Algorithms and Problem Solving-1 Algorithms and Problem Solving.
Get Ready for Problem Solving
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Publisher JAYS' EDUCATION704 Old Cleveland Rd EastWellington Point Queensland 4160phone 07 3822 [email protected]
GETREADYFORPROBLEMSOLVING
Author Hana Jay
Cover design Dana Sundgren
Illustrations Dana Sundgren
Computer compilation Tom Jay
1stedition (July 2010)
Jays Education
ISBN 978-1-921622-31-1
Reproduction and communication for educational purposesThe Copyright Act 1968allows a maximum one chapter or 10% of the pages of this work,whichever is the greater, to be reproduced etc. by an educational institution for its ownpurposes, provided that the institution has given a notice to CAL Australia (in othercountries to the national Copyright Agency).
However the publisher is here with granting the right to reproduce 100% of this book tothe original purchaserfor classroom or personal use. Commercial use is prohibited.
Electronic copying, storage or transmission is permitted only for the use of the originalpurchaser. The pdf file must be left intact and in the original format and content.
Jays' Education is reserved and must be kept displayed on each sheet copied.
CAL Copyright Agency LimitedLevel 15233 Castlereagh StreetSydney 2000Phone 02 9394 7600 Fax 02 9394 [email protected]
Reproduction and communication for other purposesExcept as permitted by the Copyright Act 1968 (for example a fair dealing for the purposesof study, research, criticism or review) no part of this book may be reproduced, stored in a
retrieval system, communicated or transmitted in any form or by any means without priorwritten permission. Direct all inquiries to the publisher, see address at the top of this page.
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II Getting Ready for Problem Solving Jays Education
CONTENTCONTENTCONTENTCONTENTSSSSContentsContentsContentsContents
IntroductionIntroductionIntroductionIntroduction
Mini LUK Self Checking SystemMini LUK Self Checking SystemMini LUK Self Checking SystemMini LUK Self Checking System
Progress ChartProgress ChartProgress ChartProgress Chart
Addition activities expressed in wordsAddition activities expressed in wordsAddition activities expressed in wordsAddition activities expressed in wordsHow many altogether? ...three boys and two girls
What is the total of ...three plus four
How many do you have...? ...four and two make
What is the... ...total of eight and four
How many are... ...two more than five
What is the... ...sum of four and three
What do you get if you ...increase eight by three
How big if you... ...enlarge nine by three
How many if you... ...double three
What is the total of... ...three and three and one
Subtraction activities expressed in wordsSubtraction activities expressed in wordsSubtraction activities expressed in wordsSubtraction activities expressed in words
What is left? ...from five take four
What do get if you... ...take three from five
What will you get if you... ...subtract two from seven
What are the answers? ...six minus three
Find the... ...difference between 2 and 9
Find the answers... ...three less than seven
What is left if you... ...decrease four by three
How much more is... ...eleven than five
Mixed activities... ...decrease or increase by...
Mixed addition and mixed subtraction problems
Multiplication activities expressed in wordsMultiplication activities expressed in wordsMultiplication activities expressed in wordsMultiplication activities expressed in words
What is the product of... ...times three
What is the... product of 1 and 3
How many in... ...groups of 4
Work out how many. lots of or times or double...
Find the products. times... or groups of... or double...
How many will you get? - all mixed -
Division activitiesDivision activitiesDivision activitiesDivision activities
What is... ...half of eighteen
What will you have if... ...you divide ten by two
What is... ...the quotient of six and three
Divide... ...eight sticks among four childrenShare your... ...twelve jellybeans with dad and mum
Mixed division problems
IIIIIIIIIIII
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1111 ---- 10101010
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7
8
9
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11111111 ---- 20202020
11
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15 - 16
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18
19 - 20
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22- 23
24242424 ---- 2222924
25
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30303030 ---- 36363636
30
31
32
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35 - 36
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IIIGetting Ready for Problem Solving Jays Education
INTRODUCTION
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() 12 , 12 . 12 .
.
1. 12 1 12 .
12 1 12 .
2. ().
3. 1 1. . . . . 1 2+2= 4 1 4. 2 2 . 2 4+3=7, 2 7. 12
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4. , . . .
