Bar Model Junior

7/28/2019 Bar Model Junior

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Infinite Math Bar Model

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MODEL-DRAWING to solve problems

Level 1.1

Finding an unknown number. Study the following

examples.

Question 1a: Find the unknown number in the box.

- 7 = 5

From the above model you can see that trhe unknown

number in the box is equal to 7 + 5, which is 12.

(Double check - 7 = 5)

7

Take 7 awa Leaves 5

?


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Finding an unknown number.

Question 1b: Find the unknown number in the box

- 18 = 9

Draw your own model on a piece of paper to answer this

questions.

Its great if you can calculate the answer mentally,

without drawing the model. Then check the answer.

9

- 18 =9

= 9 + 18

= 27

- 18 = 9

The number in the box is 27

?

?

27

18 ?

?

?

27


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Now you should be able to find the unknown numbers

without model drawing!

- 13 =8

= 8 + 13 (So it is actually an addition sum!)

= 21

- 13 = 8

can do these

Practice 1 :

Try the following exercise: (You can do these mentally)

?

?

21

1.

- 12 = 10 4.

- 30 = 60

2. - 15 = 15 5. - 65 = 100

3. - 20 = 25 6. - 73 = 127


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Question 2a

Pam had some stamps. After she gave away 280 stamps

to her brother, she had 754 stamps left. How many

stamps did Pam have at first?

The number sentence for this problem is :

- 280 = 754This model stands for the unknown numbers of stamps.

?

Solution to Q2a

Number sentence - 280 = 754

?

Gave away280 754

?

= 754 + 280

= 1034

1034 - 280 = 754

Pam had 1034 stamps at first.

You can solve this problem without drawing this model, once

you know how to write a number sentence for it!

(saves your time)


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Question 2b

Mrs Brown went shopping . She spent 125 dollars on a

dress. Thn she had 137 dollars left. How much money

didi she have at first?

?

dress

Solution to Q2a

Number sentence - 125 = 137

Spent

RM125RM 137 left

?

? = 137 + 125

= 262

262 - 125 = 137

At first Mrs Brown had 262 dollars.


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Question creation: (Work on a piece of paper)

Create your own question and solution. (You can use the

guideline below.)

Get someone (eg parents) to help check the answer.

If you have done correctly, you have mastered the

concept of solving this type of problem. Congratulation!

Have fun creating problems for your friends to solve!

Mary baked some tarts for her party. Her friends ate

______ of the tarts during the party. There were _____

tarts left over. How many tarts did Mary bake?

Practice 2:

1) Mary had some money in her bank. Then shetook out RM25 to buy a birthday present for her

brother. After that she had RM35 left in her

bank. How much money was there in her bankat first?

?

Money left in bank Cost of present

Number sentence :

- 25 = 35

RM 35RM 25

?


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2) Ben had some stamps in his album. Then hegave 175 stamps to his sister. Then he found

that he had only 245 stamps left. How many

stamps did he have at first?

3) Mel wanted to pick her picture cards into a box.The box could hold only 396 cards. He still had

236 more cards left over. How many picture

cards did he have altogether?4) Many children visited the zoo on Sunday. The

first 200 children were given a free balloon

each.150 children were disappointed because

they did not receive any balloons. How many

children visited the zoo on Sunday?

5) Mr Brown bought a packet of sweet for achildrens party. The children ate 148 sweets.

After the party, Mr Brown still had 52 sweetsleft. How many sweets were there in the

packet?

6) After spending RM 35.50, Max had RM 20.50left. How much money did Max have at first?

?

Stamps left in album Gave sister

Number sentence :

- 175 = 245

245 175

?


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MODEL-DRAWING to solve problems

Level 2.1


Question 1a: 35- ? = 13 (What is the number in the

box?)

Study the following example.

35

? 35

35- =13

35 13 =

35 13 = 22

The number in the box is 22.

?

?


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Question 1b: Find the unknown number in the box.

99 - = 43

Draw your own model on a piece of paper to answer this

question.

Then check the answer.

?

99

The number in the box is 56

99 - = 43

= 99 43

= 56

?

?

43

Take away

?


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Now you should find the numbers without model

drawing!

Example : 85 - = 38

= 85 38

= 47

Practice 1

Try the following exercise:

1. 97 - = 16 4. - 30 = 601. 97 - = 16 5. - 65 = 1001. 97 - = 16 6. - 73 = 127

?

?


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Question 2a:

Jack went to a book store to buy a dictionary. He gave a

cashier a RM 100 note. He got a back RM 22 change.

