e v o r p m I o T g Strivin
Integers Integers is one of eight books in the Striving To Improve series. This series is targeted at students aged between 11 and 15 years of age who, for whatever reason, are struggling to keep up with their peers. The activities in this book are designed to prevent students from regressing any further at school. Each worksheet is based on a modi�ied curriculum, and tasks have been designed so that students can work at their own pace and without constant supervision from the teacher.
e v o r p m I o T g n i v i r St
Integers For students aged 11 - 15 years who are underachieving at their year level.
Integers will help students consolidate written and mental methods of calculation. Addition and subtraction with two and three digit sums, division, multiplication, place value, rounding, estimation, factors, multiples and the concept of directed number are all addressed in this book.
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STRIVING TO IMPROVE
Integers ISBN 978 186 397 850 7
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Ready-Ed Publications
Edited by Mirella Trimboli
This is a Ready-Ed Publications' book preview.
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This is a Ready-Ed Publications' book preview. Series: Striving to Improve Title: Integers © 2013 Ready-Ed Publications Printed in Australia Edited by Mirella Trimboli Contributing authors are: Jane Bourke, Mirella Trimboli
Acknowledgements i. I-stock Photos. ii. Clip art images have been obtained from Microsoft Design Gallery Live and are used under the terms of the End User License Agreement for Microsoft Word 2000. Please refer to www.microsoft.com/permission.
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2.
Copies are made only by reprographic means (photocopying), not by electronic/digital means, and not stored or transmitted;
3.
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4.
Every copy made clearly shows the footnote, ‘Ready-Ed Publications’.
Any copying of this book by an educational institution or its staff outside of this blackline master licence may fall within the educational statutory licence under the Act. The Act allows a maximum of one chapter or 10% of the pages of this book, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that
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ISBN: 978 186 397 850 7 2
Contents
This is a Ready-Ed Publications' book preview. Teachers’ Notes Curriculum Links
4 5
Understanding Integers: Teachers’ Notes Place Value 1 Place Value 2 Place Value 3 Greater Than/ Less Than Rounding 1 Rounding 2 Estimation 1 Estimation 2 Counting By Multiples Factors Imagining Negative Numbers Where Am I?
6 7 8 9 10 11 12 13 14 15 16 17 18 19
Calculating with Integers: Teachers’ Notes Rule Of Order 1 Rule Of Order 2 Addition 1 Addition 2 Addition: Regrouping 1 Addition: Regrouping 2 Addition: Regrouping 3 Addition: Regrouping 4 Subtraction 1 Subtraction 2 Subtraction: Regrouping 1 Subtraction: Regrouping 2 Subtraction: Regrouping 3 Subtraction: Regrouping 4 Addition And Subtraction 1 Addition And Subtraction 2 Real Life Addition Real Life Subtraction Real Life Addition And Subtraction Multiplication: Regrouping 1 Multiplication: Regrouping 2 Multiplication: Regrouping 3 Multiplication: Regrouping 4 Multiply These! Division 1 Division 2 Division With Remainders 1 Division With Remainders 2 Division With Regrouping 1 Division With Regrouping 2 Real Life Multiplication Real Life Division
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
Answers
53
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Teachers’ Notes
This is a Ready-Ed Publications' book preview. This resource is focused on the Number and Algebra Strand of the Australian Curriculum for lower ability students and those who need further opportunity to consolidate these core areas in Mathematics. Each section provides students with the opportunity to consolidate written and mental methods of calculation, with an emphasis on process and understanding. The section entitled Understanding Integers enables students to reencounter ideas of place value, rounding, estimation, factors, multiples and the concept of a directed number. These activities are a useful way to scaffold a new unit of Mathematics and will help build confidence for lower ability students to attempt more challenging problems at their year level. The section entitled Calculating With Integers walks students through the four core calculations. The activities are designed to guide student learning with minimal input from the teacher and there is a strong emphasis on process and understanding. Students explore addition and subtraction with two and three digit sums and can apply what they have learned to some real life application problems. Similarly, students explore the various levels of multiplication and division before applying them to a variety of applications. The activities can be used for individual students needing further consolidation in a mainstream classroom or as instructional worksheets for a whole class of lower ability students. The activities are tied to Curriculum Links in the Australian Curriculum ranging from grade levels of Year 4 through to Year 7 and are appropriate for students requiring extra support in Years 7, 8 and 9. It is hoped that Integers will be used to help teachers provide appropriate resources and support to those students in greatest need. The book as a whole can be used as a programme of work for those students on a Modified Course or Independent Learning Programme. Activities are sufficiently guided so that students can work independently and at their own pace without constant supervision and guidance from the teacher.
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Curriculum Links
This is a Ready-Ed Publications' book preview. Understanding Integers
Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)
Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) Investigate everyday situations that use positive and negative whole numbers and zero. Locate and represent these numbers on a number line (ACMNA124) Calculating With Integers Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123) Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Solve problems involving multiplication of large numbers by one- or twodigit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
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Teachers’ Notes
This is a Ready-Ed Publications' Understanding Integers book preview. The activities in this section allow students to revise many of the core Number properties and ideas. Before introducing lower ability students to new work on Integers, these activities will encourage students to consolidate concepts from previous years. The concepts covered include:
Place Value
Students have the opportunity to explore what they know about place value for integers and to understand the composition and relative magnitude of numbers. These activities are particularly useful before moving on to calculations and work with numbers involving decimals.
Rounding
As a concept with which many students experience difficulty, it is important to allow for a thorough consolidation of rounding integers to specified place values. This is important work to include prior to work on rounding decimals, working with scientific notation and significant figures.
Estimation
To assist students with building their appreciation and understanding of working with numbers, estimation is a core skill. These activities will encourage students to reflect on whether their calculations are providing reasonable solutions.
Factors and Multiples
As a precursor to working on patterns and number theory, students need to have a strong grasp of the factors and multiples that compose a number. These activities allow students to revise these concepts.
Directed Numbers
As the majority of work on Directed Numbers is taught in Lower Secondary, these activities allow students to understand, through real life applications, the contexts for negative integers.
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* Place Value 1
This is a Ready-Ed Publications' book preview. Example zz If the number is whole, then the last digit on the right is in the ones column. Digit value tells you how much a digit is worth in a number. Look at the digits in the number 1 234 589 below:
Digit
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
1
2
3
4
5
8
9
200 000
30 000
4 000
500
80
9
Value 1 000 000
* Task a
Write the values for the numbers in the table below.
Start by placing the last whole digit in the ones column, then work from right to left until there are no more digits. Thousands
Hundreds
Tens
Ones
3 000
600
40
7
3 647 8 427 3 975 5 927
* Task b
Write the value of the 4 in each number.
Number
Value
Number
e.g. 347
40
1004
4 273
Value
3430
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4638
3 476
10342
7
* Place Value 2 zz If the number is whole, then the last digit on the right is in the ones column. Digit value tells you how much a digit is worth in a number. Look at the digits in the number 1 234 589 below:
This is a Ready-Ed Publications' Example book preview. Digit
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
1
2
3
4
5
8
9
200 000
30 000
4 000
500
80
9
Value 1 000 000
* Task a
Write the values for these digits. Work from right to left.
Number
Thousands
Hundreds
Tens
Ones
3 647
3 000
600
40
7
2 364 9 845
* Task b
Number
Write the value of the bold digit. Value
Number
347
599
5 738
3 126
3 921
5 991
9 032
4 679
* Task c
Value
Use these to write the number.
Thousands
Hundreds
Tens
Ones
Number
5000
300
40
2
5342
2000
400
70
6
8000
200
60
6
9000
500
50
3
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8
* Place Value 3
Task A Write this number so that the digits are in the correct columns. * Seven million, four hundred and fifty-six thousand, three hundred and twenty-two.
This is a Ready-Ed Publications' book preview. Millions
1 000 000
* Task b
Hundred Thousands 100 000
Ten Thousands 10 000
Thousands
Hundreds
Tens
Ones
1 000
100
10
1
Show these numbers on the table below. 1 000 000 100 000
10 000
1 000
100
10
1
5 498 765 2 098 634 4 200 049 187 685 280 097 35 497
* Task c
Write the following numbers in expanded form.
