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A LWAY S L E A R N I NG
Part of the Abacus toolkit, the textbooks and workbooks provide:theperfectbalanceofpracticeandproblemsolvingforeachareaofmaths
pictorialrepresentationstosupportchildrensconceptualunderstanding
clearlylaidoutquestionswithinstructionsthatareeasytofollow
aself-assessmentopportunityoneverypage
colourtoindicatethedifferentmathsareaswithintheprogramme.
Abacus is a unique maths toolkit for inspiring a love of maths and ensuring progression for every child. Written by an expert author team for the 2014 curriculum for England, it has been carefully crafted on a robust approach to creating inspired and confident young mathematicians.
Freedom when you want it, structure where you choose it.
Series Editor: Ruth Merttens Authors: Jennie Kerwin and Hilda Merttens
Textbook and workbook sample pages
3
Pick up a handful of counters. Estimate how many. < 10? 1020? >20? Now count them.
Cross out each grape as you count it.
Count the grapes in each bunch. How many are there?
Counting grapesContents
Key of page coloursNumber and Place value
Shape and Measure
Multiplication and Division
Addition and Subtraction
Fractions
Mixed Operations
Year 1 Workbook 1 pages:
Counting grapes p3
Adding 2; 1 more p1213
Straight or curved; Monster sort p1819
Write numbers to 20; Ordering numbers to 20 p2021
Addition facts; Bonds to 20 p1011
Counting in 10s; More and less p2829
Counting in 2s, 5s and 10s; 2s, 5s and 10s p6061
Year 3 Textbook 1 pages:
Multiplying and dividing by 3, 4, 5 and 10 p2223
Subtract by counting up p4647
Finding fractions of shapes and amounts p5455
Puzzles p9495
Year 4 Textbook 1 pages:
Metres, centimetres and millimetres p4041
Column addition of 3-digit numbers p4243
Unit fractions and equivalence p5455
Rounding 4-digit numbers p7475
Year 5 Textbook 1 pages:
Two decimal places p2224
Length and perimeter p3335
Mental multiplication strategies p2829
Year 2 Workbook 1 pages:
Finding missing numbers; Comparing 2-digit numbers p45
Comparing fractions and fi nding equivalents p5253
12
Adding 2
Write your own additions adding 2. Make them different from the ones on this page.
Use a number track to help you.
Write the next two numbers on the tracks. Complete all the additions.
13 14 15
25 26 27
17 18 19
20 21 22
14 15 16
23 24 25
26 27 28
15 + 2 =
27 + 2 =
19 + 2 =
22 + 2 =
16 + 2 =
25 + 2 =
28 + 2 =
13
Text... Text...
1 more
6 4
10 14
12 17
15 20
Write numbers where the next number ends in 0.
Use a bead string to help you.
Draw one more bead and write the next number.
Join each shape to its correct place in the hoops.
18
Straight or curved
Make a collection of shapes with curved sides.
Draw different shapes that have both straight and curved sides.
straight sides curved sides
Join each monster to its correct place in the hoops.
19
Monster sort
Make a monster from circles, squares, triangles and rectangles. How many arms does your monster have? How many eyes does it have?
Draw a monster which belongs in both hoops.
two arms three eyes
Write the missing numbers on the track starting each digit at the dot given.
20
Write numbers to 20
Use a number track to help you. Choose three numbers to write in words.
1
1112
19
2021
Write the sets of three numbers in order.
21
Ordering numbers to 20
Use a number track to help you. Choose three cards from a shuffled pack of 120 cards. Put them in order.
6
7
9
69
7 1210
11
1411
161315
18
1619
1535
4
179
211820
15
4
Write the next ten numbers after 100 on the square.
Use counters to cover numbers on the 100-square. Ask your partner to work out what the numbers are.
Write in the missing numbers on the 100-square.
Finding missing numbers
1
11
21
31
41
51
61
71
81
91
2
12
32
42
52
82
92
3
43
53
63
83
93
4
14
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
66
76
86
96
7
17
27
37
67
77
8
18
28
38
68
78
88
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
5
Comparing 2-digit numbers
Your partner shows you a number on a bead string. Write a bigger number. Write the pair down.
