year 4 maths practice questions answer booklet 4 maths practice... · the exercises in the maths...
TRANSCRIPT
1
Introduction for teachers and parents
In this book there are single-page exercises covering most of the mathematics work that children will meet in Year 4.
On each page there are some examples/hints along with a set of questions for children to answer. There is space for answers to be written in the book.
Each exercise ends with a challenging question for the more able children.
At the end of each page, children are invited to answer a self-assessment question.
Using this book
The exercises in the Maths Practice Questions books are not intended to be used in the initial teaching of new mathematics topics.
However, they can be used as:
• Homework activities - to consolidate work done in class.
• End of topic class activities - to give children the opportunity to check their understanding of a particular topic.
• Assessment tasks - allowing teachers to establish whether or not children are secure in their understanding of a topic.
Year 4Maths Practice Questions
4
3
Dactyl Publishing PO Box 130 RETFORD DN22 9YPTel: 01427 884450 Fax: 01427 884455 www.dactylpublishing.com
2
2
Contents
Number and Place Value 3 - 11
Addition and Subtraction 12 - 19
Multiplication and Division 20 - 27
Fractions 28 - 36
Measurement 37 - 43
Geometry 44 - 48
Statistics 49 - 51
Appendix - Information for Parents 52 - 54
Notes 55 - 56
Are you ready for
this?
3
Number and Place Value
Place valueA6214 is a four-digit number with 6 thousands, 2 hundreds, 1 ten and 4 ones.
100
2
10
1
1
4
1000
6
thousands
thousands
How many thousands are in each number?
6611 has
2010 has
2
I’m confi dent I’m nearly thereI know the ‘place value’ of each digit in a four-digit number.
Can you use partitioning to complete these calculations?3
4321 =
8880 =
+
+
300 +
+ 80
+
+
1
3
Here are some cards with digits on them:4
2 8 6 5
What is the largest 3-digit number you could make using three different cards?
What is the smallest 4-digit number you could make using four different cards?
Complete these sentences using words:5
The 2 in 2653.1 shows
The 6 in 5612.3 shows
The 5 in 6215.3 shows
The 1 in 2653.1 shows
two thousands
Tricky!
What digit is in the hundreds column of each of these numbers?1
264
987
2301
Let’s get started!2
3
9
6
2
4000
8000 800
20
0
865
2356
ix
e
h
4
I’m confi dent I’m nearly thereI can count in multiples of 6, 7, 9, 25 and 1000.
Starting at 50, what are the next 4 multiples of 25?4
50
Can you complete this chain?5
2 10x 25 ÷ 10 x 6 x 3 ÷ 9
Counting in multiples of 6, 7, 9, 25 and 1000B
Can you count 81 sheep by counting in 9s?
Answer: 9 18 27 36 45 54 63 72 81
Which of these numbers are multiples of 9? Circle the correct answers.3
28 36 46 54 66 81
Try counting backwards in sevens:2
and forwards in 1000s:
70 63 7
3000 9000
Can you count in sixes? Complete the following:1
6 12 60
2 14
a)
b)
6 Write down the multiples of 9 that are less than 80.
Which of these numbers is also a multiple of 3 and 7?No!
9
18 544842363024
504438322620 568
56 142128354249
80004000 5000 6000 7000
75 100 125 150
30 90550
18 726354453627
63
6 ÷3 =3 2 1
6 ÷3 =7 9
5
I’m confi dent I’m nearly thereI can count back through zero using negative numbers.
Less than zeroC
This number line shows how much money Jake and Izzy have in their bank accounts. Izzy has less than zero! She is overdrawn.
1
-10 0 10 20 30 40-20
Izzy Jake
(£) pounds
How much money does Jake have?
How much more money does Jake have than Izzy has?
£
You can’t have less
than zero...
Yes you can, I’ve got
minus three!
3 At the bottom of a mountain it was 6 oC. When the climber reached the top, the temperature had fallen by 27 oC.
What was the temperature at the top? oC
Challengetime!
2
-10 0 10 20-20
oC
30
Milly went to Spain for a holiday. When she arrived the temperature was a warm 24 oC.
Draw an arrow on the number line to show the temperature in Spain.
In the UK the temperature was -3 oC. Draw another arrow to show the temperature in the UK.
How many degrees warmer was it in Spain than in the UK? oC
£
15
25
27
-21
-3 oC 24 oC
6
Comparing numbers and putting them in orderD
I’m confi dent I’m nearly thereI can compare and order 4-digit numbers.
1256 is more than 1246
2325 is less than 2338
We can write this using a > symbol
We can write this using a < symbol
1256 > 1246
2325 < 2338
Using all 4 of these cards what is the smallest 4-digit number you can make?
29 8 2 7
What is the largest 4-digit number you can make?
5
Answer:
4936 is bigger than 3964.
By how much is it bigger?
Oh no!
Write the correct symbol in the boxes below:1
1584
2002
1583
2001
2140
9621
2150
9261
Put these numbers in order starting with the smallest.
1324 2341 1234 3214 2143 1432 1243 2134
3
By hanging the shirts on the line in a different order, what is the second smallest 4-digit number you could make?
49 4 6 1
How many 4-digit numbers smaller than 4000 can you make using all four of these digits?
>
> >
<
2789
9872
1234 3214234121432134143213241243
1496
6
1 4 6 9
1 4 9 6
1 6 4 9
1 6 9 4
1 9 4 6
1 9 6 4
972
9 34
9 63
9 7
−
3 18 16
4
2
7
EThe time is approximately quarter to six.
Rounding numbers
299 is approximately 300
12
6
39
12
457
8
1011
With numbers ending in 5 we always round up. For example: ‘15 rounded to the nearest ten’ is 20.
I’m confi dent I’m nearly thereI can round numbers to the nearest 10, 100 and 1000.
Now try rounding to the nearest 1000.3
849 1010 6450
4 What is 981 rounded to the nearest 1000?
to the nearest 100?
to the nearest 10?
5 For his birthday, Charlie received £30 rounded to the nearest £10.
What is the most he could have received? (to the nearest 1p)
What is the least he could have received? (to the nearest 1p)
£
£
Here we go...
Try rounding these numbers to the nearest 100.2
88
250
261
406
Can you round these numbers to the nearest 10?1
29
11
25
38
61
89
64
30
10
30
6060
9040
300100
400300
1000 60001000
1000
980
1000
25..00
34..99
8
Solving problems using roundingF
0 mm 10 mm 20 mm 30 mm1 Sam measures the length of a block of wood with a ruler.
How long is the block to the nearest 1 mm?
How long is the block to the nearest 10 mm?
mm
mm
Can you fi ll in the gaps?4
25x 5 + 1000
Rounded to the
nearest 10
I’m confi dent I’m nearly thereI can use rounding to solve problems.
Two cities are 2500 miles apart to the nearest 100 miles.
Which of these could be the accurate distance between them? Circle your answers.
3
2548 2651 2502 2555
Mon
Tue
Wed
Day Number of Cars To the nearest 1000 To the nearest 100 To the nearest 10
1382
1521
1752
1000
1500
1750
Zac carried out a survey of the cars passing his house between 5 pm and 6 pm over three days. Can you fi ll in the gaps?
2
Dave had 2 boxes of maggots (yuk!). He counted them to the nearest 10. In one box he counted 230 and in the other box he counted 190.
What is the largest number of maggots he could have had?
What is the smallest number of maggots he could have had?
5
Oh no!