3 487 978
E.g. (3 x 1 000 000) + (4 x 100 000) + (8 x 10 000) + (7 x 1000) + (9 x 100) + (7 x 10) + (8 x 1).
_______________________________________________________________________ 2 876 543 _______________________________________________________________________ 7 653 012 _______________________________________________________________________
* Task d Number
Write the place value and the face value for the underlined numbers below. Place Value
Face Value
Number
20 000
5 364 243
Place Value
Face Value
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3 425 643 ten thousands 3 298 765
2 509 345 9
* Greater Than / Less Than zz > means “greater than” < means “less than”. The “pointed part” always points to the smaller number, and the “wide open part” opens to the larger number. Look at the examples below.
This is a Ready-Ed Publications' book preview. Example
Compare 460 and 4007.
Which number has MORE place values (before the decimal point)? Thousands Hundreds 4
Tens
Ones
6
0
Thousands Hundreds 4
0
460 does not have anything in the Thousands, so 4007 is larger.
Tens
Ones
0
7
460 < 4007
Compare 4570 and 4507.
Example
If both numbers have the same number of place values, start comparing from the left until you find the number that has the FIRST largest place value. Thousands Hundreds
Tens
Ones 0
4
5
7
Same
Same
Larger
Thousands Hundreds
Tens
Ones 7
4
5
0
Same
Same
Smaller 4570 > 4507
7 is larger than 0, so 4570 is larger. This is written as …
* Task a
Place the > or < in between these sets of numbers to show which is greater. 1. 276
______
982
9. 44
______
1200
2. 986
______
709
10. 9778
______
9807
3. 401
______
410
11. 45 961
______
45 916
4. 1872
______
1287
12. 49 876
______
49 878
5. 780
______
708
13. 415 987 ______
415 899
6. 1457
______
999
14. 986 002 ______
986 020
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7. 2790
______
2900
15. 788 987 ______
98 987
8. 3000
______
2899
16. 565 231 ______
542 956
* Task b
10
Use a separate piece of paper to write your own.
* Rounding 1 zz Rounding means finding the closest 10, 100 or 1000. When the number ends in 5, like 5, 15, 25 you can round up or down (usually up).
This is a Ready-Ed Publications' book preview. 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
Task a Circle the number 12. * How many squares is it away from 10?__________ How many squares is it away from 20?__________ 12 is closer to 10, so you round 12 to 10.
1
2
3
* Task b
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
Round these numbers to the nearest 10. Circle the correct answer.
8 = 10 or 20
13 = 10 or 20
19 = 10 or 20
16 = 10 or 20
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
* Task c
Round these numbers to the nearest 10.
15 = ______ or ______
18 = ______
25 = ______ or ______
27 = ______
12 = ______
30 = ______
10
* Task D
20
30
40
50
60
70
80
90
100
Use these numbers to find the rounded answers.
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23 = ______
67 = ______
45 = ______ or ______
99 = ______
52 = ______
38 = ______
75 = ______ or ______
14 = ______
11
* Rounding 2 zz Rounding means finding the closest 10 or 100 or 1000. When the number ends in 5, like 5, 15, 25 you can round up or down (usually up).
This is a Ready-Ed Publications' book preview. Circle the number 12 in the number grid below. Is it closer to 10 or 20? 12 is closer to 10, so you round 12 to 10.
Example 1
2
3
4
* Task a 2
3
* Task b
6
7
9 10 11 12 13 14 15 16 17 18 19 20 21 22
8
Round these numbers to the nearest 10.
6 = _______
1
5
13 = _______ 18 = _______ 20 = _______ 15 = _______ or _______
4
5
6
7
9 10 11 12 13 14 15 16 17 18 19 20 21 22
8
Use the number grid below to find the rounded numbers.
22 = _______
64 = _______
10
20
30
35 = _______ or _______
40
Task c * Fill in the missing numbers to show
where you would round up or down to the nearest 100.
50
60
70
80
98 = _______
90
100
Task d * Fill in the chart like you did left, then
round the number to the nearest 100. Round Down
Half way
100
0
50
100
80
150
200
100
150
200
120
250
300
200
250
300
399
400
401
Round Down
Half way
Round Up
0
50
100
350 450 600
Round Number Answer Up
100
OR
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600
800
850
1000 12
500
500
600
626
700
772
* Estimation 1
This Taskisa a Ready-Ed Publications' * book preview. Look, guess then count the number of boxes.
Guess: ____________
* Task b
Count: ____________
Was it close? ____________
Look, guess then count the number of diamonds:
Guess: ____________
Count: ____________
Was it close? ____________
Task c Round numbers and do the sum. * 31 31 is close to 30 Estimate: 30 + 60 = 90
+ 58 Answer 89
58 is close to 60
Count up by 10’s in your head.
22 + 47 Answer 69
22 is close to ________ 47 is close to ________
Estimate:
* Task d
+
=
Estimate by rounding. Work out the real sum on a spare piece of paper.
37 + 22
Estimate:___________
Answer:___________
Was it close? ___________
51 + 79
Estimate:___________
Answer:___________
Was it close? ___________
36 + 58
Estimate:___________
Answer:___________
Was it close? ___________
31 + 68
Estimate:___________
Answer:___________
Was it close? ___________
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48 + 49
Estimate:___________
Answer:___________
Was it close? ___________
19 + 99
Estimate:___________
Answer:___________
Was it close? ___________
13
* Estimation 2
zz To estimate an answer we can think about what each number is close to. The number 43 is close to 40. 162 is close to 160.
This is a Ready-Ed Publications' Task a * book preview. Fill in each of the empty boxes to help you estimate what the answer should be. The first one is done for you.
a)
70 .
So the answer is about c)
79 − 19 is about
−
289 − 32 is about
d)
. −
So the answer is about
32 + 11 is about
+
.
.
So the answer is about .
So the answer is about e)
b)
61 + 8 is about 60 + 10 .
151 + 39 is about
+ .
So the answer is about f)
. .
531 − 49 is about
.
+
. .
So the answer is about
Task b * Circle the best and closest answer, without doing any calculations. a. 52 + 9 =
70
60
65
b. 89 – 32 =
50
60
55
c. 368 + 11 =
370
380
390
d. 831 – 29 =
790
800
810
e. 247 + 19 =
270
260
250
f. 998 – 12 =
980
990
1000
g. 1232 + 328 =
1550
1560
1570
Task c: small group challenge *Form a small group of 4 to 5 students.
• Measure your heights in centimetres and then estimate the total of your heights. • Write down the time it takes for each of you to travel to school in minutes and then estimate your total travel time. • Write down the amount of television each of you watches each week in minutes and then estimate your total television viewing time.
Height (centimetres)
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14
Travel time to school (minutes)
Television viewing per week (minutes)
* Counting By … * Task a
Complete the number patterns to count by …
This is a Ready-Ed Publications' book preview. Twos:
2, 4, 6, 8,_____________________________________________ 20
Threes:
3, 6, 9,_______________________________________________ 30
Fours:
4, 8, 12, _ ____________________________________________ 40
Fives:
5, 10, 15,_____________________________________________ 50
Sixes:
6, 12, 18,_____________________________________________ 60
Sevens:
7, 14, 21, _ ___________________________________________ 70
Eights:
8, 16, 24,_____________________________________________ 80
Nines:
9, 18, 27,_____________________________________________ 60
Tens:
10, 20, 30,___________________________________________ 100
Elevens:
11, 22, 33___________________________________________ 110
Twelves:
12, 24, 36 ___________________________________________ 120
Thirteens:
13, 26, 39___________________________________________ 130
Fourteens:
14, 28, 42___________________________________________ 140
Fifteens:
15, 30, 45___________________________________________ 150
Sixteens:
16, 32, 48___________________________________________ 160
Seventeens: 17, 34, 51___________________________________________ 170 Eighteens:
18, 36, 54___________________________________________ 180
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Nineteens:
19, 38, 57___________________________________________ 190
Twenties:
20, 40, 60___________________________________________ 200
15
* Multiples
Task a * List the first 10 multiples for each of these numbers. The first one has been done for you.
