WRITTEN BY RON SHAWT H E A C T I V I T I E S I N T H I S B O O K A D D R E S S M A N Y O U T C O M E S I N T H E S Y L L A B U S
Smarten up inMaths
for students 8-9 years old
Smarten up in Maths (age 8-9) Intelligent Australia Productions
First published in 2008 by Intelligent Australia Productions
© Ron Shaw 2008
ISBN 978-0-9805774-3-3
IAP 037
Intelligent Australia Productions PO Box 670 Hillarys, WA 6923 Australia
Tel: (08) 9307 8365 Fax: (08) 9402 2339 Email: [email protected]
Dedicated to the students of Beaconsfield Primary School
COPYING OF THIS BOOK BY EDUCATIONAL INSTITUTIONS A purchasing educational institution may only photocopy pages within this book in accordance with the Australian Copyright Act 1968 (the Act) and provided the educational institution (or body that administers it) has given a remuneration notice to the Copyright Agency Limited (CAL) under the Act.
Acknowledgements
In this book Intelligent Australia Productions has used graphics that were obtained under licence from Jupiter Images. IAP is indebted to rightful copyright holders of other graphics and illustrations who kindly consented to their use here. Yet other images used in this work are freely available in the Public Domain. In the few cases where attempts to gain permission for use from original copyright holders were not successful: If you believe in good faith that materials used by us infringe your copyright, you (or your agent) may send us a written notice that includes the following information:
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Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 2
• Postal Address IAP PO Box 670 Hillarys, WA Australia 6923 • Email [email protected]
• Telephone (08) 9307 8365 Int’l (618) 9307 8365
• Fax (08) 9402 2339 Int’l (618) 9402 2339
www.intelligentaustralia.com
Intelligent Australia Productions is committed to raising standards in Literacy and Numeracy in Australian schools.
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 3
CCCCCCCCoooooooonnnnnnnntttttttteeeeeeeennnnnnnnttttttttssssssss TTeeaacchheerrss NNootteess 4
Addition Adding a three-digit number to a three-digit number: no carrying 5
Addition Adding a three-digit number to a three-digit number: carrying 6
Subtraction Subtracting a three-digit number from a three-digit number: no carrying 7
Subtraction Subtracting a three-digit number from a three-digit number: carrying 8
Multiplication Multiplying a two-digit number by a one-digit number (carrying)
9
Multiplication Times Tables Grids
10
Division How to set out division problems (two ways) 11
Number Sentences Insert a + or – sign to make the number sentence true (three-digit numbers) 12
Doubling & Halving A quick way to double and halve many large numbers.
13
Number Patterns Whole Numbers Increasing & Decreasing. Write the missing number.
14
Number Patterns Whole Numbers Increasing & Decreasing. Write the missing numbers. 15
Numbers to 999 Reading & Writing Numbers 16
Numbers to 999 Ordering Smallest first; Largest first 17
Place Value Thousands, Hundreds, Tens & Units
18
Numbers to 9999 Ordering Smallest first; Largest first 19
Fractions Halves, Quarters & Eighths 20
Fractions Halves, Quarters & Eighths 21
Fractions Tenths & Hundredths 22
Decimals Tenths & Hundredths Decimal & Fractional equivalence
23
Fractions & Decimals Tenths & Hundredths 24
Ordering Decimal & Fractional Quantities Tenths & Hundredths
25
Telling the Time Minutes to and past the hour: multiples of 5 minutes Writing times.
26
Telling the Time Minutes to and past the hour: multiples of 5 minutes Drawing hands.
27
Measuring with a Ruler Measuring lines to the nearest millimetre 28
Plane Shapes Naming and drawing shapes 29
Solid Shapes Name the shape and give a real-life example 30
Problem Solving Money 31
Problem Solving Measurement 32
Problem Solving Time 33
Problem Solving Real-life Situations 34
SSoolluuttiioonnss
35
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 4
TTTTTTTTeeeeeeeeaaaaaaaacccccccchhhhhhhheeeeeeeerrrrrrrrssssssss NNNNNNNNooooooootttttttteeeeeeeessssssss About This book has been written to complement core Mathematics texts for Australian students aged 8 and 9. In some States this equates to year three and in others to year four.
In many classrooms there is an age range of twelve months or more; this may mean there are students in the class who are barely 8 years old while others are well past their 9th birthday. The pages that follow endeavour to address this anomaly by providing activities that cater to ages across such a range.
What this book offers * exercises in the most important concepts from the Mathematics syllabus * worksheets with easy-to-follow instructions and space for working-out * solutions at the back of the book, for ready reference * activities that are equally useful as in-class lessons or home assignments
Benefits of Use Teachers who use these worksheets with their students will be pleased with the results. There is plenty of scope for consolidation of previously-learned concepts and ample opportunities for accomplished maths students to demonstrate their skills.