17
20
2000
2000 1800
1520
13801400
125 1125 1130
428
410
3 42
9 41
2 84
+
1
2 52
8 51
1 04
+
1 1
9
Roman numeralsG
I’m confi dent I’m nearly thereI can read Roman numerals up to 100.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
70
80
90
100
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIV
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIV
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
XL
L
LX
LXX
LXXX
XC
C
58
35
LXIV
XCIII
Decimal number Roman numeral
Ready to try some more? Fill in the empty boxes.3
OK!
4 Now let’s see if you really know your Roman numerals! Do these calculations giving your answers in Roman numerals.
XXIV
XXII
XXII
LXII
+
+
=
=
Now try these:2
=
=
XXXI
LXIII
=
=
XXXIV
LXXIV
=
=
XLIV
XCII
a)
d)
b)
e)
c)
f)
Write the correct number for each Roman numeral shown.1
=
=
=
I
X
XI
a)
d)
g)
=
=
=
II
L
XXI
b)
e)
h)
=
=
=
III
C
XIV
c)
f)
i)
Turn the page upside down to check your answers!
1
11
10
2
21
50
3
14
100
31
63
44
92
34
74
64
93XXXV
LV
XLV
LXXXV
22
42
64
+
26
22
48
+
10
H Decimal numbers and fractions
In a hundred there are In ten there are
In a unit there areIn a tenth there are
10 tens10 units10 tenths10 hundredths
100
1
10
2
1
3
.
. 1 4
3 ones 1 tenth1 hundred 4 hundredths
1
10
1
100
2 tens
I’m confi dent I’m nearly thereI can write some numbers that are not whole numbers as decimals or fractions.
4 We can write fractions as decimals. You can try these:
= = =310
510
710
0.3
1
5 of the bar is shaded. = 0.55
10
5
10
What other fraction is the same as ?5
10
Answer:2
2 Can you fi ll the empty boxes using decimal numbers?
0.1
1 2 30
6 What is the difference between 3.2 and 14.1? Answer:Ouch!
3 We can write decimals as fractions. Try these:
0.1 =101
0.2 =10
0.4 =
This picture shows 1 chocolate bar and 1 tenth of a bar.
There are 1.1 bars altogether.
Can you complete this?
This picture shows whole bars and tenths.
There are altogether.bars
c h o c o l a t e c
c h o c o l a t e
c h o c o l a t e c h o
!
!
!
1 0
2..3
0..7 2..62..01..3
0..5 0..7
10..9
410
2
1
11
I’m confi dent I’m nearly thereI can answer word questions about number and place value.
Word questionsI
1 What is a thousand more than 6501? Write your answer in words.
4 What number is twenty-eight less than ten?
5 Sarah thought of a number and added 2000. Her answer was 5432.
What number did she think of?
7 Can you write six tenths as a decimal?
8 My brother said that 485 rounded to the nearest 10 is 480. Was he right? Explain your answer.
6 What is three thousand, four hundred and twelve rounded to the nearest hundred? Write your answer in digits.
2 If you were counting up in sevens, what would the next two numbers be?
twenty-two twenty-nine
3 Can you count backwards (down) in nines starting at eighty-one and seventy-eight?
81
78
Wow!
n d e d d
y-ix y-
72 2736455463
69 2433425160
-18
3432
3400
0..6
No, 485 d o t 10 490.
4 35
0 02
4 3
−
2
0
23
0= 6.16
4 1 23
12
Addition and Subtraction
I’m confi dent I’m nearly thereI can add numbers to a 4-digit number.
A Adding mentally How quickly can you add
2 + 3 + 4 + 5 ?
Try adding these numbers in your head:1
Try following these steps in your head to fi nd the answer:2
Without writing anything down, try these:4
Challengetime!
Without writing anything down, try adding these numbers together:3
1234 + 7 =
2321 + 86 =
a)
c)
1234 + 16 =
1300 + 1700 =
b)
d)
+
+
+
+
+
+
+
+
+
=
=
=
1000
2000
3000
800
300
380
200
50
60
20
60
12
a)
b)
c)
1
2
3
+
+
+
8
6
5
+
+
+
3
4
4
+
+
+
5
8
9
+
+
+
3
5
2
=
+
+
6
1
=
+ 6 =
a)
b)
c)
1234
3456
1450
+
+
+
366
144
550
=
=
=
a)
b)
c)
1241
2407
1250
3000
2020
2410
3452
20
31
30
1600
2000
3600
13
I’m confi dent I’m nearly thereI can subtract units, tens and hundreds from a 4-digit number.
688 – 44 =
1234 – 25 =
777 – 37 =
1444 – 26 =
Try these to get started:1
Find the missing numbers in these calculations:2
–
–
1240
1450
= 1000
= 1220
–
–
1240
2345
= 1020
= 1111
Follow the steps to fi nd the answers:3
146 – 18 =
1241 – 102 =
233 – 44 =
1306 – 407 =
If you are feeling lucky, try these:4 Heregoes!
Subtracting mentallyB
2468 – 444 = 2024
100
4
10
6
1
8
1000
2
100
4
10
4
1
4
100
0
10
2
1
4
1000
2– =
Don’t forget to partition numbers in your head into thousands, hundreds, tens and ones.
a)
c)
b)
d)
a)
c)
b)
d)
a)
c)
b)
d)
– – – =1320 200 10 6
– – – =2446 300 50 6
a)
b)
644
1209
740
1418
240
230
220
1234
1104
2090
128
1139
189
899
14
I’m confi dent I’m nearly thereI can add numbers with up to 4 digits using column addition.
Written additionC 100
4
3
7
10
6
2
9
1
6
7
3
1
Start with ones, then tens,then hundreds then thousands.
+
1000
2
2
Start by trying these:1
2 6 1
+ 4 3 5
3 2 1
+ 2 4
1 2 3
+ 3 4
Now try these:2
1414 + 216 2548 + 163 2317 + 1492
Ready for some harder ones? Hint: You could check this one using your mental maths!3
1499 + 111 1999 + 123 2469 + 7552
1
4
4
5
Wow!
6 9 6 4 53 5 5 71 9
2
1 6
+
1 4
1
3
1
1
6
0
4
1
2 7
+
2 5
6
1
4
1
3
1
8
1
4
3 8
+
2 3
9
0
1
2
9
7
1
1
1
1 6
+
1 4
1
1
9
1
0
9
1 1
1
2
+
1 9
2
2
9
3
2
9
1 11
1
5
0
+
2 4
5
2
6
2
1
9
1 11
0
7
1
15
Written subtractionD
I’m confi dent I’m nearly thereI can do subtraction using numbers with up to 4 digits.
100
3
4
9
10
4
3
1
1
5
4
1
–
1000
2
1
11Don’t forget that, if you need to,
you can change:
a ten intoa hundred into
or a thousand into
10 ones10 tens10 hundreds
Begin by trying these:1
Now it’s time for these!2
To prove you can subtract like a champion, try these. Hint: You will need to change a hundred into 9 tens and 10 units in this question.
3
1 2 8
– 2 8
2 4 4
– 2 4
3 8 4
– 6 32
8
6
4
2
1
1
1 4 6
– 1 4
1 5 4
– 2 6
2 5 3
– 6 2
2
4
4
3
4
2
1 2 3
– 3 4
1 4 6
– 9 8
3 1 0
– 2 2
4
5
1
9
1
2
Let’sdo this!