How much did the dictionary cost?

Question 2a:

On your paper or exercise book, write a number

statement for the problem.

- =

Draw the model for the above number statement on your

paper or book.

100 ? 22

Gave

cashier

Unknown

cost

Change


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Answer for Q2a

Question 2b:

100

? 22

Take away cost of dictionary

Number sentence 100 - = 22

= 100 22

= 78

The dictionary cost RM 78

?

?

You can solve the problem without drawing the model,

once you know how to write a number sentence for it!

(saves your time)


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There were 520 students in Hillview Primary School in

January. In June, some students left to join another

school. Only 23 students remained in the school. How

many students went to join other school?

Answer to Q 2b:

Hints for Q 2b:

On your paper, write out the number statement. Use the

guideline below.

- =

Draw a simple model on your paper to solve this problem

or find the answer by working out the number sentence.Then check your answer on the next slide.

No. of

students

in Jan

Dont know

how many

left

How manyremained?

520

520 - = 213

= 520 213

= 307

?

?

307 students went to join the other school

?213went to another

school


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There were _____ balloons for a sale at a fair. By the end

of the day _____ balloons were left. How many balloons

were sold at the fair?

Practice 2:

Try to solve these problems. Draw a model to understand

each problem. If you can understand each problem

without drawing the model, just write a number

sentence to solve it.

1. On Monday, a store had 2348 toy cars for sale. ByWednesday there were only 456 toy cars left. Ho

many toy cars were sold?

2. Kelly has RM27. Annie has RM 5.50 less thanKelly.

a) How much money does Annie have?b) How much money do both of them have

altogether?

3. George and Ben bought a present for Ann.George paid RM 6.80 and Ben paid RM4.90.

a) How much did the present cost?b) How much less did Ben pay?

4. Mr. Donald has RM125. He needs RM12.90 moreto buy a watch. How much does the watch cost?

5. 2345 people visited the circus last Sunday. 986were adults and the rest were children.

a) How many more visitors were children?b) How many more children than adults

visited the circus?


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Model Drawing to solve problems

Level 3.1

A quick recap:

(Counting by 2s)2,4,6,8,10,12,14,16,18,20,22,24

(Counting by 3s)3,6,9,12,15,18,21,24,27,30,33,36

(Counting by 4s) - 4,8,12,16,20

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,

23,24,25,26,27,28

(Counting by 5s)5,10,15,20,25,30,35,40,45,50,55,60

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,

23,24,25

(Counting by 10s) 10,20,30,40,50,60,70,80,90,100,

110,120

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,

23,24,25,26,27,28,29,30

You need to understand and memorize these

multiplication tables.

Prerequisite for level 3: an understanding of the

multiplication tables 2,3,4,5 & 10


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Sample problem:

There are 5 rows of chairs. Each row has 4 chairs. How

many chairs are there altogether?

Method 1:

model drawing

Method 2: Quick drawing

cccc

cccc

cccc

cccc

cccc

R1

R2

R3

R4

R5

1 2 3 4

8

12

16

20

5 rows 4 chairs =

20 chairs

There are 20 chairs

altogether

5 4 = 20 chairs

There are 20 chairs

altogether

Method 3:Mental Calculation

I know

multiplication

tables!

5 4 = 20


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Problem 1a:

Work out this problem in your exercise book or paper.

You can use any method, as long as you get the correct

answer.

Davids pocket money is RM3 a day. How much money

does he receive in a week?

RM

3

RM

3

RM

3

RM

3

RM

3

RM

3

RM

3

7 3 = 21

He gets 21 dollars a week. There are

7 days in

a week.


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Question 1b:

Work out this problem in your exercise book or paper.

Can you calculate the answer mentally?

There are 10 similar of beads. Each box has 5 red beads

and 4 blue beads. How many beads are there altogether?

5 + 4 = 9

There are 9 beads in each box.

10 9 = 90

There are 90 beads altogether.


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Q 2a:

After buying 6 melons at RM8 each, Jane had RM 12 left.

How much money did Jane have at the beginning?

Solution to Q 2a:

6 8 = 48 RM 12

Janes money at the beginning.

6 8 = 48

Jane spent RM 48 on 6 melons

48 + 12 = 60

She had RM60 at the beginning


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Question 2b:

After buying 3 tins of milk and 7 boxes of chocolates, Mrs

Brown had RM9 left. How much did she have at first?