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 5
1)
413 + 352
____
2) 296
+ 103
____
3) 441
+ 134
____
4) 336
+ 101
____
5) 209
+ 750
____
6) 545
+ 120
____
7) 373
+ 103
____
8) 321
+ 217
____
9) 563
+ 102
____
10) 342
+ 320
____
11) 290
+ 506
____
12) 115
+ 542
____
13) 372
+ 103
____
14) 473
+ 215
____
15) 416
+ 140
____
16) 382
+ 114
____
17) 117
+ 412
____
18) 436
+ 220
____
19) 593
+ 204
____
20) 464
+ 103
____
Adding a three-digit number to a three-digit number (no carrying)
AAAAAAAAddddddddddddddddiiiiiiiittttttttiiiiiiiioooooooonnnnnnnn
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 6
1) 214
+ 468
____
2) 507
+ 269
____
3) 381
+ 409
____
4) 172
+ 418
____
5) 227
+ 118
____
6) 326
+ 480
____
7) 456
+ 192
____
8) 287
+ 682
____
9) 691
+ 192
____
10) 448
+ 370
____
11) 467
+ 379
____
12) 553
+ 287
____
13) 487
+ 248
____
14) 198
+ 198
____
15) 356
+ 465
____
16) 479
+ 332
____
17) 458
+ 199
____
18) 723
+ 189
____
19) 658
+ 158
____
20) 379
+ 296
____
Adding a three-digit number to a three-digit number (carrying)
AAAAAAAAddddddddddddddddiiiiiiiittttttttiiiiiiiioooooooonnnnnnnn
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 7
1) 346
- 125
____
2) 803
- 601
____
3) 495
- 272
____
4) 708
- 307
____
5) 771
- 611
____
6) 582
- 152
____
7) 139
- 116
____
8) 347
- 201
____
9) 642
- 612
____ ____
10) 999
- 346
____ ____
11) 557
- 151
____
12) 886
- 324
____ ____
13) 290
- 180
____ ____
14) 711
- 501
____ ____
15) 852
- 312
____ ____
16) 683
- 640
____ ____
17) 701
- 300
____
18) 195
- 115
____
19) 375
- 261
____
20) 483
- 121
____
Subtracting a three-digit number from a three-digit number (no carrying)
SSSSSSSSuuuuuuuubbbbbbbbttttttttrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnn
Smarten up in Maths (age 8-9)
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1) 436
- 228
____
2) 535
- 119
____ ____
3) 487
- 268
____
4) 153
- 119
____
5) 654
- 518
____
6) 327
- 229
____
7) 877
- 269
____
8) 446
- 328
____
9) 510
- 203
____
10) 620
- 118
____
11) 466
- 158
____
12) 236
- 229
____
13) 478
- 129
____
14) 220
- 101
____
15) 347
- 128
____
16) 543
- 267
____
17) 640
- 189
____
18) 802
- 447
____
19) 600
- 291
____
20) 590
- 394
____
Subtracting a three-digit number from a three-digit number (carrying)
SSSSSSSSuuuuuuuubbbbbbbbttttttttrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnn
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 9
1) 23 x 6
2) 65 x 5
3) 37 x 4
4) 28 x 3
5) 42 x 7
6) 58 x 9
7) 36 x 7
8) 29 x 9
9) 84 x 8
10) 26 x 3
11) 19 x 7
12) 38 x 4
13) 92 x 6
14) 79 x 3
15) 25 x 8
16) 54 x 9
17) 63 x 7
18) 18 x 7
19) 86 x 6
20) 67 x 3
Multiplying a two-digit number by
a one-digit number (carrying)
MMMMMMMMuuuuuuuullllllllttttttttiiiiiiiipppppppplllllllliiiiiiiiccccccccaaaaaaaattttttttiiiiiiiioooooooonnnnnnnn
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 10
How fast can you complete these grids? Your teacher will tell you when to start and stop.
x 5 2 4 x 9 8 3
2
8
4
3
5
9
x 0 6 7 x 5 2 4
7
8
6
3
0
9
x 5 2 4 x 9 8 3
7
0
6
6
0
7
Times Tables Grids
MMMMMMMMuuuuuuuullllllllttttttttiiiiiiiipppppppplllllllliiiiiiiiccccccccaaaaaaaattttttttiiiiiiiioooooooonnnnnnnn
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 11
Example: How many 7s in 21? ?
This may be written 21 ÷ 7 = ? or 7)21
I want to find how many lots of 7 fit into 21.
I draw 7 circles, then another 7, then another 7, as shown here. (I stop because I now have 21).
3 3 Answer: 21 ÷ 7 = 3 or 7)21
Use this method to find the answers to the following division questions. Draw very small circles as above. Write your answers in the two ways shown here. 1) How many 4s in 16? 2) How many 9s in 18? 3) How many 3s in 12? 4) How many 6s in 24?
5) How many 8s in 16? 6) How many 3s in 15? 7) How many 7s in 14? 8) How many 4s in 20?
9) How many 5s in 25? 10) How many 2s in 12?
11) How many 3s in 18?
12) How many 4s in 24?
13) How many 6s in 30?
14) How many 8s in 24?
15) How many 7s in 28?
16) How many 9s in 27?
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
DDDDDDDDiiiiiiiivvvvvvvviiiiiiiissssssssiiiiiiiioooooooonnnnnnnn
ooooooo
ooooooo
ooooooo
How to set out division problems (two ways) Dividing is about finding how many groups.
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 12
Write a + or – sign in the circles to make the number sentences true.
1)
158 234 = 392
2)
188 155 = 343
3)
410 299 = 111
4)
742 477 = 265
5)
703 434 = 269
6)
721 299 = 422
7)
450 471 = 921
8)
800 564 = 236
9)
884 567 = 317
10)
357 617 = 974
11)
567 412 = 155
12)
693 213 = 906
13)
477 178 = 655
14)
867 584 = 283
15)
755 432 = 323
16)
255 278 = 533
17)
199 198 = 397
18)
174 302 = 476
19)
578 156 = 422
20)
844 632 = 212
(three-digit numbers)
NNNNNNNNuuuuuuuummmmmmmmbbbbbbbbeeeeeeeerrrrrrrr SSSSSSSSeeeeeeeennnnnnnntttttttteeeeeeeennnnnnnncccccccceeeeeeeessssssss
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 13
Many numbers may be doubled or halved by doubling or
halving their individual digits.