0 01 2 2 02 2 2 11 0
3 11 8 2 81 1 9 11 2
8 8 9 4 7 2 8 72 9
5 4 1 1 1
0 111 12 0 113 15 2 110 9
2 0 2
– 1 3
0
2
3 0 0
– 1 1
3
42
6 6 6
– 7 7
6
7
1 19 11
8 8 81
2 19 9
8 8 9
5 115 15
8 8 95
1
16
I’m confi dent I’m nearly thereI know my addition and subtraction facts.
Addition and subtraction factsE
Because 40 + 60 = 100 we know that 100 – 60 = 40 and 100 – 40 = 60
Write down the subtraction facts for these additions. The fi rst is done for you.2
46
100
100
+
–
–
54
54
46
=
=
=
100
46
54
18 +
–
–
82 =
=
=
100 28 +
–
–
45 =
=
=
73 120 +
–
–
15 =
=
=
OK!
Can you complete these?1
25 + 75 = 100
62 + 38 = 100
so
so
100 – 25 =
100 – = 38
and
and
100 –
100 –
= 25
= 62
a)
b)
We can use subtraction facts to fi nd missing numbers.3
We know
Example 100 – 28= ? 100 – 72= 28 100 – 28= 72so 72is?
Find these missing numbers:
a)
b)
c)
d)
100
90
120
–
–
–
81
16
51
=
=
=
?
?
?
?
–
–
–
=
=
=
=
100
90
120
79
81
16
51
19We know
We know
We know
We know
–
–
–
–
=
=
=
=
81
16
51
100
90
120
79
19 ?
?
?
?
is
is
is
is
4
a)
b)
c)
82
115
841
+
+
+
100
227
962
=
=
=
?
?
?
so
so
so
+
+
+
=
=
=
82
115
841
100
227
962
18 ?
?
?
is
is
is
Try these
We know
We know
We know
–
–
–
=
=
=
100
227
962
1882
115
so
so
so
so
–
79 – 17=
75 75
62 38
100
100
82
18
18
82
73
73
28
45
45
28
135
135
120
15
15
120
135
17 62
69
74
62
69
74
17 62
69
74
19
841 121
112
121
112
121
112
18
17
I’m confi dent I’m nearly thereI can estimate and use ‘inverse’ calculations to check answers.
Estimating and checkingF
Don’t forget that you can check a calculation by doing the ‘inverse’ calculation.
E.g. 120 – 30 = 90
check: 90 + 30 = 120
Try these calculations and check them. The fi rst one is done for you. Try these using your mental maths skills.
1
1244 – 120 =
2412 – 402 =
3426 – 1232 =
120 =
402 =
1232 =
1124 1124 1244
Estimate the answers to these calculations by rounding the numbers to the nearest 10.The fi rst one is done for you.
2
199 + 199
2001 + 3001
848 + 151
is approximately
is approximately
is approximately
+ =
+ =
+ =
200 200 400
Let’s fi nd the answer to 499 + 499 + 499.3
4 9 9
+ 4 9 9 + 4 9 9
Use the
answer
Let’s check your answer.
Here goes!
Step 1 Step 2
So 499 + 499 + 499 =
499 + 499 + 499 is approximately 500 + 500 + 500 =
Do you think your answer is right?
+
+
+
so
so
so
2010
2194
2010
2194
2412
3426
2000
850
3000
150
5000
1000
9 9 8
9 9 8
4 9 711 1 1 1
1497
1500
Y
43
2
2 1
−
32
3
9
16
2
4
1
18
2
I’m confi dent I’m nearly thereI can solve problems using addition and subtraction.
Adding and subtracting to solve problemsG
1 Super-speedy Sam the snail was climbing up the shed wall.
He climbed 1230 mm but then slipped 180 mm back down.
How far up had he moved altogether?Answer: mm
2 Fritz had 1200 Euros in his savings. He spent 320 Euros and his parents gave him 50 Euros for his birthday.
How much does he have now?Hint: Solve this problem using 2 steps.
Answer:
1200 – 3201 2
Look at this shopping receipt.
Can you work out the total cost of these 3 things?
Hint: Keep a careful eye on the decimal point.
31 2 8
£ 2 4
0
0
1 4 5
.
.
.
.
£
£
wood
nails
glue
Fiona had 4231 stamps in her collection. She sold some and now she has 888.
How many did she sell?
4Here
we go!
Answer:
1050
930
880 + 50
6£ 1 6 51
3343
1
1
1 0
−
13
8
5
10
0
0
21
3
8
−
110
2
8
00
0
0
8
9
+
8
5
3
0
0
01
24
8
3
−
113
8
4
31
8
33
12
19
I’m confi dent I’m nearly thereI can answer word questions about addition and subtraction.
Word questionsH
1 Can you use mental maths to add two hundred and fourteen to one thousand one hundred and twelve?
Check your answer using written addition.
2 What number would you get if you added 1234 to 5678 and then subtracted 106?
5 Use what you know about subtraction facts to fi nd the missing number.
540 – = 364
6 Zoe said “I can check my answer to 48 + 18 = 66 by subtracting 18 from 48.” What should she have said?
“I can check my answer to 48 + 18 = 66 by
Phew!
Jacko had six thousand fi ve hundred stamps in his collection. He gave eight hundred to his dad and twelve to his sister.
How many did he keep?
3
Show how you would estimate the answer to 98 + 199 + 702.
Write down your estimate and then work out the correct answer.
4
AnswerEstimate
+ + =
1326
6806
5688
100 1000700200 999
176
g 18
m 66.”
2
1
1 3
+
1
1
2
4
2
6
1
5
8
5 6
−
0
1
8
0
2
8
65 14 9 1
9
9
9 9
+
8
9
9
1
0 27
1
5 4
6
1 7
−
130
4
6
1
3
4
2
6 9
+
3
1
1
6 7
1
4
8
2
5
1
6 9 1 2 − 1 0 6= 6 8 0 6
20
Multiplication and Division
I’m confi dent I’m nearly thereI know the times tables up to 12 x 12.
A The times tables How well do you know the times table facts up to 12 x 12 ?
Hint: Make sure you are confi dent with the 2x, 5x and 10x tables and know the square numbers up to 12 x 12
Give yourself a quick test.1
Complete this table of square numbers.2
1 x 1 2 x 2 3 x 3 4 x 4 5 x 5 6 x 6 7 x 7 8 x 8 9 x 9 10 x 10 11 x 11 12 x 12
We can sometimes make questions easier like this: What is 8 x 7? If we know 7 x 7 = 49 then adding one more 7 would give 56.
Try these:
3
8 x 8 =
6 x 6 =
10 x 7 =
10 x 8 =
8 x 5 =
so
so
so
so
so
9 x 8 =
7 x 6 =
9 x 7 =
11 x 8 =
9 x 5 =
Try some division.4
13 x 8 =
12 x 13 =
19 x 4 =
12 x 15 =
21 x 6 =
31 x 8 =
Now for some tough ones. Hint: Split them into easier steps.5
Go!
a)
b)
c)
d)
e)
4 x 4 =
2 x 11 =
1 x 9 =
6 x 5 =
4 x 3 =
12 x 0 =
3 x 8 =
3 x 5 =
0 x 11 =
a)
d)
g)
b)
e)
h)
c)
f)
i)
a)
d)
36 ÷ 6 =
24 ÷ 8 =
12 ÷ 3 =
88 ÷ 11 =
16 ÷ 4 =
60 ÷ 12 =
a)
d)
b)
e)
c)
f)
b)
e)
c)
f)
16
9
22
30
0
12
24
0
15
64
40
80
70
36
72
45
88
63
42
6
3
4
5
4
8
104
156
126
248
76
180
41 169 3625 6449 10081 144121
21
Mental multiplication and divisionB
Hint: Always take your time and look for the easiest way to do a mental calculation.
