Inspire Maths and SATs

Inspire Maths
and SATs
How can Inspire Maths help
you and your Year 6 pupils
prepare for SATs?
1

Introduction
How can Inspire Maths help you and
your Year 6 pupils prepare for Key
Stage 2 SATs?
We have selected a number of questions from the 2016
KS2 SATs papers and highlighted relevant pages from
the Inspire Maths Pupil Textbooks which will help your
Year 6 pupils to answer these questions.
Pupils following the Inspire Maths programme will build
and consolidate knowledge and understanding year
on year. Inspire Maths will give them the mathematical
language, deep understanding and confidence so they
are fully prepared for SATs.
View some example SATs questions and the practice that Inspire Maths can provide

Paper 1:
10 879 × 3 =
Arithmetic
11 71 × 8 =
1 mark
Let’s Learn!
Multiplication Unit 6
Multiplication with regrouping in ones, tens and hundreds
1 68 × 2 = ?
Hundreds
Tens
Ones
First multiply the ones by 2.
6 8
× 2
6
1
Hundreds
Tens
Ones
8 ones × 2 = 16 ones
Regroup the ones:
16 ones = 1 ten 6 ones
12 50 × 70 =
1 mark
Hundreds
Tens
Ones
Then multiply the tens by 2.
6 8
× 2
1 3 6
Curriculum objective:
Write and calculate mathematical statements for
multiplication and division using the multiplication
tables that they know, including for two-digit
1 mark
numbers times one-digit numbers, using mental and
progressing to formal written methods.
Hundreds
Tens
Ones
1
6 tens × 2 = 12 tens
Add the tens:
12 tens + 1 ten = 13 tens
Regroup the tens:
13 tens = 1 hundred 3 tens
68 × 2 = 136
83
E00060A0720
Page 7 of 20
(M)UKIMPB3A_U06.indd 83
Pupil Textbook 3A, Unit 6, Multiplication (page 83)
1/26/15 3:24 PM
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 1:
19 3 2 + 10 =
Arithmetic
1 mark
Let’s Learn!
Dividing by tens, hundreds and thousands
Dividing by 10
Decimals Unit 7
1 a Starting from 1, Peter takes 10 equal steps backwards on the number
line and lands on the point 0. What is the length of each step?
20 0.9 ÷ 10 =
0 1
? ? ? ? ? ? ? ? ? ?
1 ÷ 10 = 1 × 1
10
1
=
10
= 0·1
The length of each step is 0·1.
1 mark
b
Starting from 0·1, Ruby takes 10 equal steps backwards on the number
line and lands on the point 0. What is the length of each step?
21 4 − 1.15 =
Curriculum objective:
Identify the value of each digit in numbers given
to three decimal places and multiply and divide
numbers by 10, 100 and 1000 giving answers up to
1 mark
three decimal places.
Page 10 of 20
E00060A01020
0 0·1
? ? ? ? ? ? ? ? ? ?
0·1 ÷ 10 = 1
10 ÷ 10
= 1
10 × 1
10
1
=
100
= 0·01
The length of each step is 0·01.
15
(M)UKINPB5B_U07.indd 15
Pupil Textbook 5B, Unit 7, Decimals (page 15)
18/6/15 12:31 pm
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 1:
Arithmetic
24
4
7 + 5 7 = 1 mark
Unit 12 Fractions
Let’s Learn!
Adding and subtracting like fractions
1 Ella eats 1 of a pizza.
5
Tai eats 3 of it.
5
What fraction of the pizza do
they eat altogether?
1
5 and 3 are like fractions.
5
This number is the same.
1
5
3
5
25 20% of 1,800 =
Curriculum objective:
Add and subtract fractions with the
same denominator.
50
1
3
5
5
1
5 + 3 5
= 1 fi fth + 3 fi fths
= 4 fi fths
4
5
1
5 + 3 5 = 4 5
They eat 4 5 of the pizza altogether.
1 mark
(M)UKinsPB2B_U12.indd 50
Pupil Textbook 2B, Unit 12, Fractions (page 50)
11/28/14 8:58 AM
*
All questions 26 were 15 taken × 6.1 from = the 2016 Key Stage 2 national test papers
More examples

Paper 1:
Arithmetic
Let’s Learn!
Percentage of a quantity
Percentage Unit 10
1 There were 400 seats on an aeroplane. 60% of the seats were in economy
class. How many seats were in economy class?
Method 1
400 seats
29 15% × 440 =
60% (? seats)
100% 400 seats
400
1%
100 = 4 seats
60% 60 × 4 = 240 seats
There were 240 seats in economy class.
100% of the seats is the
total number of seats.
30
6 5 7 4
× 3 1
Curriculum objective:
Solve problems involving the calculation of
Show
percentages [for example, of measures, and such
your
method
as 15% of 360] and the use of percentages for
comparison.
1 mark
2 marks
Method 2
60% of seats = 60% of 400
= 60
100 × 400
= 60 × 4
= 240
There were 240 seats in economy class.
77
(M)UKINPB5B_U10.indd 77
Pupil Textbook 5B, Unit 10, Percentage (page 77)
18/6/15 4:16 pm
*
All questions were taken from the 2016 Key Stage 2 national test papers
Paper 2: Reasoning
examples