Example 1 Doubling the individual digits in 30 results in 60 Example 2 Doubling the individual digits in 124 results in 248
Example 3 Halving the individual digits in 22 results in 11 Example 4 Halving the individual digits in 486 results in 243
- Doubling -
1) Double 2.
…………….….
2) Double 4.
…………….….
3) Double 3.
…………….….
4) Double 5.
…………….…. 5) Double 10.
…………….….
6) Double 20.
…………….….
7) Double 30.
…………….….
8) Double 40.
…………….…. 9) Double 100.
…………….….
10) Double 200.
…………….….
11) Double 300.
…………….….
12) Double 400.
…………….….
13) Double 11.
…………….….
14) Double 22.
…………….….
15) Double 33.
…………….….
16) Double 44.
…………….….
17) Double 12.
…………….….
18) Double 23.
…………….….
19) Double 41.
…………….….
20) Double 123.
…………….….
- Halving -
21) Halve 4.
…………….….
22) Halve 10.
…………….….
23) Halve 6.
…………….….
24) Halve 20.
…………….…. 25) Halve 8.
…………….….
26) Halve 12.
…………….….
27) Halve 40.
…………….….
28) Halve 60.
…………….…. 29) Halve 80.
…………….….
30) Halve 22.
…………….….
31) Halve 44.
…………….….
32) Halve 200.
…………….…. 33) Halve 400.
…………….….
34) Halve 600.
…………….….
35) Halve 800.
…………….….
36) Halve 842.
…………….….
There is a quick way to double and halve many large numbers.
DDDDDDDDoooooooouuuuuuuubbbbbbbblllllllliiiiiiiinnnnnnnngggggggg &&&&&&&& HHHHHHHHaaaaaaaallllllllvvvvvvvviiiiiiiinnnnnnnngggggggg
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 14
1) 14, 17, 20, 23, ____, 29, 32
___
2) 10, 13, 16, ____, 22, 25, 28
___ 3) 71, 73, 75, ____, 79, 81, 83
___
4) 3, 5, ____, 9, 11, 13, 15, 17
___ 5) 11, 15, ____, 23, 27, 31, 35 ____
6) 43, 47, 51, ____, 59, 63, 67 ____
7) 5, ____, 17, 23, 29, 35, 41 ____
8) 2, ____, 16, 23, 30, 37, 44
___ 9) 4, ____, 14, 19, 24, 29, 34
10) 8, ____, 28, 38, 48, 58, 68
11) 22, ____, 16, 13, 10, 7, 4, 1
12) 31, ____, 23, 19, 15, 11, 7
13) 42, ____, 36, 33, 30, 27, 24 ____
14) 60, ____, 46, 39, 32, 25, 18
15) 54, ____, 42, 36, 30, 24, 18
16) 100, ____, 94, 91, 88, 85
17) ____, 51, 43, 35, 27, 19, 11
18) ____, 87, 83, 79, 75, 71, 67
19) ____, 46, 39, 32, 25, 18, 11
20) ____, 88, 79, 70, 61, 52, 43
Whole Numbers Increasing & DecreasingWhole Numbers Increasing & DecreasingWhole Numbers Increasing & DecreasingWhole Numbers Increasing & Decreasing Write the missing number
NNNNNNNNuuuuuuuummmmmmmmbbbbbbbbeeeeeeeerrrrrrrr PPPPPPPPaaaaaaaatttttttttttttttteeeeeeeerrrrrrrrnnnnnnnnssssssss
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 15
1) 56, 59, ____, 65, 68, ____
___
2) 57, 63, ____, 75, 81, ____
3) 5, 13, ____, 29, ____, 45 ____
4) 37, 44, ____, 58, 65, ____
___ 5) 7, 16, 25, ____, 43, ____
6) 11, ____, 25, 32, ____, 46 ____
7) 23, 31, ____, 47, ____, 63 ____
8) 6, 13, ____, 27, 34, ____
___ 9) 9, ____, 21, 27, ____, 39
10) 14, 20, ____, 32, 38, ____
11) 44, 53, ____, 71, 80, ____
12) 19, 30, 41, ____, 63, ____
13) 56, 52, ____, 44, 40, ____
14) 71, 67, 63, ____, 55, ____
15) 37, 31, ____, 19, 13, ____
16) 49, 41, ____, 25, 17, ____
17) 50, 43, ____, 29, ____, 15
18) 63, 57, ____, 45, ____, 33
19) 80, 72, 64, 56, ____, ____
20) 60, 51, ____, 33, ____, 15
Whole Numbers Increasing & DecreasingWhole Numbers Increasing & DecreasingWhole Numbers Increasing & DecreasingWhole Numbers Increasing & Decreasing Write the missing numbers
NNNNNNNNuuuuuuuummmmmmmmbbbbbbbbeeeeeeeerrrrrrrr PPPPPPPPaaaaaaaatttttttttttttttteeeeeeeerrrrrrrrnnnnnnnnssssssss
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 16
B. Read the number to yourself (in your mind) & then write it in figures.
1) Nine hundred and thirteen ………………….…….……
2) Four hundred and twenty-one ……………….……….……
3) Six hundred and seventy-two …………………….….……
4) Two hundred and four ……………….………….…
5) Five hundred and ninety-nine ………………….…….……
6) Eight hundred and sixteen ………………………..……
7) One hundred and fifty-one ………………………..……
8) Eight hundred and twenty-seven ………………….…….……
9) Three hundred and eighty ………………………..…… B. Say the number to yourself (in your mind) and then write it in words.