I’m confi dent I’m nearly thereI can multiply and divide numbers mentally.
Sometimes we can make calculations easier by swapping the order fi rst. Try these (the fi rst one is done for you).
2
2 x 12 x 5
16 x 2 x 5
17 x 5 x 2
multiply
multiply
multiply
x
x
x
x
x
x
=
=
=
2 5 12 120
Try these:3
2 x 3 =
4 x 2 =
4 x 50 =
2 x 30 =
40 x 2 =
3 x 300 =
2 x 300 =
400 x 2 =
2 x 2000 =
a)
d)
g)
b)
e)
h)
c)
f)
i)
Now try these:4
45 ÷ 5 =
64 ÷ 8 =
81 ÷ 9 =
450 ÷ 5 =
640 ÷ 8 =
810 ÷ 9 =
a)
c)
e)
b)
d)
f)
Give these a go!5
Lift off!3 x 4000 =
720 ÷ 9 =
3 x 2500 =
7 x 8 x 25 =
a)
c)
b)
d)
Try these pairs of calculations.1
a) 2 x 3 x 4 =
b) 4 x 5 x 2 =
c) 6 x 3 x 2 =
3 x 4 x 2 =
2 x 4 x 5 =
3 x 2 x 6 =
What did you notice about them?
24
36
40
24
36
40
2
5
5
2
16
17
160
170
6
200
8
60
900
80
600
4000
800
9
9
8
90
90
80
12000
80
7500
1400
Wn u y r, t n’t r t r u
o t n.
22
Some important rulesC
I’m confi dent I’m nearly thereI know some important maths rules.
Can you complete the gaps below? This is how we split multiplication problems into easier steps.3
a) 23 x 4 =
=
+
+
20 x 4
80
3 x 4
12 = 92
b) 26 x 5 =
=
+
+
20 x 5
=
c) 31 x 6 =
=
+
+ =
x 5
4 Try this using the same idea:
123 x 6 =Ouch!
Try these pairs of calculations.1
a) 4 x 5 =
b) 6 x 0 =
c) 7 x 6 =
5 x 4 =
0 x 6 =
6 x 7 =
What did you notice?
What about these?2 What did you notice?
1 x 2 x 4 =
3 x 2 x 6 =
4 x 3 x 10 =
2 x 1 x 4 =
6 x 2 x 3 =
10 x 3 x 4 =
a)
b)
c)
2 x 4 x 8 = 4 x 8 x 2 = 64 8 x 6 = 6 x 8 = 48
When x and + are in the same calculation, do the x fi rst.32 x 4 30 x 4 2 x 4 128= =+
20
42
0
20
42
0
8
120
36
8
120
36
4 x 5
5 x 4, 0 x 6
6 x 0 d
7 x 6
6 x 7
T r
n u
r
of .
30 x 6
180
1 x 6
6
100 30 130
186
6
0 x 6 = 7 2
3 x 6 = 1
21 0
8
7 3 8738
23
I’m confi dent I’m nearly thereI know what factor pairs are and how to fi nd them.
D Pairs of factors 1 x 6 = 62 x 3 = 6
1 , 2 , 3 and 6 are factors of 6.The factor pairs are 1 and 6 and 2 and 3.
Can you complete these to fi nd the factor pairs of 12?1
x
x
1 =
=
12
124
x2 = 12
Write down the factor pairs of 16.2
Can you complete the gaps to make the calculations correct?5
x = 45 x = 64 x = 108
These numbers only have one pair of factors. Fill in the gaps below.3
2 3 5 7 11 13
1 and 2
These numbers are members of a family called prime numbers.
A prime number only has two factors, itself and .
Which of these is a factor of 810? Circle your answer.6
60 70 80 90 100
How many factor pairs does 36 have? (you may need to write them down!)
Brainstrain!
4 How many factor pairs do these numbers have?
18 has
20 has
21 has
factor pairs
factor pairs
factor pairs
12
3
6
1 d 16, 2 d 8, 4 d 4
1 d 7 1 d 11 1 d 131 d 51 d 3
1
3
2
3
9 5 8 8 12 9
5
1 x 3 6
2 x 1 8
3 x 1 2
4 x 9
6 x 6
1 x 1 8
2 x 9
3 x 6
1 x 2 0
2 x 1 0
4 x 5
1 x 2 1
3 x 7
24
I’m confi dent I’m nearly thereI can multiply 3-digit numbers by 1-digit numbers.
Use the grid method or short multiplication to answer these questions.2
4 x 246 4 x 233 6 x 166 5 x 678
E Written multiplication
Example: We want to fi nd the answer to 4 x 134
4 x 100 4 x 30 4 x 4+ +
1 3 4
x 4
5 3 61 1
Short MultiplicationGrid Method
4
40012016
536
x
100304
We partition 134 and multiply each part by 4.
8 x 46 =
5 x 123 =
3 x 288 =
+
+
+
8 x 40
+
+x
x
x8
5
x
x5
3 x
x5
Fill in the missing numbers below.1
a)
b)
c)
This time you will need to decide how to work out the answers.3
Answer:
If there are 273 jelly beans in each jar, how many would there be in 7 jars?
How many hours are in a week (7 days)?
So, how many hours are there in 9 weeks?
Answer: Answer:
OK!
100
200
20
80
6
3 83
3
2 4 6
4
9 8 4
x
21
1 6 6
6
9 9 6
x
33
x
0 0
3 0
3
4
082
1 2
1
39
0
0
2
2
x
0 0
7 0
8
5
036
3 5
4
33
0
0
0
9
0
0
2 7 3
7
1 1
x
1 9 25
1911 1512
168
2 4
8
x
1 62
7
1 6 8
9
1 2
x
1 5 76
25
I’m confi dent I’m nearly thereI can divide 2-digit and 3-digit numbers by 1-digit numbers.
F Written division
Example: What is 98 ÷ 7 ?
Expanded Method
9
7
2
2
8
0
8
8
0
7
1 4
(10 x 7)
(4 x 7)
Short Division
9 87
1 4
–
Have a go at these:1
–
2
4 people share 336 pound coins equally between them.
2
Answer:
How many will each of them get?
How many weeks are in 112 days?3
8 13
1 23 3
9 64
2 47 5
Answer:
Wow!
84 16
(10 x 7)
1 1 2
7 0
4 2
4 2
0
7
1 6
−
− (6 x 7)
3 34
8 4
61
2 7
6 0
2 1
2 1
0
−
−
2 4
8 0
1 6
1 6
0
−
−
(20 x 4)
(4 x 4)
4 1 3 53
(20 x 3)
(7 x 3)
26
Solving problems with multiplication and divisionG
I’m confi dent I’m nearly thereI can solve problems using multiplication and division.
Look at these calculations. Circle the correct answers.4
a) 1 + 9 x 2 = 20
b) 2 x 4 + 6 = 14
or
or
1 + 9 x 2 = 19
2 x 4 + 6 = 20
When + and x are in a calculation, we always do the fi rst.
(+ or x)
There were 3 fi elds, each with 28 rabbits. Each rabbit has 4 legs and 1 tail.5
Answer:
Tricky!
One hundred and thirteen pigs each ate 6 potatoes. How many potatoes were eaten altogether?
1
Answer:
A box of 120 crayons was shared equally between 8 children.How many did each one get?
2
Answer:
51 x 8 is the same as + x 8x50 =
3 In a mental maths quiz Charlie was asked to work out the answer to 51 x 8. He did this using an important rule. Can you fi ll in the spaces to show how he got his answer?