5. . , ! ! , ,
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1 2 3 4 5 6
7 8 9 10 11 122222
1111
IV Getting Ready for Problem Solving Jays Education
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Page Pattern Date Page Pattern
1 13
2 14
3 15
4 16
5 17
6 18
7 19
8 20
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10 22
11 23
1224
Date Page
25
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36
Pattern Date
Progress Chart Students name: ....................................................................
VGetting Ready for Problem Solving Jays Education
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three boys and two girls
a doctor
eight runners and two swimmers
one man and five boys
two babies and two children
a mother and a child
nine football players andthree soccer players
two teachers and five swimmers
six men and three women
five boys and six girls
mother, father and a baby
two boys, two girls, four babies
1
2
3
4
5
6
7
8
9
10
11
12
How many altogether?
1 Getting Ready for Problem Solving Jays Education
Add (plus) the people and write the total number in the box.
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three plus four
two plus three
one plus two
one plus one
five plus five
six plus six
five plus three
five plus six
two plus two
one plus zero
five plus four
four plus two
What is the total of ......... ?
2Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Plus (add) the two numbers and write the total number in the box.
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three and two make
zero and one make
two and two make
four and two make
five and five make
one and one make
six and six make
four and three make
two and one make
five and six make
five and four make
four and four make
How many do you have ....... ?
3 Getting Ready for Problem Solving
Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Add the two numbers and write the total number (the sum) in the box.
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What is the ......... ?
4Getting Ready for Problem Solving Jays Education
total of two and one
total of eight and four
total of five and two
total of three and one
total of zero and one
total of ten and one
total of six and four
total of four and two
total of three and five
total of six and three
total of one and one
total of three and two
1
2
3
4
5
6
7
8
9
10
11
12
Add (plus) the two numbers and write the total (number) in the box.
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two more than five
two more than three
two more than eight
one more than one
one more than three
four more than eight
three more than five
three more than eight
two more than seven
one more than zero
one more than two
two more than four
How many are ....... ?
5 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Add (plus) the two numbers and write the total number in the box.
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sum of one and two
sum of two and three
sum of one and one
sum of three and one
sum of four and three
sum of three and three
sum of five and four
sum of eight and four
sum of zero and one
sum of seven and three
sum of six and two
sum of six and five
What is the ........ ?
6Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Add (plus) the two numbers and write the total (sum) in the box.
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What do you get if you ........ ?
7 Getting Ready for Problem Solving Jays Education
increase eight by three.
increase four by three.
increase six by four.
increase eight by four.
increase one by three.
increase five by three.
increase four by two.
increase zero by one.
increase six by three.
increase three by two.
increase one by two.
increase one by one.
1
2
3
4
5
6
7
8
9
10
11
12
Increase means add. Add (plus) the two numbers and write the new increased number in the box.
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How big if you ...... ?
8Getting Ready for Problem Solving Jays Education
enlarge three by two
enlarge three by one
enlarge one by one
enlarge three by three
enlarge five by three
enlarge one by two
enlarge nine by three
enlarge six by three
enlarge zero by one
enlarge eight by three
enlarge five by two
enlarge seven by three
1
2
3
4
5
6
7
8
9
10
11
12
Enlarge means add. Add the two numbers and write the new enlarged number in the box.
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How many if you ......... ?
9 Getting Ready for Problem Solving Jays Education
double two plus one
double zero plus one
double six
double five
double three
double four
double two
double three plus one
double two plus one
double four plus one
double five plus one
double one
1
2
3
4
5
6
7
8
9
10
11
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To double a number multiply the number by 2 or add the two same numbers (twins)e.g. double six means 6 + 6.
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five and five and one
three and three and one
two and two
six and six
five and five
four and four
three and three
zero and one
one and one and one
two and two and one
four and four and one
one and one
What is the total of ...... ?
10Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Add (plus) the numbers and write the total in the box.
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What is left?
11 Getting Ready for Problem Solving Jays Education
From five take three.
From twelve take two.
From eight take three.
From four take three.
From fourteen take two.
From twelve take three.
From eleven take three.
From six take two.
From ten take four.
From nine take two.
From twelve take one.
From six take three.
1
2
3
4
5
6
7
8
9
10
11
12
Take the second number from the first number.Count back e. g. 12 - 2 12 11 10 | 10 - 4 10 9 8 7 6
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What do you get if you ........ ?