1) 273 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
2) 447 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
3) 179 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
4) 668 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
5) 780 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
6) 593 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
7) 406 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
8) 993 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
9) 643 …………………………………………………………………………………………….…………………………………………………………………………………………………………...……………………………….
Reading & Writing NumbersReading & Writing NumbersReading & Writing NumbersReading & Writing Numbers
NNNNNNNNuuuuuuuummmmmmmmbbbbbbbbeeeeeeeerrrrrrrrssssssss ttttttttoooooooo 999999999999999999999999
The Eiffel Tower is
three hundred and
twenty-four metres tall.
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 17
Put these number cards in order, smallest first.
11.. ��������
22.. ��������
33.. ��������
Put these number cards in order, largest first.
44.. ��������
55.. ��������
66.. ��������
77.. ��������
Ordering to Ordering to Ordering to Ordering to 999 999 999 999 Smallest first; Largest first
NNNNNNNNuuuuuuuummmmmmmmbbbbbbbbeeeeeeeerrrrrrrrssssssss ttttttttoooooooo 999999999999999999999999
454
543
623
187
431
444
179
642
403
299
795
178
799
677
742
897
631
638
843
750
602
599
633
189
659
209
902
788
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 18
Thousands place Hundreds place Tens place Units place
4 576 A. Write the place occupied by the 6. Example: 4 603 � hundreds
1) 8 764 � ……….………………………………………….…… 2) 6 075 � …………..………………………………………….…
3) 5 216 � ……….………………………………………………..… 4) 7 461 � ……….…………..………………………………….…
5) 2 679 � ……….………………………………………….…….… 6) 2 063 � ……….…….……………………………………….…
7) 3 896 � ……….……………………………………….……….… 8) 6 902 � ……….………………………………..…………….…
9) 9 602 � ……….…………………………………………..…….… 10) 5 364 � ……….…………………………………………….…
B. Write the value of the underlined digit. Example: 7 253 � 7 000
1) 8 104 � ……….………….… 2) 1 075 � ……….………….… 3) 5 218 � ……….………….…
4) 7 421 � ……….………….… 5) 2 679 � ……….………….… 6) 2 093 � ……….………….…
7) 3 896 � ……….………….… 8) 4 906 � ……….………….… 9) 9 102 � ……….………….…
C. Write the number made up of:
Example: three tens, two thousands, zero hundreds, four units � 2 034
1) two tens, five thousands, seven hundreds, zero units � ……….…………………….…
2) one hundred, seven units, four tens, nine thousands � ……….…………………….…
3) one thousand, eight units, zero tens, six hundreds � ……….…………………….…
4) eight units, eight hundreds, nine tens, four thousands � ……….…………………….…
5) five tens, seven thousands, seven units, two hundreds � ……….…………………….…
6) zero units, seven hundreds, six tens, five thousands � ……….…………………….…
Thousands, Hundreds, Tens & Units
PPPPPPPPllllllllaaaaaaaacccccccceeeeeeee VVVVVVVVaaaaaaaalllllllluuuuuuuueeeeeeee
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 19
Put these number cards in order, smallest first.
11.. ��������
22.. ��������
33.. ��������
Put these number cards in order, largest first.
44.. ��������
55.. ��������
66.. ��������
77.. ��������
OrderingOrderingOrderingOrdering Smallest first; Largest first
NNNNNNNNuuuuuuuummmmmmmmbbbbbbbbeeeeeeeerrrrrrrrssssssss ttttttttoooooooo 99999999999999999999999999999999
6428
5837
5987
3871
3854
4002
1110
1108
1099
5434
5221
5399
9567
9576
9499
8020
8018
8100
2382
2299
2379
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 20
** Colour from left to right, coloured pieces touching **
Can you see that ½ is the same size as
2/4 ?
2/4
** Colour from left to right, coloured pieces touching ** --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Now do the same with these circles. Use blue this time. --------------------------
** Make sure coloured pieces are touching **
Alongside each circle write the fraction you coloured blue.
Can you again see that 4/8, 2/4 and
1/2 are all the same size?
Challenge: You know that 1/2 =
2/4 = 4/8 . Notice that the numerators (the top part of each fraction)
are doubling, and so are the denominators (the bottom part of each fraction).
See if you can fill in the missing numerators and denominators below: 1/2 =
2/4 = 4/8 =
/16 = 16/ =
/64 = /128 =
128/
Halves, Quarters & Eighths
FFFFFFFFrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnnssssssss
Colour ½ red.
Colour 2/4 red.
Colour 4/8 red.
Can you see that 4/8, 2/4 and
1/2 are all the same size?
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 21
Fill in the blanks on the number lines.
0 1/2 1
0 1/4
1/2 3/4 1
1/4 2
2 21/4 4
0 1/8
2/8 6/8 1
1 11/8 1
5/8 2
Halves, Quarters & Eighths
FFFFFFFFrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnnssssssss
colour 1/4 colour 3/4 colour
5/8
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 22
�
If we divide the slab into 10 equal parts, each part is called 1/10 .