Answer:
How many rabbit tails were there altogether? How many rabbit legs were there?
678 15
40818
x
84 336
1 31
6
8
x
6 7 1
1 28
1 5
04
82
3x
482
48
4x
63 13
27
I’m confi dent I’m nearly thereI can answer word questions about multiplication and division.
Word questionsH
3 Use short division to divide one hundred and nineteen by seven.
4 Sally has 284 worms in her wormery. Jayne has fi ve times as many.
How many worms does Jayne have?
5 Can you write down the factor pairs of twenty-four?
and and and and
6 On a train there are nine coaches. Each coach has thirty-two seats. Each seat can hold two people.
How many people can have a seat on a train?
OK!
1 Can you use partitioning to split 36 x 7 into two calculations and work out the answer?
2 Can you multiply 19 x 5 x 2? Explain how to do this the easiest way.
Answer:
252
190
17
1420
1 24 2 12 4 63 8
576
2 x 5 x 19 = 190
My 2 y 5 t
1 17
1 7
94
2 8 4
5
2 0
x
1 4 24
23
9x
88 12
88
2x
67 1
2
5 1
3 0 x 7 6 x 7+
2 1 0 4 2+
28
Try to put these fractions in size order (smallest fi rst).4
smallest largest
6100
18100
110
30100
210
Fractions
I’m confi dent I’m nearly thereI can count in hundredths.
A Hundredths
If we split a bar of chocolate into a hundred equal parts, each part would be .
We write in the second place after thedecimal point.
1
100
1
100
100
2
10
3
1
6
.
. 1 3
1
10
1
100
3
100
(three hundredths)
Can you count in hundredths?1
1100
2100
What is another way of writing ?10
100 10Answer:
Look at this number line: can you complete the boxes below?2
0 10
100
30
100
2100
3 We know that and10
100 =1
10
10
10 = 1 So, can you complete these?
=20100 10
=40100 10
=210 100
=610 100
=200100 ones =
500100 ones
Funtime!
3100
10100
9100
8100
7100
6100
5100
4100
1
9100
15100
20100
26100
2 4 6020
2 5
6100
30100
210
18100
110
29
I’m confi dent I’m nearly thereI can recognise and fi nd some equivalent fractions.
B Equivalent fractions
If you multiply or divide the numerator (top part) and the denominator (bottom part) by the same number you get an equivalent fraction.
312
14
=
÷ 3
÷ 3
312
14
=
14
312
=
x 3
x 3
Try completing these equivalent fractions.1
=12 4
=14 16
=110 100
x 10
x 10
=13
3=
16
3=
15
2
Shade in the grids to help you fi nd some equivalent fractions. The fi rst one is shaded for you.2
=620 10
=1236
1
=525
1
=616 8
Sometimes there are lots of equivalent fractions, can you complete this?3
Can you fi nd an equivalent fraction to these using your times table facts?4
372
=1 33
121=
This looks scary!
1224
= =1
12 6=
2=
a)
d)
b)
e)
c)
f)
10 2 4
9 18 10
3
3
5
3
6 32 4
24 113
30
I’m confi dent I’m nearly thereI can add and subtract fractions with the same denominator.
C Adding and subtracting fractions
Just like 1 + 2 = 3 + = Don’t forget or or etc. is a whole one.10
10
1
10
2
10
3
10
6
6
9
9
Try these:1
+310 10 10
=4
+610 10
=3
+14100 100
=14
+4
100 100 100=
21
Write the answers to these sums as a mixture of whole numbers and fractions (these are called mixed numbers).
3
Try to fi nd the missing numbers.4
+412 12 12
=1
–8
=8
11
86
Can you solve this problem?5
– =94
91
5
Bring it on!
–20100 100
=17
–45 5 5
=2
+58 8 8
=6
+712 12
=8
1
1
2
a)
c)
e)
b)
d)
f)
a) b)
a) b)
Look at this calculation:2610
610
+1210
= We can split into1210
1010
210
+210
= 1
Can you fi ll in the missing numbers?
+35 5 5
=3
+5
5=
We can split this into: 1
7
25
2
9
28
3
10
100
100
65
1 15
312
31
9 3
89
31
I’m confi dent I’m nearly thereI can use fractions to fi nd ‘how many’.
D Using fractions to fi nd ‘how many’
Example: What is of 120?
We need to split 120 in to 5 equal groups. We do this by dividing 120 by 5.
Answer: 120 ÷ 5 = 24 so, of 120 = 24
1
5
Start with these:1
of 6515
of 6418
of 90110
of 8814
of 20 is 2 so of 20 must be 42 1
10
2
10
Now you try:
of 42 is16
of 40 is110
of 42 is26
of 40 is210
of 42 is56
of 40 is310
Can you fi nd the missing numbers?3
of 40 = 1610
of 96 = 812
of 88 = 338
of 96 = 2412
Can you fi nd the missing numbers?4
of 144 = 60
Let’sgo!
a)
c)
b)
d)
a)
d)
b)
e)
c)
f)
a)
c)
b)
d)
1
5
9
13
22
8
4
7
12
35
8
14
512
4
1
3
3
32
E Fractions and decimals
Try changing these fractions to decimals.1
Now try these:2
Let’s use equivalent fractions to change some important fractions into hundredths. Can you fi ll in the gaps?
3
=14 100
x 25
x 25
=34 100
x 25
x 25
=12 100
x 50
x50
I’m confi dent I’m nearly thereI can change tenths and hundredths
and some other fractions into decimals.
By using equivalent fractions we can change some fractions into decimals. Try fi lling in the gaps below:
4
=14
=100
0.25 =34
=100
=12
=100
Try this:5
Oh no!
Can you write this as a decimal?+12
+34
=14 4
=100
=18100
a) =20100
b) =25100
c) =50100
d)
a) b) c)
a) b)
c)
=310
=510
=810
=5100
=7100
=8100
a) b) c)
d) e) f)
Remember is 0.01 so is 0.091
100
9
100 10 hundredths is 1 tenth
which is15
100
10
100
5
100+is 0.15
0..3
0..05
0..8
0..08
0..5
0..07
0..18 0..50..250..2
0..75
0..5
1..5
25 75 50
25 75
50
6 150
33
F Dividing by 10 and 100
I’m confi dent I’m nearly thereI can divide one and two-digit numbers by 10 and 100.
100
2
10
6
1
2
.
. 0
1
10 100 10 1
2
.
. 6 2
1
10
1
100
÷ 100 =
100
2
10
6
1
2
.
. 0
1
10 100 10 1
6
.
. 22
1
10
÷ 10 =
All the digits have moved one place to the right. They are all 10x smaller.
All the digits have moved two places to the right. They are 100x smaller.
12 ÷ 10 =
9 ÷ 10 =
24 ÷ 10 =
2 ÷ 10 =
Do you want to try some?1
24 ÷ 100 =
2 ÷ 100 =
20 ÷ 100 =
5 ÷ 100 =
Now let’s divide by 100.2
Fill in the gaps choosing from the list of answers given.3
one hundred divided by ten is
ten divided by ten is
one divided by ten is
one divided by a hundred is
a tenth
ten
one
a hundredth
Which of these is 100x smaller than 12? Circle your answer.4
1.2 120 0.12 2.1 0.21
Can you fi nd the answer?5
1.2x 10 ÷ 3 ÷ 100 doubled + 1
Nochance!
a)
c)
b)
d)
a)
c)
b)
d)
1..2
0..9
2..4
0..2
0..24
0..02
0..2
0..05
n
a h
a h
12 4 0..04 0..08 1..08
34
G Rounding and comparing decimals
Example: 12.9 is closer to 13 than 12. So 12.9 rounded to the nearest whole number is 13.