12Getting Ready for Problem Solving Jays Education
take three from five
take two from six
take two from seven
take three from four
take two from fourteen
take three from six
take four from twelve
take one from ten
take four from ten
take two from nine
take one from twelve
take three from thirteen
1
2
3
4
5
6
7
8
9
10
11
12
Take the first number from the number after the word from,e. g. 1 5 - 3 | 2 6 - 2
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What will you get if you ....... ?
13 Getting Ready for Problem Solving
Jays Education
subtract two from seven
subtract three from ten
subtract two from six
subtract two from fourteen
subtract two from twelve
subtract three from five
subtract three from nine
subtract two from three
subtract three from six
subtract one from twelve
subtract three from twelve
subtract three from eleven
1
2
3
4
5
6
7
8
9
10
11
12
Take the first number from the number after the word from,e.g. 1 7 - 2 | 2 10 - 3
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six minus three
four minus three
fourteen minus two
twelve minus two
ten minus four
twelve minus four
seven minus three
ten minus three
eight minus three
eleven minus two
twelve minus one
five minus three
What are the answers?
14Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Take the second number from the first number.
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Find the difference...
15 Getting Ready for Problem Solving
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between 2 and 10
between 2 and 14
between 2 and 11
between 2 and 9
between 2 and 5
between 2 and 13
between 2 and 3
between 2 and 8
between 2 and 12
between 2 and 4
between 2 and 6
between 2 and 7
1
2
3
4
5
6
7
8
9
10
11
12
Difference means take. Take the smaller number from the bigger number.
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between 3 and 13
between 3 and 5
between 3 and 8
between 3 and 12
between 3 and 14
between 3 and 10
between 3 and 6
between 3 and 11
between 3 and 15
between 3 and 7
between 3 and 9
between 3 and 4
Find the difference...
16Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Difference means take. Take the smaller number from the bigger number.
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three less than seven
four less than five
four less than ten
five less than eight
three less than fifteen
five less than seven
two less than twelve
three less than ten
three less than eight
two less than eleven
three less than fourteen
four less than twelve
Find the answers.
17 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Less means take. Take the first number from the second number.
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decrease four by three
decrease fourteen by three
decrease seven by three
decrease ten by two
decrease twelve by two
decrease nine by three
decrease six by four
decrease eight by three
decrease six by three
decrease eleven by four
decrease twelve by three
decrease fourteen by two
What is left if you ........ ?
18Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Decrease means take. Take the second number from the first number.
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eleven than five
twelve than three
five than four
seven than two
eleven than three
twelve than two
fourteen than two
ten than seven
five than three
thirteen than two
ten than three
seven than three
How much more is ........ ?
19 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
How much more is than means to take the smaller number from the larger number.
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fourteen than three
ten than three
twelve than eight
fifteen than three
twelve than three
ten than two
eleven than five
five than four
nine than six
eight than three
fifteen than five
six than four
How much larger is ....... ?
20
1
2
3
4
5
6
7
8
9
10
11
12
How much larger is than means to take the smaller number from the larger number.
Getting Ready for Problem Solving
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decrease twelve by three.
increase eight by four.
increase four by three.
increase seven by three.
decrease four by three.
increase seven by four.
increase one by three.
increase three by three.
decrease twelve by four.
decrease six by three.
decrease seven by five.
increase one by four.
What do you get if you ..... ?
21 Getting Ready for Problem Solving
Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Increase means to add (plus), decrease means to take the smaller number from the larger number.
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three plus four
five and six
seven minus four
take three from eleven
seven plus three
the total of seven and five
subtract four from six
from nine take four
take four from eight
take three from four
add four and five
twelve minus six
What are the answers?
22
1
2
3
4
5
6
7
8
9
10
11
12
Take notice, there are 5 addition (plus) problems and 7 subtraction (take) problems.
Getting Ready for Problem Solving
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Find the answers.
23 Getting Ready for Problem Solving
Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Notice, that there are 9 addition problems and 3 subtraction problems.Double five means 5 + 5, double three means 3 + 3.
the total of six and three
increase two by three
decrease six by four
double five
double four
double three
double two
increase seven by four
the difference between four and three
subtract three from six
add four and three
increase eight by four
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two times one
three times three
five times one
one time one
four times three
two times five
four times two
three times one
two times three
seven times one
eleven times one
two times two
What is the product of ........ ?