This is a Ready-Ed Publications' book preview. 3
a. 3:
6
9
12
15
18
21
24
4
b. 2:
35 20
d. 10:
70 75
e. 25:
175 60
f. 15: 24
g. 12:
30
18
7
c. 7:
27
105 72
120
What is a Lowest Common Multiple? A Lowest Common Multiple (LCM) is the lowest multiple that two numbers have in common. To find the LCM for 3 and 4 we list some of their multiples and then look for the lowest one they have in common. 3 and 4
3: 3, 6, 9, 12, 15, 18 …
4: 4, 8, 12, 16 …
As we can see, the lowest number they have in common is 12.
* Task b
Find the lowest common multiple for each of the following:
a. 3 and 5 b. 6 and 7 c. 10 and 15 d. 6 and 8
* Task c: Partner Challenge
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Create a one page mini quiz for your partner on multiples and LCMs. Before giving it to your partner to try, make sure you have already written out a detailed marking key with all the answers on a separate piece of paper.
16
Quiz !
* Task a
Factors * List all of the factors for each of the following numbers.
This is a Ready-Ed Publications' book preview. The first one has been done for you. 1
a. 8:
2
4
2
b. 10:
8
10
c. 24:
3
6
d. 100:
4
10
e. 36:
3
25 9
f. 48: What is a Highest Common Factor? A Highest Common Factor (HCF) is the largest factor that two numbers have in common. To find the HCF for 12 and 18 (Task B - a), we firstly list each of their factors and then look for the largest factor they have in common. As we can see, the largest number they have in common is 6. This is the HCF.
* Task b
Find the highest common factor for each of these numbers.
a. 12 and 18
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
b. 15 and 60 c. 27 and 36 d. 36 and 90 e. 20 and 24 Personal Challenge * ToTaskfindc:a faster way to find the HCF, research Euclid’s Algorithm. An algorithm is a set of rules to follow to
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complete a calculation. It’s a lot like following a recipe. Once you have understood how the algorithm works, use it find the HCF for these numbers: a) 252 and 105 b) 2322 and 654
17
* Imagining Negative Numbers * is a Ready-Ed Publications' This book preview. Task a The hilly town of Siena in Tuscany has a special sort of multi-level shopping centre. Look at the store directory sign right and study it carefully before answering the following questions.
a. What number could you use to represent the level that the Butcher and Bakery are on?
_________________________________________________
b. What do the negative level numbers represent?
_________________________________________________
c. If you park in Car Park A and travel on the lift to the Medical Centre, how many floors will you pass?
Siena Shopping Village Directory Store
Level
Appliances
5
Medical Centre
4
Post Office/Newsagent
3
Greengrocer
2
Supermarket
1
e. If you leave the Laundromat and travel up the lift 5 floors, where do you end up?
Butcher/Bakery
G
Delicatessen
-1
f. Maria parks in Car Park A, travels up 4 floors, then up 3 more floors, down one floor, up 3 floors and then down 9 floors. Write down all the places that she visited.
Laundromat
-2
Customer Service
-3
_________________________________________________
Car Park A
-4
_________________________________________________
_________________________________________________
_________________________________________________
d. You leave the Post Office and travel 4 levels down on the lift. Do you arrive at the Laundromat?
_________________________________________________
_________________________________________________
g. Gianni starts on level G, travels to level -2, then to level 3, followed by level 1, then back to level G. Describe Gianni’s movements on the lift.
_________________________________________________
_________________________________________________
_________________________________________________
18
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* Where Am I? * Task a
Use the number line to help you answer each of the following questions.
This is a Ready-Ed Publications' book preview. a. 5 is eight places above
f. -8 is five places above
b. 2 is seven places below
g. 15 is twenty places above
c. -3 is five places below
h. 3 is sixteen places below
d. 0 is ten places above
i. -12 is four places below
e. -7 is thirteen places below
j. -1 is eleven places above
* Task b
You may like to use the number line to answer each of these questions.
a. 12 more than 3 is b. 10 less than 5 is c. 6 less than -4 is d. 12 more than -18 is e. 2 more than -5 is
which is 3 less than
f. 7 less than 2 is
which is 4 more than
g. 9 more than 1 is
which is 8 less than
h. 50 less than 10 is
which is 6 more than
i. 86 more than 17 is
which is 10 less than
j. 37 more than -14 is
which is 15 less than
k. 12 less than -62 is
which is 21 more than
l. 150 less than -210 is
which is 325 more than
ask c: class Challenge * TEach member of the class is to write down one clue, similar to those above, which
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represents an integer value. Each member of the class will then state their clue to the class and the others in the class will write down the number they were thinking of. Once all class members have given their clue, go through the answers with your teacher.
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20
19
Teachersâ&#x20AC;&#x2122; Notes
This is a Ready-Ed Publications' Calculations With Integers book preview. Lower ability students struggle with their confidence in Mathematics as much as they struggle with learning new concepts. Before beginning units of work for Number in Lower Secondary, these activities encourage students to consolidate the written methods and algorithms that they have encountered previously while building confidence in their abilities. This section focuses on calculations involving addition, subtraction, multiplication and division and also includes activities for real life applications. Each subsection is well scaffolded and allows students to concentrate on one core area of calculation before moving on to the next. These activities should encourage independent learning, rather than requiring significant teacher input, and will thus enable students to build confidence in their resourcefulness and abilities.
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* Rule Of Order 1
This is a Ready-Ed Publications' book preview. zz Sometimes sums have more than one thing to do in them. The rule of order states that you must do × and ÷ before + and – . Look at these two examples: Example
6+3×4
10 – 16 ÷ 4
Example
You do the × first, i.e. 3 × 4 = 12
You do the ÷ first, i.e. 16 ÷ 4 = 4
So 6 + 3 × 4 = 6 + 12
So 10 – 16 ÷ 4 = 10 – 4
6 + 12 = 18
10 – 4 = 6
* Task a
Re-write these sums and then solve them.
a. 4 × 2 + 7
= 8 + 7 =
i. 4 ÷ 2 + 6
= 2 + 6 =
b. 2 × 3 + 2
=
+
=
j. 6 ÷ 3 + 5
=
+
=
c. 5 × 6 + 3
=
+
=
k. 10 ÷ 5 – 2 =
–
=
d. 8 × 2 + 5
=
+
=
l. 12 – 9 ÷ 3 = 12 –
3 =
e. 3 + 2 × 6
= 3 + 12 =
m. 20 – 24 ÷ 6 =
–
=
f. 4 + 3 × 5
=
+
=
n. 15 + 18 ÷ 3 =
+
=
g. 8 + 4 × 9
=
+
=
o. 21 – 12 ÷ 4 =
+
=
h. 9 – 2 × 4
=
–
=
p. 36 ÷ 9 + 3 =
+
=
Go to www.readyed.net 21
* Rule Of Order 2 zz The rule of order states that you must do × and ÷ before + and – .
This is a Ready-Ed Publications' book preview. 6+3×4
Example 1
Example 2
So 6 + 3 × 4 = 6 + 12 = 18
* Task a
10 – 16 ÷ 4
So 10 – 16 ÷ 4 = 10 – 4 = 6
Re-write these sums and then solve them.
a. 5 × 3 + 7
= 15 + 7 =
e. 11 + 9 × 5 =
+
=
b. 9 × 3 + 6
=
+
=
f. 30 – 4 × 4 =
+
=
c. 7 × 8 + 9
=
+
=
g. 45 ÷ 5 – 7 =
+
=
d. 6 + 7 × 7
= 6 + 49 =
h. 60 – 42 ÷ 6 =
–
=
zz If the sum has more than one × or ÷ part to it, you just do them in the order they appear. Look at these two examples: Example 1 4 × 5 ÷ 10 + 3 4 × 5 ÷ 10 + 3 = 20 ÷ 10 + 3 = 2 + 3 = 5 Multiply first Then divide Then add
* Task b
Example 2 65 – 30 ÷ 5 × 3 65 – 30 ÷ 5 × 3 = 65 – 6 × 3 = 65 – 18 = 47 Divide first Then multiply Then subtract
Solve these sums by following the rule of order.
a. 3 × 4 + 2 × 7
= 12 + 14
= 12 + 2 × 7
=
b. 30 ÷ 3 + 4 × 5 =
=
=
c. 7 + 16 ÷ 4 × 3 =
=
=
Go to www.readyed.net
d. 40 ÷ 8 × 2 – 3
22
=
=
=
e. 24 ÷ 6 + 48 ÷ 8 =
=
=
* Addition 1 Look at the following sum, 564 + 432.
