Springs, New York, where hergrandchildren live. The distance from the airport to Saratoga Springs is 35.5miles. What is the cost of her ride?


42/60


42

Section D Reverse Operations


43/60


43

Reverse Operations Independent Practice 1

Write the reverse for each of the following strings.

Arrow String Reverse Arrow

Example

5 + 10 x 5 - 1025 5 15 25 5 1

+ 10 x 21. 9 ____ ____ 9 ____

x 6 32. 11 ____ ____ 11 ____ _

+ 12 - 83. 14 ____ ____ 14 ____ __

- 9 x 94. 19 ___ ____ 19 ____ __


44/60


45/60


45

Reverse Operations Independent Practice 3

Write the reverse for each of the following strings.

Arrow String Reverse Arrow

Example

- 53 x 2 6 + 53 2 431 378 756 126 431 378 75

x 5 + 20 101. 824 _____ ____ ____ 824 _____ __

5 - 42 x 2

2. 625 ____ ____ ____ 625 ____

+ 122 3 - 1,0813. 3,871 ____ ____ ____ 3,871 ____ _

x 143 5 - 9994. 35 ____ ____ ____ 35 ____


46/60

dent Booklet for Expressions and Formulas (CSOS Johns Hopkins University)

46

Reverse Operations Word Problem A

Ms. Aldens class is planning a Thanksgiving dinner for a family in the school neighborhood.

Karens group is at the market to buy the turkey. Turkeys are priced $0.89 per pound. The group

has a coupon for $1.00 off the total price of a turkey.Write a formula to show how Karens group can find the price of each turkey.

The students look at 4 turkeys with the following weights: 15 pounds; 18 pounds; 20 pounds; and25 pounds.

1. Use the formula to find the cost of each turkey. Record your answers in the table.

Weight of turkey Price of Turkey

Karens group has $18 to spend on the turkey.

2. Use the formula to find the biggest turkey that Karens group can purchase.(Remember that to reverse the formula you need to reverse the operations).


47/60


47

Reverse Operations Word Problem B

The Oak Street Community Association has just opened a new clubhouse for the neighborhoodteens. It needs some finishing touches, including curtains for the windows and a puppet stage.Bobbie and Alex have volunteered to make the curtains.

To find the width of the fabric they will need, Bobbie and Alex have to measure each window.They need to multiply the width of the window by 2.5 to make the curtains full enough. They alsoneed to add 4 inches for the hems. Use this formula. Measurements are in inches.

x 2.5 + 4 (hems)width of window ______ width of fabric

1. a. Find the number of inches (width of fabric) needed to make curtains for 3windows that are

24, 38, and 45 wide.

b. Enter your answers on the chart on the next page.

2. a. The heights of the three windows are as follows; 44, 54, 63. Find thenumber of inches (length of fabric) needed to make curtains for thesewindows. Bobbie and Alex add 8 to each length for hems.

b. Use the formula to find the length of fabric they need for each window.

c. Enter your answers on the chart on the next page.

3. Bobbie and Alex also need to make a curtain for a puppet stage in a corner ofthe clubhouse. They figure that they need 154 to make the curtain wideenough.


48/60


48

a. Write a formula to find the width of the stage, based on the width formula inquestion #1. (Remember that to reverse the formula you need to reverse theoperations).

b. Use the formula to find the width of the stage.

4. They need 50 of fabric to make the curtain long enough. How high is the puppet stage?

a. Write a formula to find the height of the stage, based on the formula in question

#2. Enter your answer in the chart.

b. Use the formula to find the height of the stage. Enter your answer in the chart.

Size of window Width of Fabric Length of Fabric

24 wide44 high

38 wide54 high

45 wide63 high

Puppet Stage

____ wide

____ high

154 50


49/60


49

Section E Order of Operations


50/60


51/60


51

Expressions and FormulasVocabulary

ParenthesesParentheses are mathematical symbols that showthe order in which you should perform operations.

( )

Sometimes, they help you organize an expressionto follow the Simple Order of Operations.

12 + 5 x 10 7

12 + (5 x 10) 7

Other times, they tell you to use a different order ofoperations.