Paper 2:
Reasoning
Put On Your Thinking Caps!
5
Addition and Subtraction within 1000 Unit 2
Find the missing
number in each box.
3
Write the three missing digits to make this addition correct.
1 1 1
4 3 2
1 2
1 5
+
3 3 3
+ 4 6
8 8 8
+ 3 4 5
4 6 8
+ 4 4
1 5
2 marks
6 5 4
– 1
– 4 4 4
– 2 4
8 8
4 4 4
4 2 0
Curriculum objective:
Add and subtract numbers with up to three digits,
using formal written methods of columnar addition
and subtraction.
Practice Book 2A, p.57
59
(M)UKIMPB2A_U02.indd 59
Pupil Textbook 2A, Unit 2, Addition and Subtraction within 1000
(page 59)
11/25/14 5:47 PM
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 2:
Reasoning
Unit 13 Symmetry
5 Each shape below is half of a symmetrical shape. Copy them onto square
grid paper. Then complete each symmetrical shape using the dotted line
as a line of symmetry.
a
b
6
This diagram shows a shaded shape inside a border of squares.
Draw the reflection of the shape in the mirror line.
Use a ruler.
c
d
mirror line
1 mark
Curriculum objective:
Complete a simple symmetric figure with respect to
a specific line of symmetry.
130
E00070A0924 Page 9 of 24
(M)UKIMPB4B_U13.indd 130
Pupil Textbook 4B, Unit 13, Symmetry (page 130)
23/3/15 1:25 pm
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 2:
Reasoning
Unit 14 Fractions
Let’s Learn!
More equivalent fractions: short cut
1
2
3
4
6
2
3
= 4 6
6
= 9
=
8
12
7
Write the two missing values to make these equivalent fractions correct.
6
9
8
12
8
=
3 12
=
4
1 mark
1 mark
There is a short cut!
To fi nd an equivalent fraction,
multiply the numerator and the
denominator by the same number.
x × 2
x × 3
2
3
=
4
6
2
3
=
6
9
× x 2
x × 3
Curriculum objective:
Use common factors to simplify fractions; use
common 8 Circle multiples two numbers that to add express together to equal fractions 0.25 in the same
denomination.
72
To get 8 , we multiply
12
the numerator and
denominator of 2 3 by .
0.05 0.23 0.2 0.5
1 mark
(M)UKINPB3B_U14N.indd 72
Pupil Textbook 3B, Unit 14, Fractions (page 72)
28/1/15 2:29 pm
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 2:
Reasoning
12 n = 22
What is 2n + 9?
Let’s Learn!
Word problems
3y – y = 2y
Algebra Unit 1
1 Matt has y computer games. Anna has 3 times as many computer games
as Matt. Anna buys another 7 computer games.
a
b
a
How many more computer games does Anna have than Matt after
she buys another 7 computer games, in terms of y ?
If Matt has 25 computer games, how many more computer games
does Anna have than Matt?
Anna has (3y + 7) computer games.
3y + 7 – y = 2y + 7
Anna has (2y + 7) more computer games than Matt.
1 mark
b 2y + 7 = (2 × 25) + 7
= 50 + 7
= 57
2q + 4 = 100
Work out the value of q.
q =
Curriculum objective:
Use simple formulae.
1 mark
Anna has 57 more computer games than Matt.
2 Sophie has £m and Ahmed has £15 more.
a Find the amount of money they have altogether in terms of m.
b If Sophie has £75, how much money do they have altogether?
a Ahmed has £ ( ).
They have £ ( ) altogether.
b If m = 75, they have £ altogether.
National Curriculum
Activity 6.9, found on
Inspire Maths Online, is
also useful for this activity.
19
(M)UKIMPB6A_U01.indd 19
Pupil Textbook 6A, Unit 1, Algebra (page 19)
6/26/15 8:53 AM
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 2:
Reasoning
Unit 11 Angles
Let’s Learn!
Vertically opposite angles
1 EF and GH are two straight lines which cross each other.
∠a and ∠c are called vertically opposite angles.
∠b and ∠d are also called vertically opposite angles.
17
Calculate the size of angles a and b in this diagram.
a
b
Not
to
scale
a = °
1 mark
The fact that angles
in a quadrilateral
add up to 360° is
covered in National
Curriculum Activity
6.16 found on
Inspire Maths
Online.
∠a + ∠b = 180°
∠b + ∠c = 180°
∠a + ∠b = ∠b + ∠c
So ∠a = ∠c.
E
G
b
a
c
d
∠a and ∠b are angles on a straight line.
∠b and ∠c are also angles on a straight line.
H
F
b = °
18 Write the missing number.
Curriculum objective:
70 ÷ = 3.5
1 mark
Find unknown angles in any triangles, quadrilaterals,
and regular polygons. Recognise angles where they
meet at a point, are on a straight line, or are vertically
opposite, and find missing angles.
1 mark
102
∠a + ∠b = 180°
∠a + ∠d = 180°
∠a + ∠b = ∠a + ∠d
So ∠b = ∠d.
∠a and ∠d are also
angles on a straight line.
Vertically opposite angles are equal.
(M)UKINPB5B_U11.indd 102
E00070A01924 Pupil Textbook 5B, Unit 11, Angles (page 102)
Page 19 of 24
6/19/15 5:59 PM
*
All questions were taken from the 2016 Key Stage 2 national test papers
Paper 3: Reasoning
examples