If we divide the slab into 100 equal parts, each
part is called 1/100 .
Colour the first three columns red.
Write the fraction that is shaded �
Write the fraction that is not shaded �
Write the missing fractions….
…………….….. + ……………….. = 1
Colour the first three columns blue. Do you agree that 30/100 of the slab is blue? Can you see that 30/100 +
70/100 = 1 ? Can you see that 30/100 =
3/10 ? Do you agree that 1/10 =
10/100 ?
This is a “1” strip. �
Now the “1” strip has been divided into 10 equal parts.
Write in the missing fraction: 3/10 +……………….= 1
Write in the missing fraction: 6/10 +……………….= 1 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Tenths & Hundredths
FFFFFFFFrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnnssssssss
Colour 3/10 red.
Write the fraction that is not shaded. �
Colour 6/10 blue.
Now write the fraction that is not shaded. �
1
It is 1 unit in length.
Its size is 1 unit.
1
The “1” slab has been divided into 10 equal parts.
Now the “1” slab has been divided into 100 equal parts.
This is a “1” slab.
�
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 23
If we divide $1 evenly between ten people each person will receive 10c. That’s because 1/10 of $1 is 10c.
We may write the fraction 1/10 as a decimal number. 1/10 is 0.1 in decimal language. So we can say that 0.1 of $1 is 10c.
What happens if we divide $1 evenly between 100 people? This time each person will receive only 1c. (that’s if we had 1c pieces!) We say 1/100 of $1 is 1c. OR we could say 0.01 of $1 is 1c.
1c is such a tiny amount. How about we split up $100 rather than just $1? Can you can fill in the empty spaces in the table below?
Fractions and Decimals of $100 Amount Fraction Decimal $100
100/100 1.0
$95 95/100 0.95
$90 90/100 We write 9/10 0.90 We write 0.9
$85 85/100 0.85
$80 80/100 We write 8/10 0.80 We write 0.8
$75 75/100
$70 0.70 We write 0.7
65/100 0.65
$60 60/100 We write 6/10
$55 0.55
$50 0.50 We write 0.5
$45
0.40 We write 0.4
35/100
30/100 We write 3/10
$25
$20
$15
$10
$5
Tenths & Hundredths Decimal & Fractional equivalence
DDDDDDDDeeeeeeeecccccccciiiiiiiimmmmmmmmaaaaaaaallllllllssssssss
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 24
1. Write fractions to fill in the blanks on the number line. 0 1/10
4/10 8/10 1
2. Write decimal numbers to fill in the blanks on the number line. 0 0.1 0.2 0.5 0.7 1
3. Write fractions to fill in the blanks on the number line. 0 1/100
5/100
4. Write decimal numbers to fill in the blanks on the number line. NB The spaces along this line are the same size as those in 3 (above) because 1/100 = 0.01. 0 0.01 0.05
5. Write decimal numbers to fill in the blanks on the number line. 1 1.1 1.3 1.6 2
6. Fill in the blanks on the number line. 1 11/10 14/10 17/10 2
Tenths & Hundredths
FFFFFFFFrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnnssssssss &&&&&&&& DDDDDDDDeeeeeeeecccccccciiiiiiiimmmmmmmmaaaaaaaallllllllssssssss
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 25
Put these number cards in order, smallest first.
11.. ��������
22.. ��������
33.. ��������
Put these number cards in order, largest first.
44.. ��������
55.. ��������
66.. ��������
Tenths & Hundredths
OOOOOOOOrrrrrrrrddddddddeeeeeeeerrrrrrrriiiiiiiinnnnnnnngggggggg DDDDDDDDeeeeeeeecccccccciiiiiiiimmmmmmmmaaaaaaaallllllll &&&&&&&& FFFFFFFFrrrrrrrraaaaaaaaccccccccttttttttiiiiiiiioooooooonnnnnnnnaaaaaaaallllllll QQQQQQQQuuuuuuuuaaaaaaaannnnnnnnttttttttiiiiiiiittttttttiiiiiiiieeeeeeeessssssss
0.9
8/10
0.4
70/100
0.65
95/100
0.2
3/10
1/10
3/10
0.6
7/10
75/100
0.95
85/100
6/10
0.7
8/10
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 26
Write the time shown on each clock.
Writing times shown on clocks. Minutes to and past the hour: multiples of 5 minutes
TTTTTTTTeeeeeeeelllllllllllllllliiiiiiiinnnnnnnngggggggg tttttttthhhhhhhheeeeeeee TTTTTTTTiiiiiiiimmmmmmmmeeeeeeee
1
:
2
4
5
7 6
8
10
11
3
9
1
12
6
12
6
12 11
9 3
3 9
8
10
2
5
4
7
8
11
2
4
5 7
10
1
: :
1
:
2
4
5 7 6
8
10
11
3
9
1 12
6
12
6
11
9 3
3 9
8
10 2
5
4
7
8
11
2
4
5 7
10
1
: :
12
Is pm before noon or after noon?
Just remember…. pm is
past midday.
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 27
Draw hands on the clocks to match the times below.
1
11:05
2
4
5
7 6
8
10
11
3
9
1
12
6
12
6
12 11
9 3
3
9
8
10
2
5
4
7
8
11
2
4
5 7
10
1
8:05 4:55
1
2
4
5 7 6
8
10
11
3
9
1 12
6
12
6
11
9 3
3 9
8
10 2
5
4
7
8
11
2
4
5 7
10
1 12
I like to eat at 6.25.