Remember: 12.5 would be rounded up to 13 because it is halfway between 12 and 13.
I’m confi dent I’m nearly thereI can round decimals with one decimal place
to the nearest whole number.
Which of these numbers is closest to 10? Circle your answer.2
9.7 10.3 9.9 10.2 9.5
Round these numbers to the nearest whole number.1
a) 6.3 b) 8.4 c) 10.1
d) 9.6 e) 15.9 f) 21.7
g) 6.5 h) 12.5 i) 16.0
Use what you know about rounding to estimate the answer to this calculation in your head.5
1299.9 + 599.8 + 200.1 =
Bring it on!
Circle the biggest number in each pair.4
a) 1.26 1.27 b) 1.65 1.85 c) 3.10 3.01 d) 0.56 0.65
Write these numbers in size order (smallest fi rst).
smallest largest
12.74 12.86 13.01 12.58 12.77
We can use rounding to make estimates.
Example: If we want to do this sum 1.9 + 5.9 we can round the numbers to 2 + 6 = 8
Try these:
3
8.1 + 8.1 is approximately
29.9 + 19.9 is approximately
30.4 + 29.8 is approximately
+ =
+ =
+ =
a)
b)
c)
6
10
7
8
16
13
10
22
16
8
30
30
8
30
20
16
60
50
12..58 13..0112..8612..7712..74
2100
35
Solving problemsH
I’m confi dent I’m nearly thereI can solve problems using fractions and decimals.
4 An ant was 1.2 cm long. Zane said that his spider was 100x longer.
How long would his spider be if this was true? cm120
5 Ten identical chocolate coins weighed 64 g.
How much did each one weigh?
How much would three of them weigh?
g
g
6..4
19..2
8
96 Zoe bought a bike for £81. Cara bought a bike for of this price. How much did Cara pay?
£ 72
3 An aquarium contained 45 tropical fi sh. of them were orange.2
5
5What fraction of them were not orange? How many of them were orange? 18
3
Three people had some cake. One ate , one ate and one ate .
How much was left? Hint: Use equivalent fractions to change everything to twelfths.
7 1
4
1
3
1
12 Harder!
13
1 Dave’s mum has £104 in her purse.Dave has 100 times less in his pocket.
How much money does Dave have? Answer: £ 1..04
0 4 ÷ 1 0 01
Answer:
2 Zoe had £48. She spent of it on a new soft toy.
How much money did she have left?
1
3
£ 32
4 8 ÷ 3 = 1 6
4 8 − 1 6 = 3 2
46
4+
291
6
6 4.
.
.
.1
36
Word questionsI
I’m confi dent I’m nearly thereI can answer word questions about fractions.
3 What number do you get if you divide six by one hundred?
4 Which number is a hundred times smaller than 142?
5 Can you write twelve hundredths as a decimal?
6 Try to write in hundredths and then write it as a decimal.17
50
100=
1750
=
7 A fi fth of all the cars in a car park were white.
If there were 225 cars in the car park, how many were not white?Bring it on!
1 If you were counting down in tenths what fraction would you say after ?7
10
2 What is the answer to four eighths plus fi ve eighths?
=
610
98
181
0..06
1..42
0..12
0..34
180
34
2 25
4 5
52
2 2 − 4 5= 1 8 0
5
7
10
6
10
5
10, ,
37
20 cm
Measurement
I’m confi dent I’m nearly thereI can convert units and compare measurements.
A Using different units
1 centimetre (cm)1 metre (m)
1 kilometre (km)1 kilogram (kg)
1 litre (l)1 hour
======
10 millimetres (mm)100 centimetres (cm) = 1000 millimetres (mm)1000 metres (m)1000 grams (g)1000 millilitres (ml)60 minutes
Remember:
Can you change the units?1
15 cm
2 kg
5 km
2 hours
=
=
=
=
mm
g
m
minutes
3 m
4500 g
2.5 litres
300 minutes
=
=
=
=
cm
kg
ml
hours
Can you circle the largest measurement in each pair?2
A journey to America took 9 hours and 20 minutes. How long did the journey take in minutes?4
minutes
Jake made a crayon train like this:3
How long was his train in centimetres (cm)?
How long was it in millimetres (mm)?
How long was it in metres (m)?
cm
mm
m
25 cm
OK!
20 cm25 cm20 cm
1.69 m or 170 cm
3500 g or 3.6 kg
2.5 km or 2590 m
hours or 350 mins1
25
a)
c)
b)
d)
Answer:
150
120
5000
2000
110
5
2500
4..5
1..1
1100
560
06
9x
045
04
0+
065
2
5
300
38
PerimeterB
The perimeter is the distance all the way around the outside.
I’m confi dent I’m nearly thereI can work out the perimeters of some shapes.
What is the perimeter of this shape?
Fill in the boxes to show your working.
4
4 cm
8 cm
8 cm
4 cm
4 cm
4 cm
cm cm+ cm+ cm+ cm+ cm+ cm=
Calculate the perimeter of these squares.15 cm
12 cm
3 cm
cm cmcm
Answer: cm
This shape is made up of 4 equilateral triangles and a 4 cm x 4 cm square.
What is the shape’s perimeter?
5
Wow!
Now try calculating the perimeter of these rectangles.2
mm
7 cm
3 cm
mm
20 mm
40 mm
cm
6 cm
2 cm
The perimeter of a rectangle is: width + length + width + length.
This is: 2 x width + 2 x length.
Fill in the gaps to fi nd the perimeter of the rectangle below.
3length
width
length = 7 cm
width = 3 cm Perimeter = =2 x 2 x + cm+ =
lengthwidth
cm=
12 20 48
16 12120200
2014673
8 44448 32
32
4 x 8 = 3 2
39
I’m confi dent I’m nearly thereI can fi nd the areas of squares and rectangles.
AreasC
If a rectangle measures 3 cm by 2 cm we count the 1 cm squares to fi nd the area.
The area is 6 square centimetres (6 cm2).
You will notice that area = length x width = 3 cm x 2 cm = 6 cm2
Can you calculate the areas of these shapes using mental maths?3
6 m
4 m m2Area: 8 m
2 m
m2Area:
I’m ready!
Count the 1 cm squares to fi nd the areas of these shapes:1
cm2Area = cm2Area = cm2Area =
We can fi nd areas without counting all the squares.2
The rectangle has rows of square centimetres.
The area = x = cm2
For example, this rectangle has two rows of ten square centimetres. The area is 2 x 10 cm2 = 20 cm2
3 cm
2 cm
9 16 12
3 6
3 6 18
24 16
40
Money calculations and estimatesD
What is £8.75 to the nearest whole £? Answer: £9
I’m confi dent I’m nearly thereI can do calculations and estimations with amounts of money.
2 Emma went to the bank with a box of 1 p coins. She changed them for a £10 note, two £1 coins and one 20 p coin.
How many coins were in the box?
4 Mr and Mrs Gloomy are saving £2.50 a week towards a new TV. The one they want costs £420.
How many weeks will it take them to save up the full amount?
Wow!
tea £1.20
coffee £1.60
hot chocolate £1.70
milkshake £1.65
tea
£
coffee
£
hot chocolate
£
milkshake
£
On a café menu the drink prices are: 3
How much was each drink to the nearest £1?