Work with a partner. Each secretly make a number on a bead string. Compare numbers. Which is bigger?
Circle the biggest number in each pair.
28 32
18 15
27 24
75 71
58 72
43 55
30 13
26 62
33 42
81 18
10
Addition facts
Can you make 10 with two even numbers? Two odd numbers? An odd number and an even number?
Use your fingers to help you find the answers.
Complete the additions. Add the numbers across and down to fill the grid.
+ 5 6 7 8 912345
2 + = 10
+ 7 = 9
+ 6 = 7
5 + = 10
6 + = 8
9 + 1 =
+ 3 = 10
+ 6 = 9
5 + 4 =
6 + 4 =
3 + = 8
+ 5 = 6
5 + 2 =
7 + 1 =
1 + = 9
11
Text... Text...
Bonds to 20
+ = 20 +
= 20 +
= 20
+ = 20 +
= 20 +
= 20
+ = 20 +
= 20 +
= 20
+ = 20 +
= 20 +
= 20
What do you add to: 1 to make 20?2 to make 20?Write the next five of these.
Use interlocking cubes in two colours to help you.
Complete the additions to match the cubes.
11 9
Fill in the missing numbers on each snake.
28
Use the columns on a 100-square to help you.
Draw your own snake with numbers missing for your partner to complete.
Counting in 10s
11121
61718191
41424
44
6474
94
6
364656
7686
515
5565
95
2737
5767
87
1929
49
7989
29
Text... Text...Copy one of these crosses. Try to fill in the numbers that sit diagonally to the middle number. What is the pattern for diagonal numbers?
Use a 100-square to help you.
Write the numbers 10 more and 10 less and 1 more and 1 less.
More and less
26 72
55
83
5814
35
41 19
45
54 56
65
Fill in the missing numbers to continue the patterns.
60
Use a bead string or a 100-square to help you.
Draw more trains starting at 0 and counting in steps of different numbers. Which numbers appear on more than one train?
Counting in 2s, 5s and 10s
32 34
4035
105
20 30
108
40 50
61
Text... Text...Find a number that is in all three counts and show how to make it from 2s, 5s and 10s.
Use coins to help find the answers.
Continue to count on in 2p, 5p and 10p coins up to 10 times.
2s, 5s and 10s
p p p p p
p p p p p
p p p p p
p p p p p
p p p p p
p p p p p
2 4
5 10
Complete these divisions.
Solve these problems.
Complete these multiplications.
15 4 4 =
16 8 4 =
17 20 4 =
18 28 4 =
19 32 4 =
20 48 4 =
1 3 4 =
2 5 4 =
3 7 4 =
4 2 4 =
5 1 4 =
6 10 4 =
7 9 4 =
8 4 4 =
9 4 = 24
10 4 = 12
11 4 = 44
12 4 = 48
13 4 = 32
14 4 = 36
I am confi dent with multiplying and dividing by 4.I am confi dent with multiplying and dividing by 5 and 10. 2322
A bead string
7 5 = 35
6 6 5 =
7 10 = 60
8 5 = 40
9 10 = 40
10 50 5 =
11 80 10 =
21 Cows have 4 legs. How many legs on 12 cows?
22 There are 24 children. They get into groups of 4. How many groups?
How many multiples of 4 under 50 are also multiples of 10?
1
2
3
4
5
6 10 =
9 5 =
7 10 =
5 = 25
10 = 90
Multiplying and dividing by 3, , 5 and 10
Complete these subtractions.
I am confi dent with subtracting by counting up.
A number line
Subtract by counting up
I am confi dent with subtracting by counting up.
46 47
A bead string
8 854 849 = 9 992 983 =
Complete these subtractions.
32 27 = 5
27 320 40
3 2
1 23 16 =
2 34 28 =
3 31 26 =
4 53 47 =
5 42 35 =
6 54 46 =
23160 40
? ?
0 40
? ?
0 40
0 6047 53
? ?
0 60
? ?
35 42
0 60
? ?