24Getting Ready for Problem Solving
Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Product or times means to skip count in multiples of 2, 3, 4 etc.4 x 2 2 4 6 8 | 4 x 3 3 6 9 12
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product of 2 and 5
product of 1 and 1
product of 2 and 3
product of 3 and 3
product of 2 and 6
product of 2 and 4
product of 1 and 3
product of 1 and 7
product of 11 and 1
product of 2 and 2
product of 1 and 5
product of 1 and 2
What is the ........ ?
25 Getting Ready for Problem Solving
Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Product means times, skip count in multiples of 2 or 3.
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eleven groups of 1
one group of 7
two groups of 5
three groups of 4
two groups of 2
two groups of 4
three groups of 2
one group of 1
three groups of 3
one group of 5
three groups of 1
two groups of 1
How many in ........ ?
26Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Groups of, means times (or lots of). 2 groups of 5 5 5
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double five
one time one
the product of two and three
three lots of threes
double six
two times one
three times one
double three plus one
double two plus one
double two
two fives plus one
double four
Work out how many.
27 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Double means count in 2s. Two fives means 5 and another 5. 5 5Product means times.
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three times three
seven ones
the product of four and three
five groups of two
two groups of three
two ones
two lots of two
one time one
five groups of one
three times one
double five plus one
four lots of two
Find the products.
28Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
It is a test. can you solve the problems?
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take one from six lots of two
take one from double four
double two
the product of two and three
two groups of five
two groups of one
multiply four by three
one time one
three groups of three
take one from double three
three times one
the product of four and two
How many will you get?
29 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
1 Take one from six lots of two - first work out the lots of and then take one from the answer.
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half of eight
half of twelve
half of two
half of six
half of fourteen
half of ten
half of eighteen
half of twenty-four
half of four
half of twenty
half of sixteen
half of twenty-two
What is ........?
30Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Half means divide the number by 2.
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divide six by two
divide ten by two
divide four by two
divide eight by two
divide fourteen by two
divide twelve by two
divide twenty by two
divide twenty-four by two
divide two by two
divide eighteen by two
divide sixteen by two
divide twenty-two by two
What will you have if you ........ ?
31 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Hint:Count by 2s; e. g. divide 12 by 2 = 6, count: 2, 4, 6, 8, 10, 121 2 3 4 5 6
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quotient of 6 and 3
quotient of 24 and 2
quotient of 18 and 2
quotient of 21 and 3
quotient of 15 and 5
quotient 10 and 2
quotient of 6 and 6
quotient of 18 and 3
quotient 20 and 2
quotient of 24 and 3
quotient of 12 and 3
quotient of 44 and 4
What is the quotient of ........ ?
32Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Quotient means divide.Hint:Count the number of multiples that make up the number you are dividing.
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Divide 8 sticks among 4 children.Each will have...
Divide 18 smarties among 3 children.Each will have...
Divide 16 jellybeans among 4 boys.Each will have...
Divide 3 cupcakes among 3 people.Each will have...
Divide $40 between 4 people evenly.Each will have...
Divide 20 minties among 4 girls.Each will have...
Divide 14 lollies between 2 children.Each will have...
Divide $24 between 2 people.Each will have...
Divide 12 snakes among 4 boys.Each will have...
Divide 16 stickers between 2.Each will have...
Divide $18 between 2 people.
Each will have...
Divide $33 among 3 people.Each will have...
Would you, please ........ ?
33 Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Hint:Count the number of multiples that make up the number you are dividing.
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your 24 smarties with a friend
your 16 cookies with me
your 20 crayons with me
your 22 stickers with me
your 12 jellybeans with dadand mum
your 14 shells with your dad
your 15 stamps with your 2 friends
your 6 cookies with your mum
and dad
your 18 cars with your Peter
your 12 cards with me
your 9 tokens with your 2 friends
your 3 cakes with mum and dad
Please, share ........ ?
34Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
Dont forget to include yourself in the number of people sharing the items.
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How many pairs in 24?
Half of 16
How many threes in 12?
of 22
How many fives in 50?
Half of 14
3 children share 15 apples.Each receives?
Quotient of 14 and 7
Divide 12 by 4
Half of 12 hours
Share 18 oranges between
2 children, each receives
2 shoes make how many pairs?