Me too. And also at 6.30, 6.35. 6.40….
Drawing hands on clock faces. Minutes to and past the hour: multiples of 5 minutes
TTTTTTTTeeeeeeeelllllllllllllllliiiiiiiinnnnnnnngggggggg tttttttthhhhhhhheeeeeeee TTTTTTTTiiiiiiiimmmmmmmmeeeeeeee
12:35 3:20 9:10
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 28
Write the length of each line to the nearest millimetre.
Measuring lines to the nearest millimetre
MMMMMMMMeeeeeeeeaaaaaaaassssssssuuuuuuuurrrrrrrriiiiiiiinnnnnnnngggggggg wwwwwwwwiiiiiiiitttttttthhhhhhhh aaaaaaaa RRRRRRRRuuuuuuuulllllllleeeeeeeerrrrrrrr
a. ………………..…….
b. ………………..…….
d.
c. ………………..…….
e. ………………..…….
f. ………………..…….
g. ………………..…….
h. ………………..…….
i. ………………..…….
k. ………………..…….
j. ………………..…….
l. ………………..…….
m. ………………..…….
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 29
Write the name of each shape. Then try to draw a shape similar to it (yours can be a different size) You may use a ruler or you may draw in freehand. Shapes 4 and 5 are difficult to draw…..good luck!
1.
2.
3.
4.
5.
Naming & Drawing 2-D shapes
PPPPPPPPllllllllaaaaaaaannnnnnnneeeeeeee SSSSSSSShhhhhhhhaaaaaaaappppppppeeeeeeeessssssss
This shape is a t _ _ _ _ _ _ _
Here is mine �
This shape is a s _ _ _ _ _
Here is mine �
This shape is a r _ _ _ _ _ _ _ _
Here is mine �
This shape is a p _ _ _ _ _ _ _
Here is mine �
This shape is a h _ _ _ _ _ _
Here is mine �
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 30
mm
1.
2.
3.
4.
5.
6.
Name the shape and give a real-life example
SSSSSSSSoooooooolllllllliiiiiiiidddddddd SSSSSSSShhhhhhhhaaaaaaaappppppppeeeeeeeessssssss
This shape is a s p _ _ _ _
A real-life example is
This shape is a c y _ _ _ _ _ _
A real-life example is
This shape is a c o _ _
A real-life example is
This shape is a p y _ _ _ _ _
A real-life example is
This shape is a p r _ _ _
A real-life example is
This shape is a c u _ _
A real-life example is
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 31
1) Tammy wants to buy six stickers for her sticker collection. Each sticker costs 25c. How much money does Tammy need to buy the stickers?
2) Jonathon is saving $1.50 a week. How much will he have after six weeks?
3) Timothy paid $4.75 for his lunch on Monday. On Tuesday he spent $2.95 on lunch. How much more did Timothy spend on lunch on Monday than on Tuesday?
5) Bree bought an eraser for 95c and a ruler for $1.70. How much more did the ruler cost than the eraser?
6) Dad bought tools for $119 and a wheelbarrow that cost $183. How much more was the wheelbarrow than the tools? Do your working and write your answer below.
Money
PPPPPPPPrrrrrrrroooooooobbbbbbbblllllllleeeeeeeemmmmmmmm SSSSSSSSoooooooollllllllvvvvvvvviiiiiiiinnnnnnnngggggggg
Do your working and write your answer here. �
Do your working and write your answer here. �
Do your working and write your answer here. �
4) Eliza’s mother spends $3.50 on a magazine and $1.75 on a newspaper. How much does she spend altogether?
Do your working and write your answer below.
Do your working and write your answer here. �
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 32
1) Lennie has a bad cough and each day he has to take 5ml of cough mixture. The bottle of cough mixture holds 40ml. How many days will the medicine last?
2) Rose-Marie has a 36cm piece of string. She cuts the string into pieces, each 60mm long. How many pieces will she have?
3) Hannah is 135cm tall and her big sister Yvette is
70mm taller. How tall (in cm) is Yvette?
5) Some children visited a licorice-making factory and, as a souvenir, were each given a long stick of licorice. Jason’s licorice stick measured 300mm and Johanna’s was 32cm. a) Who had the longest piece of licorice? b)What was the difference in length between the two pieces?
Measurement
PPPPPPPPrrrrrrrroooooooobbbbbbbblllllllleeeeeeeemmmmmmmm SSSSSSSSoooooooollllllllvvvvvvvviiiiiiiinnnnnnnngggggggg
Do your working and write your answer here. �
Do your working and write your answer here. �
Do your working and write your answer below.
4) Carlos weighs 84kg. Pedro weighs 7kg less.
a) How much does Pedro weigh? b) How much do the two men weigh together?
Do your working and write your answer below.
Do your working and write your answer here. �
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 33
1) Sonya’s bus was meant to arrive at 7:55am but it was 10 minutes late. At what time did the bus arrive?
2) Jack has to be at football training at 4:15pm. It is now 3:35pm. How many minutes does Jack have before he is due at football training?
3) The swimming race will start in 1½ minutes. How many seconds before the race begins?
Time
PPPPPPPPrrrrrrrroooooooobbbbbbbblllllllleeeeeeeemmmmmmmm SSSSSSSSoooooooollllllllvvvvvvvviiiiiiiinnnnnnnngggggggg
Do your working and write your answer here. �
Do your working and write your answer here. �
Do your working and write your answer below.