RM 10 each RM 5 each

Milk (3 RM 10) Chocolates (7RM 5) RM 9

3 tins of milk 3 RM 10 = RM 30

7 boxes of chocolates 7 RM 5 = RM 35

She spent RM 30 + RM 35 = RM 65

RM 65 + RM 9 = RM74

Mrs Brown had RM 74 at first.

Milk Chocolate


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Practice 1: Try solving this problems yourself.

1. A toy car cost RM 8. Bob bought 4 toy cars and abag for RM42. Find the cost of the bag.

2. A teacher bought some sweets for her class of20 students. After giving 5 sweets each, she had

10 sweets left. How many sweets did she buy?

3. A baker bought 4 trays of eggs. Each tray had 12eggs. He used some eggs to bake 3 cakes. Then

he had 18 eggs left. How many eggs did he use?

4. Mary read 12 pages of a story book per day. Shefinished reading the book in 5 days. How many

pages are there in the book?

ANSWER TO PRACTICE 1: Q1:

A toy car cost RM 8. Bob bought 4 toy cars and a bag for

RM42. Find the cost of the bag.

RM 42

Bag 4 toy cars

? 4 RM 8

4 toy cars 4 RM 8 = RM 32

Bags RM 42 - RM 32 = RM 10

The bag cost RM 10


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A teacher bought some sweets for her class of 20

students. After giving 5 sweets each, she had 10 sweets

left. How many sweets did she buy?

Total number of sweets

10 20 5

? 4 RM 8

Sweets for 20 students 20 5= 100

Number of sweets 100 + 10 = 110

She bought 110 sweets


A baker bought 4 trays of eggs. Each tray had 12 eggs.

He used some eggs to bake 3 cakes. Then he had 18

eggs left. How many eggs did he use?

4 trays of eggs

4 12 = 48

The baker bought 48 eggs.

48 eggs

48 18 = 30

Used for left

cakes

He used 30 eggs.

12 12 12 12

? 18


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Mary read 12 pages of a story book per day. She finished

reading the book in 5 days. How many pages are there in the

book?

Whole book

12 12 12 12 12

Pages read per day 12

Pages read in 5 days 5 12 = 60

There are 60 pages in the storybook.

After buying ____ books at RM ____ each, Alice had

RM ____ left. How much money did Alice have at first?


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Mental sums (1):

Try the mental sums. Look at the model drawing.

- 20 = 42

?

Take

away

20 42

more than 42 is 64

64

more

42 ?

56 - = 30

56

Take

away

? 30

45 is less than 100

100

? less

20 42

Mental sums (1): Answers

1. 62 20 = 42 2. 56 26 = 303. 22 more than 42

is 64

4. 45 is 55 less than100

? ?

? ?


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Mental sums (2): Find then missing number in the box

1. 45 = 502. 77 + = 903. 40 is more than4. is 35 less than 80Mental sum (2): Answers

1. 45 = 502. 77 + = 903. 40 is more than4. is 35 less than 80

?

?

?

?

13

27

45

95


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Practice 2:

Solve the following problems. Model-drawing is

encouraged but you may also use any other method as

long as the steps are clearly worked out.

1. Ken has 5 stickers. Lenny has 5b times as many asstickers. How many stickers do both of them have

altogether?

2. There are 6 rows of desks in Marys classroom. Thereare 5 desks in each of the first 4 rows and 3 desks in

the last 2 rows. How many desks are there in Marys

classroom?

3. Mrs Brown baked some tarts. She gave 9 tarts to eachof her 4 friends. Then she had 15 tarts left. How many

tarts did Mrs Brown bake?

4. Mr Roberts collected 4 piles of 10 worksheets fromclass 3A and 6 piles of 8 worksheets from class

3B.How many worksheets did Mr Robert collect fromthe 2 classes?

5. 7 classes of students went to watch a show. Eachclass had 3 students and 2 teachers. How many

people went to watch the show?


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Question 1:

There are 424 apples in Basket A and 381 in Basket B.

How many apples are there in two baskets?

There are apples in the two baskets

Question 2:

Michael has 55 stickers. James has 28 fewer stickers than

Michael. How many stickers that James have?

James has stickers


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Question 3:

Eric has 350 seashells. He has 60 seashells more than

Anna-Maria. How many seashells does Anna-Mariahave?

Anna-Maria has seashells.

Question 4:After lending Michiko 64 pieces of colored paper, Henry

had 49 pieces left. How many pieces of colored paper did

Henry have in the beginning?

Henry had pieces of colored paperin the beginning


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Question 5:

Madison completed 431 questions in her workbook. 214

of her answers were correct. How many answers werewrong?

answers were wrong.