Example
This is a Ready-Ed Publications' book preview. + + + Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
5
6
4
5
6
4
5
6
4
4
3
2
4
3
2
4
3
2
9
6
9
9
6
6 Step 1: Add the Ones 4+2=6
Step 2: Add the Tens 6+3=9
Step 3: Add the Hundreds 5+4=9
zz Remember to work from right to left.
* Task a +
Try these.
H
T
O
H
T
O
H
T
O
5
6
4
2
5
5
8
5
2
4
2
1
4
3
3
1
3
1
* Task b
+
+
Try these sums.
42 + 22
46 + 51
264 + 721
852 + 147
221 + 573
343 + 625
465 + 322
337 + 622
Go to www.readyed.net 23
* Addition 2
Look at the following sum, 564 + 432.
Example
This is a Ready-Ed Publications' book preview. + + + Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
5
6
4
5
6
4
5
6
4
4
3
2
4
3
2
4
3
2
9
6
9
9
6
6 Step 1: Add the Ones 4+2=6
Step 2: Add the Tens 6+3=9
Step 3: Add the Hundreds 5+4=9
zz Remember to work from right to left.
* Task a
Try these sums.
35 + 24
21 + 70
537 + 422
243 + 515
842 + 131
346 + 143
582 + 411
235 + 624
832 + 121
373 + 522
864 + 121
253 + 735
* Task b
Try these on some spare lined paper.
Go to www.readyed.net
626 + 373
847 + 142
448 + 321
793 + 102
4263 + 5132
6351 + 3220
1262 + 7127
4462 + 3231
24
* Addition: Regrouping 1 Look at the following sum: 564 + 428.
Example
This is a Ready-Ed Publications' book preview. 1
+
1
5
6
4
4
2
8
+
5
6
4
4
2
2
9
2
2 Step 1: Add the Ones 4 + 8 = 12 The 2 is placed in the Ones column and the 1 is regrouped to the Tens.
1
Step 2: Add the Tens 1+6+2=9
+
5
6
4
4
2
8
9
9
2
Step 3: Add the Hundreds 5+4=9
zz Remember to work from right to left.
* Task a +
Try these.
5
6
4
4
2
9
+
2
5
7
4
3
7
* Task b
Now try without the grid.
48 + 22
46 + 36
254 + 729
+
8
5
6
1
3
5
856 + 137
Go to www.readyed.net
367 + 129
416 + 229
7348 + 1439
4526 + 1347
25
* Addition: Regrouping 2 Look at the following sum: 564 + 428.
Example
This is a Ready-Ed Publications' book preview. 1
+
1
5
6
4
4
2
8
+
5
6
4
4
2
2
9
2
2 Step 1: Add the Ones 4 + 8 = 12 The 2 is placed in the Ones column and the 1 is regrouped to the Tens.
1
Step 2: Add the Tens 1+6+2=9
+
5
6
4
4
2
8
9
9
2
Step 3: Add the Hundreds 5+4=9
zz Remember to work from right to left.
* Task a
Try these.
35 + 27
11 + 79
37 + 24
243 + 219
546 + 136
336 + 247
546 + 315
228 + 524
437 + 225
328 + 523
258 + 128
237 + 239
* Task b
Go to www.readyed.net Try these on some spare lined paper.
224 + 349
647 + 128
435 + 226
293 + 108
4257 + 3136
6147 + 2225
1545 + 3126
3429 + 3138
26
* Addition: Regrouping 3 Look at the following sum: 565 + 359.
Example
This is a Ready-Ed Publications' book preview. 1
+
5
6
5
3
5
9
+
1
1
5
6
5
3
5
9
2
4
4 Step 1: Add the Ones 5 + 9 = 14 The 4 is placed in the Ones column and the 1 is regrouped to the Tens.
* Task a +
+
1
1
5
6
5
3
5
9
9
2
4
Step 2: Add the Tens Step 3: Add the Hundreds 1+5+3=9 1 + 6 + 5 = 12 The 2 is placed in the Tens column and the 1 is regrouped to the Hundreds.
Try these.
4
6
4
4
5
9
* Task b 668 + 252
+
2
5
7
4
4
7
+
7
7
6
1
3
5
+
656 177
Now try without the grid. 346 + 576
254 + 649
Go to www.readyed.net +
674 266
588 + 134
463 + 277
+
462 359
27
* Addition: Regrouping 4 Look at the following sum: 464 + 459. Remember to work from right to left. Each time the answer is 10 or more, you must regroup the 1 in the next column.
This is a Ready-Ed Publications' book preview. Example
+
1
1
4
6
4 9
* Task a
4
Step 1:
Add the Ones 4 + 9 = 13 Put down the 3, regroup the 1.
5
9
Step 2:
Add the Tens 1 + 6 + 5 = 12 Put down the 2, regroup the 1.
2
3
Step 3:
Add the Hundreds 1+ 4 + 4 = 9 Put down the 9.
Try these.
135 + 477
481 + 129
677 + 224
243 + 269
576 + 136
386 + 347
446 + 395
198 + 524
237 + 285
378 + 424
257 + 168
287 + 237
* Task b
Try these on some spare lined paper.
185 + 349
697 + 129
236 + 286
297 + 358
4257 + 3186
6148 + 2275
1547 + 3186
3429 + 3179
9873 + 149
1684 + 2157
7483 + 2189
9862 + 3169
28
Go to www.readyed.net
* Subtraction 1 Look at the following sum: 964 – 632.
Example
This is a Ready-Ed Publications' book preview. –
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
9
6
4
9
6
4
9
6
4
6
3
2
6
3
2
6
3
2
3
2
3
3
2
–
2 Step 1: Take away the Ones 4 –2=2
–
Step 2: Take away the Tens 6 –3=3
Step 3: Take away the Hundreds 9 –6=3
zz Remember to work from right to left.
* Task a –
Try these.
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
5
6
2
9
5
3
8
5
2
4
5
1
4
3
3
6
3
1
* Task b 42 – 22
–
–
Try these sums. 52 – 41
864 – 721
859 – 747
Go to www.readyed.net
998 – 773
847 – 625
465 – 352
937 – 622
29
* Subtraction 2 Look at the following sum: 964 – 632.
Example
This is a Ready-Ed Publications' book preview. –
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
9
6
4
9
6
4
9
6
4
6
3
2
6
3
2
6
3
2
3
2
3
3
2
–
2 Step 1: Take away the Ones 4 –2=2
Step 2: Take away the Tens 6 –3=3
–
Step 3: Take away the Hundreds 9 –6=3
zz Remember to work from right to left.
* Task a
Try these sums.
35 – 24
81 – 70
37 – 26
846 – 515
942 – 831
388 – 143
692 – 471
835 – 624
832 – 721
373 – 162
864 – 621
859 – 735
* Task b
Try these on some spare lined paper.
Go to www.readyed.net
998 – 373
847 – 642
448 – 326
793 – 392
8263 – 7142
6391 – 5260
8268 – 7157
4462 – 3251
30
* Subtraction: Regrouping 1
Look at the following sum, 964 – 636.
Example
This is a Ready-Ed Publications' book preview. –
9
6
4
6
3
6
9
5
6
–
1
6
4 6
3
8 Step 1: Take away the Ones. 4 – 6 can’t be done so regroup from the Tens. 5
9 6
–
1
6
Step 2: The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8
9
4
3
6
2
8
–
Step 3: Take away the Tens 5 –3=2
5
1
6
4
6
3
6
3
2
8
Step 4: Take away the Hundreds 9 –6=3
zz Remember to work from right to left.