46 54
48 34 = 14
0 100
6 8
4834
1 164 156 =
2 223 215 =
3 377 364 =
4 486 478 =
5 535 527 =
6 649 636 =
7 768 753 =
100 200
? ?
156 164
200 300
? ?
300 400
? ?
400 500
500 600
600 700
700 800
Finding fractions of shapes and amounts
Write > or < between each pair of fractions.
What fraction of each shape is shaded?
I am confi dent with recognising fractions as equal parts of a whole.
Can you write any of the fractions above using smaller numbers?
Is this statement true or false? For unit fractions (those that have the numerator 1) the larger the denominator, the smaller the fraction.
I am confi dent with recognising fractions as equal parts of a whole, and comparing fractions.54 55
1 Which shape is divided into s?
2 Which shape is divided into s?
3 Which shape is divided into s?
14
16
15
Write the fraction that is shaded for each shape.
2 6 10
3 7 11
2 8 11
1 5 9
13
14
15
16
17
18
16
14
13
18
13
15
16
18
16
15
13
14
a c e
b d f
5 8 11
6 9 12
4 7 10
Grid puzzles Cube puzzles
1 Choose a pair of 2-digit numbers from the cube and fi nd their total and their difference.
94 95
You can use any method you think best. For example:
Can you fi nd a pair of numbers from the cube that has:
2 the total 100 and the difference 42?
3 the total 110 and the difference 4?
4 the total 93 and the difference 35?
5 Choose three 2-digit numbers from the cube and fi nd the total.
6 Can you fi nd three 2-digit numbers from the cube that have a total that is a multiple of 10?
20 + 80 = 100 9 + 8 = 1 7 1 1 7
29 + 88
88 30 = 5858 + 1 = 59
88 29
29 and 88: total 117, difference 59
Four numbers are written in a square. Four products can be found, multiplying across and diagonally.
2 50, 40, 10 and 8?
3 20, 12, 35 and 21?
4 75, 85, 30 and 34?
Can you fi nd four numbers that give these products:
1 Choose four different numbers to write in a square. Find the products. Do this several times.
5 6 7
Find the four products for each of these.
12 3
10 4
3 5
9 4
11 4
7 3
5 7
4 8
4 7 = 28
5 7 = 35
4 8 = 32
5 8 = 40
Metres, centimetres and millimetres
I am confi dent with estimating measurements in metres, centimetres and millimetres.
Answer these length questions.
1 Which of these animals could measure 123 cm in length?
2 Which of these could measure 2 m 15 cm in length?
3 Which of these could measure 50 mm in length?
4 Which of these could measure 34 cm 2 mm in length?
Make up several puzzles of your own like these.
I am confi dent with converting between centimetres and millimetres.
1 3 cm = mm
2 cm = 40 mm
3 6 cm 4 mm = mm
4 9 cm 3 mm = mm
5 cm mm = 39 mm
6 72 cm = mm
7 cm = 39 mm
8 10 cm 4 mm = mm
9 cm = 600 mm
10 cm = 124 mm
11 cm mm = 203 mm
12 102 cm = mm
Write these lengths in order, starting with the smallest.
240 mm 23 cm 2 mm 25 cm 229 cm 30 mm
40 41
Copy and convert these lengths.
13 194 cm = cm mm
14 23 cm 2 mm = cm
15 20 cm 6 mm = cm
16 289 cm = cm mm
17 16 cm 1 mm = cm
18 253 cm = cm mm
a b c
a b c
a b c
a b c
0 cm1
23
45
0 mm
1020
3040
50
67
8
6070
80
Use this method to do these additions.
I am confi dent with adding 3-digit numbers using column addition.
Column addition of 3-digit numbers
Use this method to do these additions.
1 273 + 54 =
2 645 + 38 =
3 772 + 83 =
4 326 + 45 =
5 482 + 264 =
6 354 + 185 =
7 634 + 238 =
8 381 + 357 =
I am confi dent with adding 2- and 3-digit numbers using the expanded method.
Write an addition question that has an answer between 830 and 870.