(12 + 5) x (10 7)

17 x 3 = 5


52/60


52

Order of Operations Independent Practice 1

Follow the order of operations rule to place parentheses in each problem. Thensolve the problem.

Example 144 12 x 11

144 (12 x 11)

144 132 = 12

1. 22 x 10 59 2. 936 9 + 20

3. 643 x 2 + 14 4. 745 300 6

5. 30 + 131 x 3 6. 98 7 + 686

7. 1,330 45 x 8 8. 2,076 + 1,924 4


53/60


53


Follow the order of operations rule to place parentheses in each problem. Thensolve the problem.

Example 44 16 + 3 x 20

44 16 + (3 x 20)

(44 16) + 60

28 + 60 = 88

1. 15 + 29 56 8 2. 27 3 + 42 + 9

3. 110 11 + 18 5 4. 62 41 + 81 9

5. 53 x 3 50 17 6. 64 8 + 33 + 55

7. 42 x 5 6 + 150 8. 39 14 + 72 x 2


54/60


54

Arithmetic Tree

An Arithmetic Tree is a mathematical map that

shows the order in which you should performoperations.

2 6

+

7 5 3 8

+

12

9 2 2 1

4

x x18 2

+20


55/60


55


Complete these arithmetic trees.Example 1.

11 9 6 25

12

+ +20 ___

_ _8 ___

2. 3.

38 47 55 8961

+ + ___

_ _

____


56/60


56


Complete these arithmetic trees.

Example 1.

0.5 3 7 1.10.7

+ +3.5 ____

_ _2.8 ____

2. 3.

21 4.2 0.6 0.98.1

+ +

____

_ _

____


57/60


58/60


58

Order of Operations Word Problems A, BOrganize Information Using Parentheses

A. Ms. Singh wants to make treat bags for the children in her day care center.She needs 4 boxes of granola bars at $2.00 a box; 2 bags of chocolate candy

at $5.00 a bag; and 6 packages of raisin treats at $1.00 a package. How much willthis cost altogether?

Solve the problem by writing a math sentence and using parentheses toorganize the information.

B. Colin plans to make popcorn balls to sell at his schools Halloween party.He needs to buy 4 boxes of microwave popcorn at $4.00 a box; 1 pound of sugar at$3.50/lb; 2 bottles of corn syrup at $2.00 a bottle, and 3 jars of dry-roasted peanutsat $3.00 a jar. How much will this cost altogether?



59/60


59

Order of Operations Word Problems C, DOrganize Information Using Parentheses

C. Sam needs to know how much money he will need for clothes for a ski tripwith friends. He has this list of things he will need and their prices: 6 pairs

of thermal socks that cost $9.50 a pair; three pairs of thermal underwearthat cost $30.00 a pair; two pairs of ski mittens that cost $25.00 a pair; andtwo pairs of ski pants that cost $ 60.00 a pair. The ski jacket that he wantscosts $100.00. What is the total cost for Sams ski clothes?


D. Sean is in charge of ordering craft supplies to make small gifts to sell in theOnly a Dollar booth at his schools spring fair. He will purchase 5 packagesof felt squares that cost $10.00 a package; 3 cartons of glue sticks that cost$9.75 a carton; 18 scissors that cost $2.25 each; and 20 bags of beads at$1.50 a bag. What will Seans total order cost?



60/60


Order of Operations Word Problems E, FOrganize Information Using Parentheses

E. A recipe for fruit punch uses 3 quarts of orange juice at $1.99 per quart; 2quarts of lemonade at $1.49 per quart; 4 bottles of ginger ale at $0.99 abottle; and 3 pints of orange sherbet at $2.98 pint. What is the cost tomake the fruit punch?

Start by estimating the cost. Write your estimate.


F. Sandi has volunteered to make costumes for six actors in the school play. Tomake the costumes she needs 15 yards of green satin that costs $12.98 ayard. She needs 22 yards of gold trim that costs $8.29 a yard; and sheneeds 6 zippers that cost $4.69 each. What will Sandi spend to make thecostumes?

Start by estimating the cost. Write your estimate.

Solve the problem by writing a math sentence and using parentheses to

organize the information.

ef student booklet

Documents