* Task a –
Try these.
5
6
2
4
5
4
–
9
5
3
4
3
6
* Task b
Now try without the grid.
46 – 28
64 – 47
–
8
5
2
6
3
5
Go to www.readyed.net 865 – 729
851 – 747
31
* Subtraction: Regrouping 2
This is a Ready-Ed Publications' book preview. Look at the following sum, 964 – 636. Remember to work from right to left.
Example
5
9
–
6
1
4
Take away the Ones. 4 – 6 can’t be done so regroup from the Tens. The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8
6
3
6
Take away the Tens 5 –3=2
3
2
8
Take away the Hundreds 9 –6=3
* Task a
Try these.
35 – 27
91 – 79
33 – 24
243 – 119
546 – 136
336 – 247
546 – 315
528 – 224
437 – 225
528 – 323
458 – 128
937 – 239
* Task b
Try these on some spare lined paper.
Go to www.readyed.net
844 – 329
647 – 128
435 – 226
293 – 108
4257 – 3136
6547 – 2225
9545 – 3126
3425 – 3138
32
* Subtraction: Regrouping 3 Look at the following sum, 964 – 676. Remember to work from right to left.
Example
This is a Ready-Ed Publications' book preview. –
9
6
4
6
7
6
9
5
6
–
1
6
4 6
7
8 Step 1: Take away the Ones. 4 – 6 can’t be done so regroup from the Tens. 8
15
9 6
–
1
6
Step 2: The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8 8
4
7
6
8
8
–
Step 3: Take away the Tens 5 – 7 can’t be done so regroup from the Hundreds. The 5 becomes 15 and the 9 becomes 8.
* Task a –
5
1
6
4
6
7
6
2
8
8
Step 4: Take away the Hundreds 8 –6=2
Try these.
6
6
2
4
8
4
* Task b
9
–
9
5
3
4
7
6
–
8
4
2
6
6
5
Now try without the grid.
Go to www.readyed.net 736 – 658
964 – 777
865 – 589
651 – 267
33
* Subtraction: Regrouping 4
This is a Ready-Ed Publications' book preview. Look at the following sum, 964 – 636. Remember to work from right to left.
Example
8
–
9
15
6
1
4
6
7
6
2
8
8
Take away the Ones 4 – 6 can’t be done so regroup from the Tens. The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8
Take away the Tens 5 – 7 can’t be done so regroup from the Hundreds. The 5 becomes 15 and the 9 becomes 8. 15 – 7 = 8 Take away the Hundreds 8 –6=2
* Task a
Try these sums.
835 – 257
411 – 179
524 – 337
623 – 239
533 – 146
446 – 237
536 – 345
828 – 524
427 – 235
838 – 593
628 – 159
857 – 279
864 – 399
627 – 148
425 – 236
563 – 198
* Task b
Challenge:
Go to www.readyed.net
4237 – 3156
34
8127 – 2245
9535 – 3186
9449 – 3188
* Addition And Subtraction 1 Calculate each of the following using the written strategies you have learnt. Be sure to clearly show your working out.
This is a Ready-Ed Publications' book preview. a
d
g
j
84 – 47
32 + 51 + 12
68 – 11 – 25
74 – 36
b
e
h
k
75 + 42
58 + 27
87 – 12 – 35
95 – 49
c
f
i
l
23 + 10 + 45
53 -24
84 + 32
62 – 47
Go to www.readyed.net 35
* Addition And Subtraction 2 Calculate each of the following using the written strategies you have learnt. Be sure to clearly show your working out.
This is a Ready-Ed Publications' book preview. a
d
g
j
672 – 538
775 – 491
724 + 269
462 – 225
b
e
h
k
453 – 236
262 + 374
529 – 381
246 + 671
c
f
i
l
542 + 813
995 – 128
341 + 923
949 – 362
Go to www.readyed.net 36
* â&#x20AC;&#x2030; Real Life Addition
Answer each of these word problems and be sure to show how you got your answer.
This is a Ready-Ed Publications' book preview. a
c
e
g
If James has $25 and Melissa has $32 more than James, how much does Melissa have?
In the summer months the Bradley household uses 742 units of electricity and in the winter months they use 595 units of electricity. How much have they used altogether?
Michael is 12 years older than Nicole. Nicole is 32 years older than Jamie. Jamie is 8 years old. How old is Michael?
Max looks at his bank statement and sees that he spent $230 on clothes, $157 on groceries and $75 on petrol. How much did he spend altogether?
b
d
f
The Kirtz family drank 5423 ml of milk last week and this week theyâ&#x20AC;&#x2122;ve drunk 2374 ml of milk. How much milk have they drunk in two weeks?
Brett and Susie are going on a holiday. They drive 175 km from Perth to Bunbury and then another 279 km. How far is the total journey?
In a local primary school there are 24 students in Year 1, 31 students in Year 2 and 29 students in Year 3. How many students are there in total in these three year groups?
h Samantha is writing a story. On
Monday she wrote 435 words, on Tuesday she wrote 240 words and on Wednesday she wrote 562 words. How many words has she written so far?
Go to www.readyed.net
37
* Real Life Subtraction Answer each of these word problems and be sure to show how you got your answer.
This is a Ready-Ed Publications' book preview. a
c
e
g
Jonathon is 12 years younger than Amy, who is 44 years old. How old is Jonathon?
Jack has $50 to spend at Seaworld. He has already spent $23. How much money does he have left to spend?
The Lims have a jar of money in their kitchen with $75 in it. Lucy took $11, Mrs Lim took $22 and Mr Lim took $32. How much money is left in the jar?
On a particular T.V. game show, Team A has 125 points, Team B has 187 points and Team C has 163 points. How many points does Team A need to beat Team B?
b
d
f
h
A group of friends are playing Pass-theParcel at Cynthia’s birthday. Cynthia’s mum wrapped the parcel 20 times and 7 layers of paper have been removed. How many layers are left?
Martin is reading a book that has 356 pages. So far he has read 125 pages. How many pages does he have left to read?
Tania is watching a YouTube video which is 195 seconds long. She pauses the video and sees she has 80 seconds left to watch. How much has she watched already?
The Dibley family have 25 000 MB of internet data to use each month. So far they have used 13 500 MB. How much do they have left to use this month?
Go to www.readyed.net
38
* Real Life Addition And Subtraction Answer each of these word problems and be sure to show how you got your answer.
This is a Ready-Ed Publications' book preview. a
c
e
g
Michelle is writing a short story for her teacher. It has to be 1 200 words long. So far Michelle has written 865 words. How many more words does she need before she’s completed her story?
Rebecca’s dad is 186 cm tall. Rebecca is 55 cm shorter than her dad. How tall is Rebecca?
There are 18 433 cities and towns in the USA. Pierre has visited 125 cities and 62 towns. How many places hasn’t he been to in the USA?
The McKay family are doing a 1 000 piece jigsaw puzzle. Kelly has completed 123 pieces of the jigsaw. Michael has completed 340 pieces of the jigsaw. Mr McKay has completed 238 pieces of the jigsaw. How many pieces do they have left to complete?
b
d
f
h
A set of triplets have just been born. Timothy weighs 2 200 grams, Teneille weighs 3 100 grams and Tash weighs 2 750 grams. How much do the triplets weigh altogether?
Sam and Emily are on the same team playing a computer game. Sam has scored 245 points and Emily has scored 223 points. Oliver and Jane are on the other team and Oliver has scored 195 points and Jane has scored 264 points. Which team is winning?
There are 40 320 ways to arrange 8 people in a line for a photo. The fussy photographer has so far tried 280 different ways to arrange these 8 people. How many more ways can the photographer arrange these 8 people?
Paul has 16 000 MB of space on his phone. He has used 8 200 MB for his photos, 4 300 MB for his songs and 245 MB for his phone list. How much space does he have left?