Paper 3:
Reasoning
National Curriculum Activity
6.9, available on Inspire Maths
Online, also covers formulae.
2n and 3n are examples of algebraic expressions in terms of n.
Algebra Unit 1
This example question also requires division by a
1-digit number, shown in Pupil Textbook 4A. The
skills required to answer this question are built
up from Inspire Maths 1, as these challenging
problems in Pupil Assessment Book 1 show:
Challenging Problems 1
Date:
4
Each shape stands for a number.
3n is 3 × n or
3 groups of n.
1 × n or n × 1
is equal to n.
12p is 12 × p
or p × 12.
1 Write the numbers 1 to 6 in the circles.
The numbers along each side must add up to 10.
You can use each number only once.
Total 100
12 Answer these questions.
a 4k = ×
Total
96
b 7j = ×
c 5p means groups of .
d 8 groups of x is × .
2 What numbers do t and ♥ stand for?
Work out the value of each shape.
=
=
1 mark
1 mark
13 Refer to the table below. There are n marbles in a packet. Find the number of
marbles in terms of n. Then fi nd the number of marbles for the given values
of n.
Number of Number of Number of Marbles When:
Packets Marbles n = 15 n = 20
1 n 15 20
4 4n 4 × 15 = 60
3
♥
t
♥
9
7
10
t =
Curriculum objective:
Use simple formulae.
(M)UKIMPB6A_U01.indd 7
15
Pupil Textbook 6A, Unit 1, Algebra (page 7)
7
6/29/15 4:03 PM
05(M)UKIMPAB1_CP1.indd 15
♥ =
Challenging Problems 1
15
12/2/14 10:39 AM
E00080A0724
Page 7 of 24
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 3:
Reasoning
Decimals (2) Unit 10
4 A coat costs £66·45. A jumper costs £28·65. Ruby's dad has £75.
How much more money does he need to buy the coat and the jumper?
£ + £ = £
The total cost of the coat and the jumper is £ .
£
6
Jacob cuts 4 metres of ribbon into three pieces.
Coat and jumper
?
The length of the first piece is 1.28 metres.
Ruby's dad
The length of the second piece is 1.65 metres.
£75
Work out the length of the third piece.
£ – £ = £
He needs £
more to buy the coat and the jumper.
Show
your
method
metres
5 A piece of material 4 m long is cut into two pieces. The first piece is
1·25 m long. How much longer is the second piece of material?
m
? m
2 marks
1st piece
2nd piece
m
Curriculum objective:
Solve simple measure and money problems
involving fractions and decimals to two
decimal places.
? m
m – m = m
The length of the second piece is m.
m – m = m
The second piece is m longer than the first piece.
59
(M)UKIMPB4B_U10(57-64).indd 59
Pupil Textbook 4B, Unit 10, Decimals (2) (page 59)
3/23/15 4:58 PM
*
All questions were taken from the 2016 Key Stage 2 national test papers
E00080A0924
Page 9 of 24
More examples