4) Dad is due home from work in 2½ hours. How many minutes before dad is due home?
Do your working and write your answer below.
5) The clock on the wall shows the time as 5:05. We know that the clock is 15 minutes fast. What is the actual time?
Do your working and write your answer below.
6) Hanna finished at the dentist’s at 4:15. The bus arrived to take her home at 4:35. For how long did Hannah have to wait for the bus? Do your working and write your answer below.
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 34
1) On Monday at Brolga Creek Primary School 53 children buy their lunch at the school canteen and 9 children take their lunch from home. How many more children have a canteen lunch than a home-made lunch? Do your working and write your answer here. �
2) Tim counts the spokes on the front wheel of his bicycle. There are 84 spokes. Tim counts 78 spokes on the back wheel. How many spokes are their altogether on the two wheels? Do your working and write your answer here. �
3) Tracey likes to read 6 pages each night in bed. In October she read every night, always 6 pages. How many pages did Tracey read in October? Do your working and write your answer here. �
4) Shep, my pet dog, has 4 shampoos a year. Each shampoo lasts 30 minutes. How many minutes of shampooing does Shep have in a year? Do your working and write your answer below.
5) Kaz did 84 hoop twirls and Shelley did 46. a) How many more hoop twirls did Kaz do than Shelley? b) How many hoop twirls did the girls do altogether? Do your working and write your answer here. �
6) Charlie and Oscar went fishing. Charlie used a different kind of bait from the bait that Oscar used and with this bait he caught 3 times as many fish as did Oscar. Oscar caught 24 fish. How many fish did Charlie catch? Do your working and write your answer here. �
Real-life Situations
PPPPPPPPrrrrrrrroooooooobbbbbbbblllllllleeeeeeeemmmmmmmm SSSSSSSSoooooooollllllllvvvvvvvviiiiiiiinnnnnnnngggggggg
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 35
SSSSSSSSoooooooolllllllluuuuuuuuttttttttiiiiiiiioooooooonnnnnnnnssssssss
ppaaggee 55 AAddddiittiioonn Adding a three-digit number to a three-digit number: no carrying
11)) 765 22)) 399 33)) 575 44)) 437 55)) 959 66)) 665 77)) 476 88)) 538
99)) 665 1100)) 662 1111)) 796 12) 657 13) 475 14) 688 15) 556 16) 496 17) 529 18) 656 19) 797 20) 567
ppaaggee 66 AAddddiittiioonn Adding a three-digit number to a three-digit number: carrying
11)) 682 22)) 776 33)) 790 44)) 590 55)) 345 66)) 806 77)) 648 88)) 969
99)) 883 1100)) 818 1111)) 846 12) 840 13) 735 14) 396 15) 821 16) 811 17) 657 18) 912 19) 816 20) 675
ppaaggee 77 SSuubbttrraaccttiioonn Subtracting a three-digit number from a three-digit number: no carrying
11)) 221 22)) 202 33)) 223 44)) 401 55)) 160 66)) 430 77)) 23 88)) 146
99)) 30 1100)) 653 1111)) 406 12) 562 13) 110 14) 210 15) 540 16) 43 17) 401 18) 80 19) 114 20) 362
ppaaggee 88 SSuubbttrraaccttiioonn Subtracting a three-digit number from a three-digit number: carrying 11)) 208 22)) 416 33)) 219 44)) 34 55)) 136 66)) 98 77)) 608 88)) 118
99)) 307 1100)) 502 1111)) 308 12) 7 13) 349 14) 119 15) 219 16) 276 17) 451 18) 355 19) 309 20) 196
ppaaggee 99 MMuullttiipplliiccaattiioonn Multiplying a two-digit number by a one-digit number (carrying)
11)) 138 22)) 325 33)) 148 44)) 84 55)) 294 66)) 522 77)) 252 88)) 261
99)) 672 1100)) 78 1111)) 133 12) 152 13) 552 14) 237 15) 200 16) 486 17) 441 18) 126 19) 516 20) 201
ppaaggee 1100 MMuullttiipplliiccaattiioonn Times Tables Grids teacher to check
ppaaggee 1111 DDiivviissiioonn How to set out division problems (two ways) teacher to check
ppaaggee 1122 NNuummbbeerr SSeenntteenncceess Insert a + or – sign to make the number sentence true (three-digit numbers)
11)) + 22)) + 33)) - 44)) - 55)) - 66)) - 77)) + 88)) - 99)) - 1100)) + 1111)) - 12) +
13) + 14) - 15) - 16) + 17) + 18) + 19) - 20) -
ppaaggee 1133 DDoouubblliinngg && HHaallvviinngg A quick way to double and halve many large numbers. 11.. 4 22.. 8 33.. 6 44.. 10 55.. 20 66.. 40 77.. 60 88.. 80 99.. 200 1100.. 400
1111.. 600 1122.. 800 1133.. 22 1144.. 44 1155.. 66 1166.. 88 1177.. 24 1188.. 46 1199.. 82
2200.. 246 2211.. 2 2222.. 5 2233.. 3 2244.. 10 2255.. 4 2266.. 6 2277.. 20 2288.. 30
2299.. 40 3300.. 11 3311.. 22 3322.. 100 3333.. 200 3344.. 300 3355.. 400 3366.. 421
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 36
ppaaggee 1144 NNuummbbeerr PPaatttteerrnnss Whole Numbers Increasing & Decreasing. Write the missing number.