42 43
482 + 64 =
+400 80 2 60 4400 140 6 = 546
327 + 254 =
+300 20 7200 50 4500 70 1 1 = 581
1 181 312 + 425
2 217
444 + 135
3 363
342 + 283
4 282
162 + 474
5 554 162 + 245
6 661
128 + 165
7 483
312 + 412
8 566
303 + 625
9 373 114 + 413
10 817 336 + 327
11 784
552 + 527
12 868 616 + 917
1 2320845 1 1782
+
Answer these and explain what patterns you notice.
123 + 987
456 + 654
789 + 321
1 2320845 1
+
23
>
35
13
13
13
12
12
110
110
110
110
110
110
110
110
110
110
19
19
19
19
19
19
19
19
19
18
18
18
18
18
18
18
18
17
17
17
17
17
17
17
16
16
16
16
16
16
15
15
15
15
15
14
14
14
14
111
111
111
111
111
111
111
111
111
111
111
112
112
112
112
112
112
112
112
112
112
112
112
1 Whole
I am confi dent with fi nding equivalent fractions and simplifying fractions.
Copy these pairs of fractions and write > or < between them.
I am confi dent with ordering unit and non-unit fractions and recognising fractions of a shape.54 55
What fraction of each shape is shaded?
Can you write any of the fractions above using smaller numbers?
9 12 15
10 13 16
11 14 17
Complete the equivalent fraction pairs.
1 36 =
1
2 34 = 8
3 15 = 10
4 4 = 28
5 26 =
1
6 4
= 810
7 46 = 3
8 48 = 6
Simplify these fractions.
9 68 11
410 13
36 15
28
10 24 12
26 14
810 16
610
1
2
3
4
5
6
7
8
16
110
15
110
19
112
18
25
34
27
47
78
77
58
39
112
I am confi dent with rounding 4-digit numbers.
Round each number to the nearest 10, 100 and 1000.
Write a number to match each description.
Rounding 4-digit numbers
I am confi dent with rounding 4-digit numbers.
74 75
A number lineRound these to the nearest 10.
3 7450 74607455
1
2
1230 1240
1237
2660 2670
2668
4 1287
5 6844
6 8304
Round these to the nearest 100.
7 1200 13001237
8 4578 10 5885
11
Round these to the nearest 1000.
1000 2000
1237
12 4578 14 1885
Write a number which rounds to 5000 to the nearest 1000, 4500 to the nearest 100 and 4520 to the nearest 10.
1 1287
2 3623
3 2535
4 6729
5 4572
6 4302
7 3608
8 5937
9 6851
10 7777
11 9440
12 5781
13 3514
14 8535
15 8448
16 It rounds to 2570 to the nearest 10.
17 It rounds to 8300 to the nearest 100.
18 It is less than 3600 but rounds to 4000 when rounded to the nearest 1000.
19 It rounds to 4000 to the nearest 1000 and to 3500 to the nearest 100.
20 It rounds to 3500 to the nearest 100 and to 3000 to the nearest 1000.
9 2845
13 5145
Write the outputs for each input.
I am confi dent with place-value multiplications and divisions involving decimals.
Two decimal places
I am confi dent with place value of decimals to two decimal places.
1 The 2 in 4721.
2 The 3 in 6387.
3 The 1 in 791.
4 The 6 in 2236.
5 The 0 in 3705.
6 The 8 in 38329.
7 The 6 in 13761.
8 The 9 in 24519.
9 the tenths digit is two more than the tens digit.
10 the hundredths digit is one less than the tenths digit.
11 the tens digit is fi ve more than the hundredths digit.
12 the hundreds digit is double the hundredths digit.
13 the tenths digit is three times the tens digit.
Write a number where:
2322
A place-value grid
Write what the given digit represents in each number.
100s 10s 1s 0.1s 0.01s
3 7 0 5
The 5 in 37.05. The 5 represents fi ve hundredths, or fi ve 0.01s or 0.05.
.
.
A number less than 50 has a hundredths digit. The tenths digit and the ones digits have a total that is the same as the tens digit. If the number has no zero digits, what could it be? Find four different answers.
1 25
2 027
3 047
4 125
5 003
6 28
7 71
8 124
9 8
10 12
11 140
12 9
13 101
14 3206
314 314
10
100
10
100
10 then 10 again
I am confi dent with place-value multiplications and divisions involving decimals.