Question 6:

Ms Jackson gad some stamps. She gave 31 stamps to

Kyra, 57 stamps to Darius, and had 21 stamps left. How

many stamps did Ms Jackson have in the beginning?

stamps in the beginning


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Question 7:

Randy has 83 balloons. Kaylee has 21 fewer balloons than

him. How many balloons does Kayle have?

Kaylee has balloons

Question 8:

Mr Gracia sold 341 eggs on Monday. He sold 291 eggs on

Tuesday. How many more eggs that he sell on Monday

than on Tuesday?

more eggs on Monday than onTuesday


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Question 9:

A television set costs RN581, and a DVD player costs

RM289. Mr. Ito paid the cashier RM1000.a) How much does the television set and the DVD

player costs altogether?

b) How much change did Mr. Ito receive from thecashier?

The television set and the DVD player cost RM

Mr Ito received RM in change.

Question 10:

Dad gave Tyler and Emily the same amount of pocket

money. Emily bought a T-shirt for RM41, and she had

RM6 left. How much money did Dad give Tyler?

Dad gave Tyler RM


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Question 11:

After collecting 89 ice-cream sticks, Ahmad had 501 ice-

cream sticks altogether. How many ice-cream sticks didWhat he have in the beginning?

He had ice-cream sticks in the

beginning

Question 12:

Alexis has RM53. She needs RM29 more to buy a

scooter. What is the cost of the scooter?

The cost of the scooter is RM


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Question 13:

Joseph has 99 marbles. He has 35 more marbles than

Elijah. How many marbles does Elijah has?

Elijah has marbles.

Question 14:Alex has 281 stickers. His sister gives him another 29

stickers.

a) How many stickers does Alex have now?b) If Alex gives 99 stickers to his friends, how

many stickers does he have left?

Alex has stickers now.

He has stickers left.


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Question 15:

Taneesha has 345 stamps. Stephen has 56 fewer stamps

than her. Lily has 9 stamps more than Taneesha.a) How many stamps does Stephen have?

b) How many stamps does Lily have?

Stephen has stamps.Lily has stamps.

Question 16:

Mr Bell baked some cookies. After selling 341 cookies,

he had 39 cookies left. How many cookies did Mr Bell

bake?

Mr Bell baked cookies.


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Question 17:

Lucy had 536 stamps. She gave 312 stamps to Salima and

used 102 stamps to mail greeting cards. How manystamps did she have left?

She had stamps left.

Question 18:There are 316 boys in Green Valley Elementary School.

There are 180 more boys than girls.

a) How many girls are there in the school?b) What is the total number of students in the

school?

There are girls in the school.

The total number of students in the school is


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Question 19:

A red stick is 189 cm long. A white stick is 85 cm long.

How much longer is the red stick than the white stick?

The red stick is cm longer than the

white stick.Question 20:

Jorge sold 350 oranges in the morning and another 81

oranges in the afternoon. He still had 65 oranges left at

the end of the day. How many oranges did he have in the

beginning?

He had oranges in the beginning.


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Question 21:

There were 378 boys and 209 girls in the school choir lastyear. 95 boys and 35 girls joined the school choir last

year.

a) How many students were in the school choir lastyear?

b) How many students joined the school choir thisyear?

students were in the school choir

last year.

students joined the school choir

this year.


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Question 22:

Nicholas and his brother each have 421 marbles. Nicholas

receives 59 more marbles from his friends.a) How many marbles does Nicholas have now?

b) How many marbles do Nicholas and his brotherhave altogether?

Nicholas has marbles now.Nicholas and his brother have

marbles altogether.


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Question 23:

Mrs. Spisak baked 250 chocolates cookies. She baked 79

fewer strawberry cookies than chocolate cookies. Howmany strawberry cookies did she bake?

She baked strawberry

cookies.

Question 24:

There are 458 girls and 641 boys in the school

auditorium. How many more boys are than girls are there

in the auditorium?

There are more boys than girls in

the school auditorium.


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Question 25:

Max, Noel, Yoko, and Julia shared 36 grapes equally.

How many grapes did each of them get?

Each of them got grapes.

Question 26:Mrs, Cook has 3 bags of oranges. Each bag contains 4

oranges.

a) How many oranges does she have altogether?b) If she takes all the oranges out of the bags and

puts an equal amount on 2 plates, how many

oranges will there be on each plate?

She has oranges altogether.

There will be oranges on each

plate.


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Question 27:

Jasmine had some money in her purse. She used RM251

to buy a ring and had RM25 left. How much money didshe have in the beginning?