11.. 26 22.. 19 33.. 77 44.. 7 55.. 19 66.. 55 77.. 11 88.. 9 99.. 9 1100.. 18
1111.. 19 1122.. 27 1133.. 39 1144.. 53 1155.. 48 1166.. 97 1177.. 59 1188.. 91 1199.. 53 2200.. 97
ppaaggee 1155 NNuummbbeerr PPaatttteerrnnss Whole Numbers Increasing & Decreasing. Write the missing numbers.
AA.. 11)) 62, 71 22)) 69, 87 33)) 21, 37 44)) 51, 72 55)) 34, 52 66)) 18, 39 77)) 39, 55
88)) 20, 41 99)) 15, 33 1100)) 26, 44 1111)) 62, 89 1122)) 52, 74 1133)) 48, 36
1144)) 59, 51 1155)) 25, 7 1166)) 33, 9 1177)) 36, 22 1188)) 51, 39 1199)) 48, 40 2200)) 42, 24
ppaaggee 1166 NNuummbbeerrss ttoo 999999 Reading & Writing Numbers teacher to check
ppaaggee 1177 NNuummbbeerrss ttoo 999999 Ordering Smallest first; Largest first
11)) 187, 454, 543, 623 22)) 179, 431, 444, 642 33)) 178, 299, 403, 795
44)) 897, 799, 742, 677 55)) 843, 750, 638, 631 66)) 633, 602, 599, 189
77)) 902, 788, 659, 209
ppaaggee 1188 PPllaaccee VVaalluuee Thousands, Hundreds, Tens & Units AA.. 11)) tens 22)) thousands 33)) units 44)) tens 55)) hundreds 66)) tens 77)) units
88)) thousands 99)) hundreds 1100)) tens
BB.. 11)) 100 22)) 70 33)) 8 44)) 7 000 55)) 70 66)) 3 77)) 800 88)) 4 000 99)) 9 000
CC.. 11)) 5 720 22)) 9 147 33)) 1 608 44)) 4 898 55)) 7 257 66)) 5 760
ppaaggee 1199 NNuummbbeerrss ttoo 99999999 Ordering Smallest first; Largest first
11.. 5837 5987 6428 22.. 3854 3871 4002 33.. 1099 1108 1110
44.. 5434 5399 5221 55.. 9576 9567 9499 66.. 8100 8020 8018
77.. 2382 2379 2299
ppaaggee 2200 FFrraaccttiioonnss Halves, Quarters & Eighths teacher to check
ppaaggee 2211 FFrraaccttiioonnss Halves, Quarters & Eighths teacher to check
ppaaggee 2222 FFrraaccttiioonnss Tenths & Hundredths teacher to check
ppaaggee 2233 DDeecciimmaallss Tenths & Hundredths Decimal & Fractional equivalence
teacher to check
ppaaggee 2244 FFrraaccttiioonnss && DDeecciimmaallss Tenths & Hundredths teacher to check
Smarten up in Maths (age 8-9)
© Intelligent Australia Productions 37
ppaaggee 2255 OOrrddeerriinngg DDeecciimmaall && FFrraaccttiioonnaall QQuuaannttiittiieess Tenths & Hundredths
11.. 0.4 8/10 0.9 22.. 0.65
70/100 95/100 33..
1/10 0.2 3/10
44.. 7/10 0.6
3/10 55.. 0.95 85/100
75/100 66..
8/10 0.7 6/10
ppaaggee 2266 TTeelllliinngg tthhee TTiimmee Minutes to and past the hour: multiples of 5 minutes Writing times.
12:20 6:55 4:10 9:40 6:25 12:50
ppaaggee 2277 TTeelllliinngg tthhee TTiimmee Minutes to and past the hour: multiples of 5 minutes Drawing hands.
teacher to check
ppaaggee 2288 MMeeaassuurriinngg wwiitthh aa RRuulleerr Measuring lines to the nearest millimetre aa.. 61mm bb.. 109mm cc.. 95mm dd.. 16mm ee.. 159mm ff.. 35mm gg.. 119mm
hh.. 100mm ii.. 96mm jj.. 25mm kk.. 69mm ll.. 188mm mm.. 108mm
ppaaggee 2299 PPllaannee SShhaappeess Naming and drawing shapes
1. triangle 2. square 3. rectangle 4. pentagon 5. hexagon
ppaaggee 3300 SSoolliidd SShhaappeess Name the shape and give a real-life example
1. sphere (ball) 2. cylinder (tube or pipe) 3. cone (ice cream) 4. pyramid (Egyptian tombs) 5. prism (house roof) 6. cube (child’s building blocks)
ppaaggee 3311 PPrroobblleemm SSoollvviinngg Money 11)) $1.50 2) $9.00 33)) $1.80 4) $5.25 55)) $0:75 6) $64
ppaaggee 3322 PPrroobblleemm SSoollvviinngg Measurement
11)) 8 2) 6 33)) 142 4) a. 77kg b. 161kg 55)) a. Johanna b. 2cm (20mm)
ppaaggee 3333 PPrroobblleemm SSoollvviinngg Time
11)) 8:05am 2) 40 33)) 90 4) 150 55)) 4:50 6) 20mins
ppaaggee 3344 PPrroobblleemm SSoollvviinngg Real-life Situations 11)) 44 2) 162 33)) 186 4) 120 55)) a. 38 b. 130 6) 72
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