1
2
3
4
5
6
7
8
9
10
11
12
Work out the problems.
35
12
Getting Ready for Problem Solving
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All problems are divisions.Hint:Count the multiples that make up the number that is being divided.
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$50 10 =
Half of 2
Difference between 12 and 8
2 lots of 3
Quotient of 50 and 5
4 shoes make how many pairs?
How many shoes make 6 pairs?
How many days in one week?
Difference between 9 and 6
Half of 22
Three groups of three
The product of 4 and 2
Solve the problems.
36Getting Ready for Problem Solving Jays Education
1
2
3
4
5
6
7
8
9
10
11
12
It is a test. Can you solve all the problems?
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What is the difference between 8 and 5?
Out of 6 tadpoles 5 turned into frogs.How many tadpoles are left?
What is the product of 6 and 2?
2 lollies at 5c each would cost...
Tim walks 3 km to school and back.How many km does he walk each day?
How many shoes in 4 pairs?
Jim ate half of his 8 apples.How many apples are left?
Only half of 14 children came.
How many stayed home?
Share 15 jellybeans among 3 children.
There are three groups of 3 swimmers.How many are swimming?
What is the total of 3, 6 and 2?
Half of four eggs hatched.How many chicks do you have?
Solve the problems.
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Peter sold 2 of his 5 puppies.How many are left?
Half of 22 boys play soccer.How many do not play?
Jim had 16 stickers, he gave half away.How many does he still have?
Anna has two sets of twins.How many children does she have?
Tom had $10, he bought a book for $8.How much has he now?
Bob bought a dozen eggs.How many eggs does he have.
Gina has two $5 dollar notes.She has $.......
Share your 15 cards with 3 friends.
Each has ... cards.
14 birds, 7 flew away.There are ... birds left.
Three lots of 3 make...
6 eggs, 5 cracked.
there are ... eggs left.
Jenny sold half of her 12 lamingtons.How many are left?
Solve the problems.
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Jane had 10 chickens. She sold 7.How many are left?
We made three lots of 4 cup cakes.How many is this?
Give me half of your 14 fish and youwill have ... left.
Divide 12 cupcakes among 3 children,each will have...
There were 6 seagulls and then 5 flewaway. How many stayed?
Half of 22 children went camping.How many did not go?
3 sets of triplets = ... children
3 groups of 2 helped at a show.
How many helpers were there?
We ordered 4 pizzas, but we haveto double the number...
Half of 20 apples are rotten,how many are good?
Divide 8 marshmallows among 4
children. Each will have...
Decrease 11 by 6.
Solve the problems.
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Resources fromJays Education Reproducible Books or pr intable CDs and Downloads
Numeracy
Basic Number Concepts
Count and Write
Find the Missing Number
Starting to Add
Mental Computation Addition to 10
Subtraction Concept of 10
The Concept of 20
Money in CoinsThe Concept of Money - Coins
Tens and Ones - Focus on Money
What Time Is It?
Let's Practice Subtractions
Multiples of 2 & 20
Concept of 100 Multiples of 10 & 5
Multiply 2, 3, 4, 5
Fractions 2
Fractions 3
Fractions 4
All about Angles "A"
All about Angles "B"
Angles in Triangles
Simple Steps to Algebra
The Four Operations
J a y s J a y s J a y s J a y s EducationEducationEducationEducationPhone/Fax: 07 3822 1813Phone/Fax: 07 3822 1813Phone/Fax: 07 3822 1813Phone/Fax: 07 3822 1813
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Visual Literacy
Basic Pencil Skills
More Pencil Skills
Reading Readiness
Drawing Workshop -Learn to Draw in Few Steps
LUK Self Checking Program
Addition level 1
Addition level 2
Subtraction level 1
Subtraction level 2
Multiplication level 1
Multiplication level 2
DIVISION Halves and Quarters
Get Ready for Problem Solving
Concept of Money
Fractions
Reading & Spelling Essentials
Reading and Spelling Single Words
Literacy
Reading Readiness
Teaching Reading
Let's Start Read and Write
Using Phonics
Read About Write About Dotty
Read About Write About Spotty
Adventures with Dotty and Spotty
Magic eSounds are Simple
Spell Well to Excel 1