Go to www.readyed.net
39
* Multiplication: Regrouping 1
To multiply 25 × 3
Example
This is a Ready-Ed Publications' book preview. Tens
Ones
Tens
Ones
Tens
Ones
2
5
2
5
2
5
3
×
3
×
5
1
Step 1: Multiply the Ones by the bottom number. 5 × 3 = 15
* Task a
1
5
6
0
3
×
+
1
5
6
0
7
5
Step 3: Now you add
Step 2: Multiply the Tens by the bottom number. 2 × 3 = 6 Because you are in the Tens column, you put down a zero in the Ones column FIRST.
the answer rows.
15 + 60 = 75
Try these sums. Some parts have been done for you.
Tens
Ones
Tens
Ones
Tens
Ones
3
6
2
7
2
4
2
×
×
+
3
+
* Task b
4
×
+
Try these sums. Hundreds
Tens
Ones
2
7 4
×
Hundreds
×
8
Tens
Ones
4
9 3
Go to www.readyed.net 2
+
40
+
* Multiplication: Regrouping 2
To multiply 25 × 3
Example
This is a Ready-Ed Publications' book preview. Tens
Ones
2
5
Step 1: 5 × 3 = 15
3
Step 2:
×
+
2×3=6
6
0
7
5
Step 3: 15 + 60 = 75
Ones
Tens
Ones
2
6
1
5
2 2
2
0
Task b * 36
Try these.
Hundreds
+
Ones
2
9 4
0 +
18 × 4
2
Tens
×
+
26 × 4
+
7 5
4
×
+
+
+ 6 0
Try these. Some parts have been done for you.
Tens
1
3
1 5
Put down the zero.
5
×
×
×
1
* Task a
2 5
17 × 5
+
19 × 4
18 × 2
+
16 × 9
28 × 2
Go to www.readyed.net +
+
+
41
* Multiplication: Regrouping 3
To multiply 65 × 3
Example
This is a Ready-Ed Publications' book preview. Hundreds
Tens
Ones
6
5
Step 1: 5 × 3 = 15
(5 in the Ones column and 1 in the Tens.)
3
×
+
1
8
0
1
9
5
* Task a H
O
6
3 4
6 × 3 = 18
+
×
+
42
+ 1 8 0
(8 in the Tens column and 1 in the Hundreds.)
1 9 5
Step 3: 15 + 180 = 195
H
T
O
6
8 7
× 5
T
O
8
7 4
H
×
H
T
O
7
4 3
×
6 0
+
H
1 5
Put down the zero.
Try these.
T
×
3
×
Step 2:
5
1
6 5
T
O
3
6 5
+
H
×
T
O
2
9 6
Go to www.readyed.net +
+
* Multiplication: Regrouping 4 To multiply 65 × 3
Example
This is a Ready-Ed Publications' book preview. Hundreds
Tens
Ones
6
5
Step 1: 5 × 3 = 15
(5 in the Ones column and 1 in the Tens.)
3
×
+
1
8
0
1
9
5
* Task a H
O
4
5
6 × 3 = 18
H
×
T
O
5
7
H
7
T
O
4
8 3
×
+
47 6
1 9 5
Step 3: 15 + 180 = 195
+
×
+ 1 8 0
(8 in the Tens column and 1 in the Hundreds.)
2
* Task b
1 5
Put down the zero.
Try these.
T
×
3
×
Step 2:
5
1
6 5
+
Try these. ×
74 5
×
75 7
×
86 3
Go to www.readyed.net 43
* Multiply These!
Calculate each of the following using the written strategies you have learnt. Be sure to clearly show your working out.
This is a Ready-Ed Publications' book preview. a
d
g
j
87 × 2
514 × 7
352 × 8
48 × 4
b
e
h
k
94 × 5
83 × 4
613 × 3
721 × 2
c
f
i
l
432 × 6
97 × 5
72 × 6
654 × 3
Go to www.readyed.net 44
* Division 1 ) Example This is a Ready-Ed Publications' ) book preview. This sign means divided.
2 24
This means how many times will 2 go into 24.
1 Divide the Tens column first: 2 ÷ 2 = 1 2 ) 24 12 Divide the Ones column next: 4 ÷ 2 = 2 2 ) 24 The answer is 12.
* Task a 3 ) 63
Fill in the blanks.
This means how many times will 3 go into 63.
2 Divide the Tens column first: 6 ÷ 3 = _________ 3 ) 63 2 1 Divide the Ones column next: 3 ÷ 3 = _________ 3 ) 6 3 The answer is _________.
* Task B
Fill in the blanks.
2 ) 48
This means how many times will ________ go into ________.
2 ) 48
Divide the Tens column first: ________ ÷ ________ = ________
2 ) 4 8
Divide the Ones column next: ________ ÷ ________ = ________
Go to www.readyed.net The answer is ________.
45
* Division 2
This is a Ready-Ed Publications' ) book preview. Example
)
This sign means divided.
2 24
This means how many times will 2 go into 24?
1 Divide the Tens column first: 2 ÷ 2 = 1 2 ) 24
12 Divide theOnes column next: 4 ÷ 2 = 2 2 ) 24 The answer is 12.
* Task a 3 ) 96
Try these.
The answer goes here.
9 ÷ _____ 3 = _____ 3 and _____ 6 ÷ _____ 3 = _____ 2 Answer = _____ 32 Sums are _____
4 ) 84
Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____
3 ) 93
Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____
2 ) 26
Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____
3 ) 99
Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____
* Task b 63 ÷ 3
Write these like the ones above. (Hint: the smaller number goes first.) 60 ÷ 2
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* Division With Remainders 1
25 ÷ 2 =
2 ) 25
1 2 25
Divide the Tens column first: 2 ÷ 2 = 1 (write 1 on top of the 2)
12 r1 2 ) 25
Divide the Ones column next: 5 ÷ 2
Count by twos: 2, 4, 6
What is the highest number less than 5? = 4 (goes in 2 times) (Write 2 on top of the 5.)
How many left over before you get to 5? = 1
1 is your remainder.
This is a Ready-Ed Publications' ) book preview. This means how many times will 2 go into 25.
Answer = 12 remainder 1 or 12 r 1
* Task a Fill in the blanks.
57 ÷ 5 = 5 ) 57
5 ) 57 5 ) 57
This means how many times will 5 go into ________.
Divide the Tens column first: ________ ÷ ________ = ________ Divide the Ones column next: ________ ÷ ________ = ________ Count by twos: 5, 10
What is the highest number less than 7?
How many left over before you get to 7? ________ is your remainder.
Answer = ________ r____
= ________ (goes in ____ times) = ________
these. Task b Try to www.readyed.net * Go
4 ) 86
2 ) 29
3 ) 68
6 ) 69
47
* Division With Remainders 2 25 ÷ 2 =
2 ) 25
1 2 25
Divide the Tens column first: 2 ÷ 2 = 1 (write 1 on top of the 2)
12 r1 2 ) 25
Divide the Ones column next: 5 ÷ 2
Count by twos: 2, 4, 6
What is the highest number less than 5? = 4 (goes in 2 times) (Write 2 on top of the 5.)
How many left over before you get to 5? = 1
1 is your remainder.
This is a Ready-Ed Publications' ) book preview. This means how many times will 2 go into 25.
Answer = 12 remainder 1 or 12 r 1
* Task a
4 ) 83
2 ) 49
3 ) 91
6 ) 67
4 ) 46
2 ) 69
3 ) 98
6 ) 69
2 ) 46
3 ) 99
2 ) 60
3 ) 69
* Task b
Word problem:
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There are 34 students in the class. If I want to make 3 rows, how many students are in each row? How many are left over?
3 ) 34
48
Try these.
* Division With Regrouping 1
This is a Ready-Ed Publications' ) book preview. In division, you regroup if you cannot divide into the first digit evenly. 2 34
Divide the Tens column first: 3 ÷ 2 = 1 r 1 (Does not divide evenly)
Regroup by writing the remainder next to the Ones. 1 2 ) 314 17
2 ) 314
Divide the Ones column next 14 ÷ 2 = 7 (Divides evenly) Answer = 17
* Task a
Fill in the blanks.
3 ) 57
Divide the Tens column first: 5 ÷ _______ = _______ r _______
Regroup by writing the remainder next to the Ones. 3 ) 5 7
Divide the Ones column next: _______ ÷ _______ = _______
3 ) 5 7
Answer = ________
* Task b 4 ) 96
Fill in the blanks.