Write the missing outputs or inputs.
24
1
2
3 2046
4
5
6 72
7
8
9 03
10 126
11
12 007
13 341
14
1357 1357
32
104
44
160
066
19
140
9036
10
100
100
10 then 100
100 then 10
Length and perimeter
I am confi dent with measuring in centimetres and millimetres.
Measure each creature and write the length in millimetres and then in centimetres. Use the red dots to help you.
2
3 4 5
8
33
6 7
1
Measure the perimeter of each rectangle in centimetres. Then write it in metres.
I am confi dent with measuring and fi nding perimeters and converting centimetres into metres.34 35
Calculate the perimeter of each photo and write it in centimetres and then in metres.
Measure each creature and write the length in millimetres and then in centimetres.
I am confi dent with measuring in centimetres and millimetres and converting between units.
1
2
3
4
5
Write each height in centimetres.
6 1250 mm 7 1370 mm 8 1955 mm
Write each length in millimetres.
9 274 cm 10 75.5 cm 11 240 cm Draw a rectangle with a perimeter of 28 cm.
4 7 10
5 8 11
6 9 12
1250 mm 1370 mm 1955 mm
274 cm 75.5 cm
240 cm
1 2 3
8 cm
5 cm
8 cm
5 cm
12 cm
6 cm
6 cm
12 cm
37 cm
21 cm
37 cm
21 cm
12 cm
20 cm20 cm
12 cm 23 cm
14 cm
23 cm
14 cm 31 cm
25 cm
31 cm
25 cm
15 cm
8 cm
15 cm
8 cm
30 cm
16 cm
16 cm
30 cm42 cm
21 cm
42 cm
21 cm
Multiply these numbers by 25.
Multiply these numbers by 9.
Multiply these numbers by 20.
1 24
2 35
3 48
4 72
5 57
6 86
7 95
8 76
9 68
I am confi dent with using mental strategies to multiply by 20, 25 and 9.
Use mental strategies to answer these questions.
I am confi dent with using mental strategies to multiply by 20, 25 and 9. 2928
10 32
11 16
12 52
13 62
14 34
15 56
16 85
17 72
18 66
19 38
20 49
21 56
22 47
23 66
24 89
25 35
26 92
27 71
Would you prefer to use the grid method or the mental strategy you have been learning to multiply by 9? Explain why.
It is easier to do these in two steps!
1 69 9 =
2 48 25 =
3 39 20 =
4 81 9 =
5 38 25 =
6 86 20 =
7 74 9 =
8 67 25 =
9 77 20 =
10 63 9 =
11 91 25 =
12 97 20 =
13 72 9 =
14 79 25 =
15 89 20 =
16 87 9 =
17 69 = 1725
18 71 = 639
19 42 = 1050
20 58 = 522
Find the missing numbers.
Write a method explaining to a Year 4 pupil how to multiply by 20 or 25. Explain why it works.
These are easier than they look!
Write pairs of letters for the equivalent fractions.
Copy and complete. Use the number lines to help you.
I am confi dent with fi nding equivalent fractions and simplifying fractions.
Use these number lines to write some pairs of equivalent fractions:
I am confi dent with recognising equivalent fractions.
Write the equivalent fractions shown in each pair of shapes.
52 53
Complete the equivalent fraction pairs.
13
=
26
1
2
3
4
5
6
7
8 34
= 8
9 4 =
28
10 15
= 10
11 4
=
810
12 48
= 6
13 46
= 3
0 112
0 148
58
38
18
68
28
78
0 124
14
34
1 14
= 8
2 12
= 4
3 48
= 4
4 34
= 8
5 12
= 8
0 123
13
0 1612
0 136
56
16
26
46
6 13
= 6
7 36
= 12
8 16
= 12
9 23
= 12
10 46
= 3
11 56
= 12
A
26
B
35
C
34
D
12
E
210
F
14
G
13
H
23
I
68
J
15
K
24
L
46
M
28
N
610
0 112
0 125
15
45
35
0 1410
510
310
110
610
210
710
810
910