Exactly how much would it cost for two coffees and a milkshake? £
How much change would you get from £5? p
£
1 Tom wanted to buy 5 books. The books were on offer at £2.99 each. He only had £16.
Can you estimate the cost of 5 books to work out if he had enough money?
Estimate
15
1220
1 2 2 2
4..85
15
168
06
5+
584
6
1
1
061 .
.
.
.
24
4
861
x
It 4 o e £10. Ty d 42 x £10
£10£2
20 p
===
1
001 0
02 0
2 0
221 0
41
The 12-hour and 24-hour clocksE
Remember: 16:40 is the same time as 4.40 pm
I’m confi dent I’m nearly thereI can use the 12-hour clock and the 24-hour clock.
Can you draw the hands on the clocks to show the times?1
4:30 pm
12
6
39
12
457
8
1011 12
6
39
12
457
8
1011 12
6
39
12
457
8
1011
02:25 15:35
Try writing these times using the 12-hour clock.2
1 6 : 2 6
4 . 2 6 pm
22 : 2 2 0 1 : 0 0 1 2 : 1 0
The clock on the train station showed the time like this:
Jack’s train was due to arrive at 5 minutes to 5.
How long would he have to wait?
3 1 6 : 4 2
Herewe go!
In the evening, the little hand on a clock points to VII and the big hand points to XII, what time is it?
How long will it be until the big hand next points to IV?
4
:
minutes
(Use 24-hour clock)
minutes
10..22 m 12..10 m1..00 m
13
19 00
20
42
Solving problemsF
How many hours are there in September? Answer: 30 days with 24 hours in each day 24 x 30 = 720 hours
I’m confi dent I’m nearly thereI can solve problems using different measurements of time.
How many months are there in 12 years? How many months are there in 120 years?3
months months
Can you convert these times? The fi rst one is done for you.1
2 weeks
5 weeks
2 years
=
=
=
days
months
3 hours
8 years
12 hours
=
=
=
minutes
months
minutes
14 days
2 Milly had a running challenge. She had to sprint for 12 secs and rest for a minute. She did this 10 times in a row.
How long did the challenge take?
minutes
Let’s do this!
4 Jon left school at 3.30 pm. He walked for 10 mins and waited at the bus stop for 90 secs. The bus journey took half an hour.
What time was it when he got off the bus?
1
2
a)
c)
e)
b)
d)
f)
35
24
96
720
180
12
144 1440
4..12 m
2 x
=
=
1 0 1
21 0
2
2 + 1 0 = 1 2
51
0+
04
03
501 .
.
.
.2 1
43
Word questionsG
1 What would 1.5 m be in millimetres?
2 If one side of a rectangle measures 24 cm and another side measures 14 cm, what is the perimeter of the rectangle?
3 The perimeter of a regular hexagon measures ninety millimetres.
What is the length of each side?
4 Sara has a £1 coin, three 50 p coins and a 20 p coin. She uses the coins to buy a magazine that costs £2.52.
How much change does she get?
6 The time shown on a digital clock is 16:07.
What is the time using the 12-hour clock?
7 A plane took off at 10 am and landed at 13:08.
How long was the fl ight in hours and minutes?
hours minutes
5Explain how you would work out the area of this irregular shape.
1 cm
1 cm
cm2
I’m confi dent I’m nearly thereI can answer word questions about measurement.
I’mtired!
The area is:
mm1500
76 m
15 m
18 p
12
4..07 m
3 8
Ct r of 1 m2
5 x1 01 0 0.
+
+
24 x 2
48
14 x 2
28 = 76
1
05
0+
02
2
.
. 7
00.1
13:08 = 1.08 m
= 51 0 0
A n 6
96
1
0
53
1
44
I’m confi dent I’m nearly thereI can identify 2D shapes.
Geometry
A 2D shapes
Remember: Regular polygons have equal length sides and all the angles are the same. regular hexagon irregular hexagon
Irregular polygons have at least one side that is a
different length or a different angle.
Can you identify these triangles using the words isosceles, scalene, equilateral or right-angled?2
Can you recognise these polygons? Include the word regular or irregular in your answers.1
Try naming quadrilaterals with no clues! If you don’t know them, try to fi nd out.3
I can do it!
r n
r n
r n
t-d ul
m
m
45
B Comparing angles
I’m confi dent I’m nearly thereI can compare angles and put them in order.
This is a right-angle.
This is smaller than a right-angle - it is called
an acute angle.
This is bigger than a right-angle - it is called
an obtuse angle.
Complete these sentences.
If a right-angle is a quarter turn, an angle would be less than a quarter turn.
An angle would be more than a quarter turn.
2
It was 3 o’clock. The big hand on the clock moved through an obtuse angle. Which of these times could it be? Circle your answers.
4
1 5 : 2 5 3 . 0 5 am3 . 2 0 pm 15 : 1 0 3 . 1 5 pm
Look at angles A B C D and E. Can you put them in order from largest to smallest?
3
A B C D E
smallest largest
Which of these angles is obtuse? Circle your answer.1
95o40o
45o120o
20o
There are 90 degrees (90o) in a right angle Less than 90o More than 90o
Angles are measured in degrees ( o )
Brain strain!
D EACB
46
I’m confi dent I’m nearly thereI know what lines of symmetry are.
C Lines of symmetry
1 line of symmetry No lines of symmetry
square regular hexagon equilateral triangleA
the letter AZ
the letter Z
How many lines of symmetry can you fi nd for these shapes?1
How many of these letters of the alphabet have no lines of symmetry? Circle your answers.3
Answer:
Bring it on!
2
Can you draw the refl ection of this shape in the mirror line?
mirror line
letters have no lines of symmetry
S
4 6 1 03
10
A C D E F G H I J K L M N O P Q R S T U V W X Y Z
47
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 100
y
x
X
X
X lighthouse
harbour
shop
1
Look at the map of this little island.
What are the coordinates of:
the shop?
the lighthouse?
the harbour?
,
,
,
I’m confi dent I’m nearly thereI can use coordinates to describe where a point is
on a grid and I can describe translations.
D Position and directionWe can use coordinates to say where the cross is on the grid.
The X is at coordinates (3,2)
2
A square is moved from A to B as shown. We say it has been translated.
How many squares has it moved to the right?
How many squares moved up?
6
5
4
3
2
1
1 2 3 4 5 6 7 8 90
y
x
B
A
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 100
y
x
3Draw an isosceles triangle with coordinates (2,3) (4,3) (3,6).
It is translated by moving it to the right 6 squares and by moving it up 3 squares.
What are its new coordinates? Draw the triangles on the grid to help.
, ,,
Brainstrain!
4
3
2
1
1 2 3 40
y
x
X
3 5
7 6
4 2
4
2
8 6 10 6 9 9
X X
X X X
X
48
Word questionsE
I’m confi dent I’m nearly thereI can answer word questions about geometry.
1 John said that two right angles added together would make an angle of 200o. Explain why this is wrong.
2 Are any of these angles acute angles? Circle any that are acute.
90o 100o 94o 88o 98o
3 A teacher asked a class to put two trapeziums together to make a hexagon. Can you draw a picture to show how to do this?
4 How many lines of symmetry are there on a regular pentagon?Hint: You may need to draw one!
Answer:
5 Can you describe what we mean when we describe a triangle as an isosceles triangle?
6 A cross (X) on a treasure map drawn on a grid has coordinates (10, 2). The treasure is actually buried 3 units up and 2 units to the right from where the cross is.
What coordinates should the cross have? ,
Woah!
A t 90o. To t r
d 180o.
5
An o l d
o l .