She had RM in the beginning.

Question 28:

1lb. of fish costs RM9. What is the cost of 3 lb. of fish?

The cost of 3 lb. of fish is RM .


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Question 29:

A red notebook costs twice as much as a pink notebook. If

the red notebook costs RM 18, what is the price of thepink notebook?

The price of pink notebook is RMQuestion 30:

There are 5 pencils in a bag. There are 3 times as many as

pencils in the same bag. How many pens are in the bag?

There are pens in the bag


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Question 31:

Clara bought a dress for RM16. She gave the cashier

RM20 and got back the change in 1dollar bills. Howmany dollar bills did she get back?

She got 1- dollar bills back.

Question 34:

Lim put 128 red marbles into Bag A, 215green marbles

into Bag B, and some white marbles into Bag C. He put a

total of 500 marbles into the 3 bags.a) How many marbles were there altogether in Bag

A and Bag B?

b) How many white marbles did he put into Bag C?

a) There were marblesaltogether in Bag A and Bag B.

b) He put white marblesinto Bag C.


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Question 35:

There are 250 adults, y60 girls and 30 boys on a train.How many more adults are there than children?

There are more adults than

children.


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Question 36:

Uncle Sam had 3 apple trees. He picked 8 apples fromeach tree.

a) How many apples did he pick altogether?b) Uncle Sam shared all the apples equally among

his 4 children. How many apples did each child

get?

He picked apples together

Each child got apples.


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Question 37:

Meena, Lauran, and Minh shared 30 crackers equallyamong themselves.

a) How many crackers did each girl get?b) How many crackers did Meena and Lauran have

altogether?

Each girl got crakers

Meena and Lauran had crackers

altogether


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Question 38:

Boxes A, B, and C have a total weight of 85kg. Boxes Aand B have a total weight of 46kg.

a) Find the weight of box Cb) If box C is 21 kg heavier than Box A, find the

weight of Box A.

a) The weight of Box C is kgb) The weight of Box A is kg


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Question 39:

Mr Rulaski gives RM30 to Bailey and Jenny. If Baileygets twice as much as money as Jenny, how much will

Jenny get?

Jenny will get RM


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Question 41:

Tierra has 7 flowers. Megan has twice as many as Tierra.How many flowers do the girls have altogether?

They have flowers altogether.


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Question 41:

Emilio bought a pen and a watch. The watch cost threetimes as much as the pen. If Emilio paid RM5 for the pen,

how much did he pay for the watch?

He paid RM for the watch.


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Question 43:

Kimiko had 18 colored pencils. She shared equally withher sisters. How many colored pencils did Kimiko get?

Kimiko got colored pencils

Question 56:

Every day, Mrs Romano mixes 22gal of water with 11 gal

of lemon syrup to make drinks to sell. How many gallonsof drinks does she make every day?

She makes gallons of drinksevery day.


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Question 57:

Jacks weight is 29kg. Binh is 9kg heavier than Jack.Cooper is 8kg lighter than Binh.

a) what is Binhs weight?b) what is Coopers weight?

a) Binhs weight is kgb) Coopers weight is kg


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Question 58:

Luis had 100 oranges. 30 of them were rotten. He packedthe rest equally into 10 boxes.

a) How many good oranges were there?b) How many oranges were there in each boxes?

There were good oranges

There were oranges in each box.


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Question 58:

Natasha has RM10. Zoe has twice as much as Natasha.

Allison has RM40 more than Zoe.

a) How much money does Zoe have?b) How much money does Allison have?

Zoe has RM

Allison has RM


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Question 60:

A workbook costs 70 cents. A box of colored pencilscosts 90 cents more than the workbook. How much do

the workbook and the box of colored pencils cost

altogether?

They cost cents altogether.


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Question 61:

Simon has 8 five-cent coins and 5 ten-cents coins.

a) How much money does he have in five-centcoins?

b) How much money does he have in ten-centcoins?

He has cents in five-cent coins

He has cents in ten-cent coins


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Question 62:

12 people took part in a race. Jonah was 7 th from the front.He later overtook 3 people. How many people were

behind Jonah at the end of the race?

people were behind Jonah at the end

of the race.


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Question 63:

Malik has 10 stamps. Kevin has 3 times as many stampsas Malik. How many stamps do they have altogether?

They have stamps altogether


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Question 64:

4 teachers and 40 girls went on an overnight trip. Therewere 5 girls in each room. The 4 teachers slept in 2

rooms. How many rooms did the group use altogether?

The group used rooms

altogether.

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Bar Model Junior