Divide the Tens column first: ______ ÷ ______ = ______ r ______
Regroup by writing the remainder next to the Ones. 4 ) 9 6
Divide the Ones column next: _______ ÷ _______ = _______
4 ) 9 6
Answer = ________
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* Division With Regrouping 2
This is a Ready-Ed Publications' ) book preview. In division, you regroup if you cannot divide into the first digit evenly. 2 34
Divide the Tens column first: 3 ÷ 2 = 1 r 1 (Does not divide evenly)
Regroup by writing the remainder next to the Ones. 1 2 ) 314 17
2 ) 314
* Task a
Divide the Ones column next 14 ÷ 2 = 7 (Divides evenly) Answer = 17
Try these.
5 ) 8 0
4 ) 6 4
3 ) 7 7
3 ) 9 8
7 ) 8 4
9 ) 9 1
3 ) 5 5
6 ) 7 5
7 ) 7 6
8 ) 9 8
3 ) 5 6
3 ) 8 8
4 ) 8 6
6 ) 9 8
7 ) 9 5
3 ) 5 0
* Task b 69 ÷ 4
50
Work these out below. 86 ÷ 4
94 ÷ 7
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â&#x20AC;&#x2030; Real Life Multiplication * Answer each of these word problems and be sure to show how you got your answer.
This is a Ready-Ed Publications' book preview. 1
2
Seven friends decide to give $6 each to buy a present for their friendâ&#x20AC;&#x2122;s birthday. How much money do they have altogether?
3
Sally is making party bags for her friends to take home after her party. She puts 3 snake lollies in each bag and she has 27 friends coming to her party. How many snakes does she need altogether?
4 A new dress-up doll comes with 7 pairs of shoes and 32 dresses. How many different outfits can be made?
5
A bus can sit 4 people in each row. If there are 17 rows, how many people can have a seat on this bus?
6 Nick can type really fast. Each minute he can type 62 words. If he has been typing for 9 minutes, how many words has he typed?
7
In a History multiple choice test you have 35 questions, each with 4 possible answers. How many possible answers are there in total?
8 Matthew is making a rice dish for some friends. It says he needs 2 cups of rice for 4 people. If he has 11 friends coming over, plus himself, how many cups of rice will he need?
Samantha has only $10 and $20 notes in her purse. If she knows she has $440 in her purse and 8 $20 notes, how many $10 notes does she have?
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â&#x20AC;&#x2030; Real Life Division * Answer each of these word problems and be sure to show how you got your answer.
This is a Ready-Ed Publications' book preview. 1
2
Michaela needs to make 48 cupcakes. She only has one cupcake tray with 12 spaces for cupcakes. How many times does she need to use this tray?
3
Miss Thompson has 30 students in her Year 3 class. She wants to arrange the desks in groups of 5. How many groups does she need?
4 A family needs to take 21 litres of drinking water on a camping trip. How many 3 litre bottles will they have to take to make sure they have enough?
5
Robert has 64 DVDs that he wants to put in his DVD shelves. If he can fit 16 DVDs on one shelf, how many shelves does he need?
6 Each week Craigâ&#x20AC;&#x2122;s parents give him $7 for doing his chores. How many weeks will he need to do chores to save up enough money to buy a $56 computer game?
7
Billy has lived in his new house for 126 days. How many weeks is this?
8 Nicole needs to write a 1 500 word report for her science project. If she uses 6 pages to write her report, how many words will be on each page?
126 people are waiting in line to ride the Ferris Wheel. If only 14 people can be on the ride each time, and all these people want two rides on the Ferris Wheel, then how many how many rides will it take to make all these people happy?
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* Answers
Place Value 1 Page 7 Task A: 8000, 400, 20, 7 3000, 900, 70, 5 5000, 900, 20, 7 Task b: 4000, 4, 400 4, 400, 4000, 40
Task c:
This is a Ready-Ed Publications' book preview. Place Value 2 Page 8 Task A: 2000, 300, 60, 4 9000, 800, 40, 5 Task b: 40, 8, 900, 702, 9000, 6, 5000, 70 Task c: 2476, 8266, 9553 Place Value 3 Page 9 Task A: 7 456 322 Task B: 5 2 4
4 0 2 1 2
9 9 0 8 8 3
8 8 0 7 0 5
7 6 0 6 0 4
6 3 4 8 9 9
5 4 9 5 7 7
Task C: (2 × 1 000 000) + (8 × 100 000) + (7 × 10 000) + (6 × 1000) + (5 × 100) + (4 × 10) + (3 × 1) (7 × 1 000 000) + (6 × 100 000) + (5 × 10 000) + (3 × 1000) + (1 × 10) + (2 × 1) Task d: Millions = 3 000 000, Thousands = 4000, Hundred thousands = 500 000 Greater Than/Less Than Page 10 1.<, 2.>, 3.<, 4.>, 5.>, 6.>, 7.<, 8.>, 9.<, 10.<, 11.>, 12.<, 13.>, 14.<, 15.>, 16.>
0 100 200 300 400 500 600 700 800 900
50 150 250 350 450 550 650 750 850 950
100 200 300 400 500 600 700 800 900 1000
Task d: 0 100 200 300 400 500 600 700
50 150 250 350 450 550 650 750
100 200 300 400 500 600 700 800
80 120 250 399 401 500 626 772
100 100 200 or 300 400 400 500 600 800
Estimation 1 Page 13 Task A: 34, Task b: 16 Task c: 22 is close to 20, 47 is close to 50, estimate = 70 Task d: Estimate Answer 60 59 130 130 100 94 100 99 100 97 120 118
Rounding 1 Page 11 Task A: 2(1 also acceptable), 8 (7 also acceptable) Task b: 8 = 10, 13 = 10, 19 = 20, 16 = 20 Task c: 15 = 10 or 20, 18 = 20, 25 = 20 or 30, 27 = 30, 12 = 10, 30 = 30 Task d: 23 = 20, 67 = 70, 45 = 40 or 50, 99 = 100, 52 = 50, 38 = 40, 75 = 70 or 80, 14 =10
Estimation 2 Page 14 Task a: b. 32 + 11 = 30 + 10 = 40 c. 79 – 19 = 80 – 20 = 60 d. 151 + 39 = 150 + 40 = 190 e. 289 – 32 = 290 – 30 = 260 f. 531 – 49 = 530 – 50 = 480 Task b: a.60, b.60, c.380, d.800, e.270, f.990, g.1560
Rounding 2 Page 12 Task A: 6 = 10, 13 = 10, 18 = 20, 20 = 20, 15 = 10 or 20 Task b: 22 = 20, 64 = 60, 35 = 30 or 40, 98 = 100
Counting By … Page 15 10, 12, 14, 16, 18 12, 15, 18, 21, 24, 27 16, 20, 24, 28, 32, 36 20, 25, 30, 35, 40, 45
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53