Paper 3:
Reasoning
Unit 14 Volume of Cubes and Cuboids
4 These solids are made up of unit cubes.
What is the volume of each solid?
a
b
10 Emma makes a cuboid using 12 cubes.
Volume = cubic units Volume = cubic units
c
d
Write the letter of the cuboid that has a different volume from
Emma’s cuboid.
Volume of cube
Volume of cuboid
= cubic units = cubic units
B
A
C
5 This is a 1 cm cube.
Each edge of the cube is 1 cm long.
The volume of the cube is
1 cubic centimetre (cm 3 ).
The cubic centimetre
(cm 3 ) is a unit of
measurement for volume.
D
E
1 cm
Page 13 of 24
1 mark
Curriculum objective:
E00080A01324
Estimate volume [e.g. using 1cm 3 blocks to build cuboids
(including cubes)] and capacity [e.g. using water].
166
1 cm 1 cm
(M)UKINPB5B_U14.indd 166
18/6/15 2:09 pm
Pupil Textbook 5B, Unit 14, Volume of Cubes and Cuboids (page 166)
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 3:
Reasoning
11 A toy shop orders 11 boxes of marbles.
Show
your
method
Each box contains 6 bags of marbles.
Each bag contains 45 marbles.
How many marbles does the shop order in total?
marbles
Curriculum objective:
2 marks
Multiply multi-digit numbers up to 4 digits by
a two-digit whole number using the formal
written method of long multiplication.
68
68
b
b
5 times
12 bags
12 bags
Miss Thompson
127 kg
each
each
drinks
Mr Brown
860 ml
8 A gardener packs 4568 seeds equally into 9 packets. He packs the
greatest possible number of seeds equally and plants any remaining
7 A shopkeeper buys 1257 tins of paint. Each tin holds 7 of paint.
seeds in his own garden.
If he sells 620 tins, how much paint does he have left? Give your answer
a in litres. How many seeds are there in each packet?
b How many seeds does he plant?
8 A gardener packs 4568 seeds equally into 9 packets. He packs the
c If he sells 7 packets, how many seeds does he have left?
greatest possible number of seeds equally and plants any remaining
seeds in his own garden.
9 Jack, Tai and Millie sell some raffl e tickets for charity. Jack sells 125 tickets.
a Tai sells How 14 many times seeds as many are tickets there in as each Jack. packet? Millie sells half as many tickets
b as Tai. How How many many seeds tickets does they plant? sell altogether?
c If he sells 7 packets, how many seeds does he have left?
Pupil Textbook 4A, Unit 3, Whole Numbers (page 68)
9 Jack, Tai and Millie sell some raffl e tickets for charity. Jack sells 125 tickets.
Tai sells 14 times as many tickets as Jack. Millie sells half as many tickets
as Tai. How many tickets do they sell altogether?
bag
total mass
bag
mass
7 A shopkeeper buys 1257 tins of paint. Each tin holds 7 of paint.
If he sells 620 tins, how much 127 kgpaint does he have left? Give your answer
in litres.
(M)UKINPB4A_U03.indd 68
total mass
mass
3/26/15 12:09 PM
Page 14 of 24
E00080A01424
(M)UKINPB4A_U03.indd 68
3/26/15 12:09 PM
*
All questions were taken from the 2016 Key Stage 2 national test papers
More examples

Paper 3:
Reasoning
17
Here are five triangles on a square grid.
Unit
5
Let’s Learn!
Area of a Triangle
Unit 5 Area of a Triangle
2 What is the area of triangle ABC?
1 cm
F
A
1 cm
E
A
Base and height of a triangle
C
B
D
E
1 ABC is a triangle.
A
B
The three sides are AB, BC and CA.
C
Let’s recall
the parts of
a triangle. It has three
sides and three angles.
B
In triangle ABC, the base BC = 6 cm and the height AD = 4 cm.
D
Area of triangle ABC = area of triangle ABD + area of triangle ADC
Area of triangle ABD = 1 × area of rectangle FBDA
2
= 1 2 × 2 × 4
= 4 cm 2
C
2 In triangle ABC:
A
A
A
Area of triangle ADC = 1 × area of rectangle ADCE
2
= 1 2 × 4 × 4
Four of the triangles have the same area.
Which triangle has a different area?
Curriculum objective:
1 mark
B
height
D
base
C
AD is perpendicular
to BC. BC is called
the base and AD is
called the height.
B
height
E
base
C
BE is perpendicular
to AC. In this case,
AC is the base and
BE is the height.
base
F
B
height
CF is perpendicular
to AB. In this case,
AB is the base and
CF is the height.
C
133
138
= 8 cm 2
So area of triangle ABC = 4 + 8
= 12 cm 2
Now area of rectangle FBCE = 6 × 4
= 24 cm 2
Half of its area = 12 cm 2
So area of triangle ABC = 1 × area of rectangle FBCE
2
= 1 2 × 6 × 4
= 1 × base BC × height AD
2
The lengths 6 cm and
4 cm of rectangle FBCE
are the base and height
of triangle ABC.
Triangle ABC is half
of rectangle FBCE.
Calculate the area of
parallelograms and triangles.
(M)UKINPB5A_U05.indd 133
Pupil Textbook 5A, Unit 5, Area of a Triangle
(page 133)
6/18/15 1:08 PM
(M)UKINPB5A_U05.indd 138
6/18/15 1:08 PM
Pupil Textbook 5A, Unit 5, Area of a Triangle
(page 137)
E00080A01924
Page 19 of 24
*
All questions were taken from the 2016 Key Stage 2 national test papers

Inspire Maths
and SATs
Find out
more about
Inspire
Maths
Contact your
local sales
representative