12 5
90o90o
0 2 4 6 8 10 12
6
4
21
3
5
X
X
49
I’m confi dent I’m nearly thereI can interpret and present data.
Statistics
Bar charts and time graphsA
Remember: Bar charts show ‘how many’ by the height of the bars.
The children in Class 4 were asked to name their favourite vegetable. Their answers are shown in the table. Draw a bar chart on the grid to show this information.
1
carrotspeasbeanssprouts
11642
Vegetable Number of children
Look at this bar chart. It shows how the children in Class 5 get to school.2
walk cycle car bus0
5
10
Num
ber
of p
upils
How many children don’t go to school by car?
How many in the class don’t walk to school?
15
3 Can you correctly label this bar chart?
Num
ber
of c
hild
ren
yellowredblue
orange
6758
Favourite colour Number of children
0
5
10
Num
ber
of0
5
10
carrots
15
Easypeasy!
18
23
d
w
n
50
Plotting a time graphB
I’m confi dent I’m nearly thereI can plot a time graph.
Jack measured the height of his bean plant every day for 8 days.
How much did the bean plant grow from day 4 to day 8?
Can you plot a time graph using this data? Use the space below.
1
12345678
246811141823
Day Height (cm)
cm
1 2 3 4 5 6 7 8
day
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
heig
ht (
cm)
0
Heregoes!
X
15
X
X
X
X
X
X
X
51
Word questionsC
I’m confi dent I’m nearly thereI can answer word questions about statistics.
1 Look at this bus timetable.
Bus station
Town centre
Train station
08:15
08:25
09:05
10:45
10:55
11:35
13:15
13:25
14:05
16:45
16:55
17:35
If you arrived at the bus station at 1 pm, how long would you have to wait for the next bus?
How long does the journey from the bus station to the train station take?
How long after the fi rst bus does the second bus leave the bus station?
a)
b)
c)
minutes15
minutes50
minuteshours2 30
2 Here is a graph to show the temperature on Christmas day.
OK!
Tem
pera
ture
(o C
)
X
X
Time
8 am 10 am noon 2 pm 4 pm 6 pm 8 pm
2
4
6
8
06 am
X X
X
X
X X
What was the temperature at 8 am?
What was the highest temperature during the day?
How long did it take for the temperature to rise from 0 oC to 6 oC?
Can you estimate the temperature at 3 pm?
By how much had the temperature changed between 8 am and 2 pm?
a)
b)
c)
d)
e)
oC2oC6
8 oC5oC4
52
By the end of Year 4, children are expected to know the facts in this section. Parents can help by regularly asking questions to test their children’s ability to recall these facts.
A little and often is the best approach, and any available fi ve minute period can be used.
Appendix - Information for Parents
Number bonds to 100
Children need to know all the pairs of numbers that add up to 100. For example:
60 + 40 = 100 40 + 60 = 100
25 + 75 = 100 75 + 25 = 100
72 + 28 = 100 28 + 72 = 100
A
They also need to know the related subtraction facts.
100 – 60 = 40 100 – 40 = 60
100 – 75 = 25 100 – 25 = 75
100 – 28 = 72 100 – 72 = 28
Try to use a range of vocabulary.
E.g. What do you need to add to 58 to get 100?
What is 100 take away 12?
What is 40 less than 100?
How many more than 82 is 100?
What is the difference between 55 and 100?
You can also use ‘missing number’ questions:
46 + = 100 100 – = 49
53
The times tables up to 12 x 12
0123456789
101112
xxxxxxxxxxxxx
1111111111111
=============
0123456789101112
1111111111111
xxxxxxxxxxxxx
0123456789101112
=============
0123456789101112
0123456789
101112
xxxxxxxxxxxxx
2222222222222
=============
024681012141618202224
2222222222222
xxxxxxxxxxxxx
0123456789101112
=============
024681012141618202224
0123456789
101112
xxxxxxxxxxxxx
3333333333333
=============
0369121518212427303336
3333333333333
xxxxxxxxxxxxx
0123456789101112
=============
0369121518212427303336
0123456789
101112
xxxxxxxxxxxxx
4444444444444
=============
04812162024283236404448
4444444444444
xxxxxxxxxxxxx
0123456789101112
=============
04812162024283236404448
0123456789
101112
xxxxxxxxxxxxx
5555555555555
=============
051015202530354045505560
5555555555555
xxxxxxxxxxxxx
0123456789101112
=============
051015202530354045505560
0123456789
101112
xxxxxxxxxxxxx
6666666666666
=============
061218243036424854606672
6666666666666
xxxxxxxxxxxxx
0123456789101112
=============
061218243036424854606672
0123456789
101112
xxxxxxxxxxxxx
7777777777777
=============
071421283542495663707784
7777777777777
xxxxxxxxxxxxx
0123456789101112
=============
071421283542495663707784
0123456789
101112
xxxxxxxxxxxxx
8888888888888
=============
081624324048566472808896
8888888888888
xxxxxxxxxxxxx
0123456789101112
=============
081624324048566472808896
B
54
0123456789
101112
xxxxxxxxxxxxx
9999999999999
=============
0918273645546372819099108
9999999999999
xxxxxxxxxxxxx
0123456789101112
=============
0918273645546372819099108
0123456789
101112
xxxxxxxxxxxxx
10101010101010101010101010
=============
0102030405060708090100110120
10101010101010101010101010
xxxxxxxxxxxxx
0123456789101112
=============
0102030405060708090100110120
0123456789
101112
xxxxxxxxxxxxx
11111111111111111111111111
=============
0112233445566778899110121132
11111111111111111111111111
xxxxxxxxxxxxx
0123456789101112
=============
0112233445566778899110121132
0123456789
101112
xxxxxxxxxxxxx
12121212121212121212121212
=============
01224364860728496108120132144
12121212121212121212121212
xxxxxxxxxxxxx
0123456789101112
=============
01224364860728496108120132144
By the end of Year 4 children should know the times tables up to 12 x 12.
Division facts
Children also need to know the division facts for each times table. For example:
Again, try to use a range of vocabulary when asking questions.
E.g. What is 6 multiplied by 4?
What is 7 times 6?
What is 36 divided by 6?
61218243036424854606672
÷÷÷÷÷÷÷÷÷÷÷÷
666666666666
============
123456789101112
61218243036424854606672
÷÷÷÷÷÷÷÷÷÷÷÷
123456789101112
============
666666666666
55
Top Tip
If your child knows the 2, 5 and 10 times tables and knows the square numbers, it may help them to answer times tables questions in steps like this:
7 x 7 = 49 so 8 x 7 = 49 + 7 =
8 x 8 = 64 so 8 x 9 = 64 + 8 =
5 x 8 = 40 so 6 x 8 = 40 + 8 =
56
72
48
8 x 7
8 x 9
6 x 8
Fractions and decimals
Children need to know these facts:
C
110
= 0.1 210
= 0.2 310
= 0.3 1010
= 1.0
1100
= 0.01 2100
= 0.02 3100
= 0.03 10100
= 0.1
12
= 0.5 14
= 0.25 34
= 0.75
110
=
Multiplying and dividing numbers by 10 and 100
Children need to know these facts for 1-digit and 2-digit numbers:
D
x 10 = 202 x 10 = 20020 x 10 = 25025
x 100 = 5005 x 100 = 400040 x 100 = 350035
÷ 10 = 660 ÷ 10 = 0.55
÷ 100 = 0.880 ÷ 100 = 0.066
You could ask any similar question and also try ‘missing number’ questions.
E.g. 60 ÷ = 6 etc.
56
Notes