24, 30, 36, 42, 48, 54 28, 35, 42, 49, 56, 63 32, 40, 48, 56, 64, 72 36, 45, 54, 63, 72, 81 40, 50, 60, 70, 80, 90 44, 55, 66, 77, 88, 99 48, 60, 72, 84, 96, 108 52, 65, 78, 91, 104, 117 56, 70, 84, 98, 112, 126 60, 75, 90, 105, 120, 135 64, 80, 96, 112, 128, 144 68, 85, 102, 119, 136, 153 72, 90, 108, 126, 144, 162 76, 95, 114, 133, 152, 171 80, 100, 120, 140, 160, 180
Rule Of Order 1 Page 21 Task a: 15, 6 + 2 = 8, 30 + 3 = 33, 16 + 5 = 21 15, 4 + 15 = 19, 8 + 36 = 44, 9 – 8 = 1 8, 2 + 5 = 7, 2 – 2 = 0 9, 20 – 4 = 16, 15 + 6 = 21, 21 – 3 = 18, 4 + 3 = 7
This is a Ready-Ed Publications' book preview. Multiples Page 16 Task A: b. 2, 6, 8, 10, 12, 14, 16, 20 c. 14, 21, 28, 42, 49, 56, 63, 70 d. 10, 30, 40, 50, 60, 80, 90, 100 e. 25, 50, 100, 125, 150, 200, 225, 250 f. 15, 30, 45, 75, 90, 120, 135, 150 g. 12, 36, 48, 60, 84, 96, 108 Task b: a. 15 b. 42 c. 30 d. 24 Factors Page 17 Task a: b. 1, 2, 5, 10 c. 1, 2, 3, 4, 6, 8, 12, 24 d. 1, 2, 4, 5, 10, 20, 25, 50, 100 e. 1, 2, 3, 4, 6, 9, 12, 18, 36 f. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Task b: b. 15 c. 9 d. 18 e. 4 Imagining Negative Numbers Page 18 a. 0 b. below ground level c. 7 d. No e. Post Office f. -4 + 4 + 3 – 1 + 3 – 9 Butcher/Bakery, Post Office/Newsagent, Greengrocer, Appliances, Car Park A g. Down 2, up 5, down 2, down 1
Rule Of Order 2 Page 22 Task A: 22, 27 + 6 = 33, 56 + 9 = 65 55, 11 + 45 = 56, 30 – 16 = 14, 9 – 7 = 2, 60 – 7 = 53 Task b: 26, 10+ 20= 30, 7 + 4×3 = 7 + 12 = 19, 5×2-3 = 10 – 3 = 7, 4 + 6 = 10 Addition: 1 Page 23 Task A: 985, 688, 983 Task b: 64, 97, 985, 999, 794, 968, 787, 959 Addition: 2 Page 24 Task A: 59, 91, 959, 758 973, 489, 993, 859 953, 895, 985, 988 999, 989, 769, 895 9395, 9571, 8389, 7693 Addition: Regrouping 1 Page 25 Task A: 993, 694, 991 Task b: 70, 82, 983, 993 496, 665, 8787, 5873 Addition: Regrouping 2 Page 26 Task A: 62, 90, 61, 462 682, 583, 861, 752 662, 851, 386, 476 Task b: 573, 775, 661, 401 7393, 8372, 4671, 6567 Addition: Regrouping 3 Page 27 Task A: 923, 704, 911 Task b: 920, 922, 903, 833 940, 722, 740, 821 Addition: Regrouping 4 Page 28 Task A: 612, 610, 901, 512 712, 733, 841, 722 522, 802, 425, 524 Task b: 534, 826, 522, 655 7443, 8423, 4733, 6608 10 022, 3841, 9672, 13 031
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Where Am I? Page 19 Task a: a.-3 b.9 c.2 d.-10 e.6 f.-13 g.-5 h.19 i. -8 j.-12 Task b: a.15 b.-5 c.-10 d.-6 e.-3, 0 f.-5, -9 g.10, 18 h.-40, -46 i.103, 113 j.23, 38 k.-74, -95 l.-360, -685 54
Subtraction 1 Page 29 Task A: 111, 520, 221 Task b: 20, 11, 143, 112 225, 222, 113, 315
Real Life Subtraction Page 38 44 - 12 = 32 yo 20 – 7 = 13 layers 50 – 23 = $27 356 – 125 = 231 pages 75 – 11- 22- 32 = $10 95 – 80 = 115 seconds 187 – 125 = 62, so 63 points 25 000 – 13 500 = 11 500 MB
This is a Ready-Ed Publications' book preview. Subtraction 2 Page 30 Task A: 11, 11, 11, 331 111, 245, 221, 211 111, 211, 243, 124 625, 205, 122, 401 1121, 1131, 1111, 1211
Subtraction: Regrouping 1 Page 31 Task A: 108, 517, 217 Task b: 18, 17, 136, 104 Subtraction: Regrouping 2 Page 32 Task A: 8, 12, 9, 124 410, 89, 231, 304 212, 205, 330, 698 Task b: 515, 519, 209, 185 1121, 4322, 6419, 287 Subtraction: Regrouping 3 Page 33 Task A: 178, 477, 177 Task b: 78, 187, 276, 384 Subtraction: Regrouping 4 Page 34 Task A: 578, 232, 187, 384 387, 209, 191, 304 192, 245, 469, 578 465, 479, 189, 365 Task b: 1081, 5882, 6349, 6261 Addition And Subtraction 1 Page 35 a.37, b.117, c.78, d. 95, e.85, f.29, g.32, h.40, i.116 j.38, k.46, l.15 Addition And Subtraction 2 Page 36 a.134, b.217, c.1355, d.284, e.636, f.867, g.993, h.148, i.1264, j.237, k.917, l.587 Real Life Addition Page 37 25 + 32 = $57 5423 + 2374 = 7797 ml 742 + 595 = 1337 units 175 + 279 = 454 km 8 + 32 + 12 = 52 yo 24 + 31 + 29 = 84 students 230 + 157 + 75 = $462 435 + 240 + 562 = 1237
Real Life Addition And Subtraction Page 39 1200 – 865 = 335 words 2200 + 3100 + 2750 = 8050 g 186 – 55 = 131 cm 245 + 223 = 468 195+ 264 = 459 Sam and Emily 18433 – 125- 62 = 18246 places 40320 – 280 = 40 040 ways 1000 – 123 – 340 – 238 = 299 pieces 16 000 – 8200 – 4300 – 245 = 3255MB Multiplication: Regrouping 1 Page 40 Task A: 72, 81, 96 Task b: 108, 147 Multiplication: Regrouping 2 Page 41 Task A: 52, 60, 116 Task b: 72, 72, 85, 36 104, 76, 144, 56 Multiplication: Regrouping 3 Page 42 252, 476, 222 348, 180, 174 Multiplication: Regrouping 4 Page 43 Task A: 90, 399, 144 Task b: 282, 370, 525, 258 Multiply These! Page 44 a. 174 b. 470 c. 2592 d. 3598 e. 332 f. 485 g. 2816 h. 1839 i. 432 j. 192 k. 1442 l. 1962 Division 1 Page 45 21, 24 Division 2 Page 46 Task A: 8÷4 = 2, 4÷4=1 Answer = 21 9÷3 = 3, 3÷3=1, Answer = 31 2÷2=1, 6÷2=3, Answer = 13 9÷3=3, 9÷3=3, Answer = 33
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Division With Remainders 1 Page 47 Task A: 5÷5=1, 7÷5 (goes in 1 time), 2 left over, 2 is your remainder. Answer = 11 r2 Task b: 21 r 2; 14 r 1; 22 r 2; 11 r 3
This is a Ready-Ed Publications' book preview. Division With Remainders 2 Page 48 Task A: 20 r 3; 24 r 1; 30 r 1; 11 r 1; 11 r 2; 34 r 1; 32 r 2; 11 r 3; 23; 33; 30; 23 Task b: 11 r 1 Division With Regrouping 1 Page 49 Task A: Divide the tens column first: 5÷3 = 1 r 2 Divide the ones column next: 27 ÷ 3 =9 Answer = 19 Task b: Divide the tens column first: 9 ÷4 = 2 r 1 Divide the ones column next: 16 ÷4 = 4 Answer = 24
Division With Regrouping 2 Page 50 Task A: 16; 14; 25 r 2; 32 r 2; 12; 10 r 1; 18 r 1; 12 r 3; 10 r 6; 12 r 2; 18 r 2; 29 r 1; 21 r 2; 16 r 2; 13 r 4; 16 r 2 Task b: 17 r 1; 21 r 2; 13 r 3 Real Life Multiplication Page 51 1. 7×6=$42. 2. 27×3=81 lollies 3. 7×32=224 outfits 4. 17×4=68 people 5. 62×9=558 words 6. 35×4=140 answers 7. 3×2=6 cups of rice 8. 28 $10 notes Real Life Division Page 52 1. 48÷12=4 times 2. 30÷5= 6 groups 3. 21÷3 = 7 bottles 4. 64÷16 = 4 shelves 5. 56÷7 = 8 weeks 6. 126 ÷7 = 18 weeks 7. 1500 ÷ 6 = 250 words 8. 18 rides
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56