Calculation
Supporting your Children at Home
St Mary of the Angels Primary School
Starter
Mathematics Curriculum - Aims
The National Curriculum for mathematics aims to ensure that all pupils:
•
become fluent in the fundamentals of mathematics, including
through varied and frequent practice with increasingly complex
problems over time, so that pupils have conceptual understanding and
are able to recall and apply their knowledge rapidly and accurately to
problems
•
reason mathematically by following a line of enquiry, conjecturing
relationships and generalisations, and developing an argument,
justification or proof using mathematical language
•
can solve problems by applying their mathematics to a variety of
routine and non-routine problems with increasing sophistication,
including breaking down problems into a series of simpler steps and
persevering in seeking solutions.
Fluency in Mathematics
A variety of strategies….
How would you expect your children to solve these?
23 + 19
78 – 26
64 x 3
23 x 30
84 ÷ 7
64 ÷ 4
Models and Images
 Objects
 Pictures
 Straws
 Dienes
 Coat hanger and pegs
 Dice
 Bead string
 Tracks and number lines
 Numicon
 Arrow cards
 Place Value Counters
1 2 3 4 5 6 7 8 9
Images
Beadstring
The beadstring may be used to model the following strategies:
-
Doubling
Counting forwards and backwards
Using the relationship between addition and subtraction
Number facts
Partitioning
Models and Images: Empty Number Line
Informal Jottings - Using a number line
Bridging through ten
57 + 28 =
57 + 3 + 20 + 5 = 85
+3
57
+5
+20
60
80
85
Models and Images: Empty Number Line
Informal Jottings - Using a number line
38 + 19 =
38 + 20 - 1
= 57
Compensation
+20
-1
57
38
45 x 9
=
=
45 x 10 – 45
405
58
Partitioning
5 6
50
6
Mental method, using partitioning
56
6
+
411
50 + 40
90
907
+
7
+
6
+
1
Partitioning in different ways
…by place value
64 x 3 = (60 x 3) + (4 x 3)
= 180
+
12
=
192
…into multiples
84 ÷ 7 = (70 ÷ 7) + (14 ÷ 7)
= 10
+
2
=
12
Teaching progression for addition
Showing the compact layout alongside the expanded format
267
+ 85
200
267
+ 85
267
12
+ 85
140
140
352
12
200
352
352
EXPANDED FORMAT
Most significant digit first
then
least significant digit first
1 1
COMPACT METHOD
Understanding Addition and Subtraction
Using the number line and bridging to count back
The baker makes 54 loaves and sells 28.
How many has he left?
54 - 28 = 26 loaves are left
- 20
-4
26
-4
30
34
54
Subtraction – mental to written
63 - 48
60 and 3
-40 and 8
Exchange 60 into 50 and 10
5 1
50 and 13
-40 and 8
10 and 5
63
- 48
15
Addition and subtraction activities at home
• calculating change - which coins, different combinations
• deciding on coins to pay a bill
• weighing fruit and vegetables in the supermarket
• counting pocket money
• calculating the price of a holiday from brochures
• estimating the final bill at the end of shopping while waiting at the checkout
• using shopping bills to calculate change
• calculating postage on letters using first or second class stamps
• calculating the cost of a meal using a menu
• calculating the cost of the contents of a lunch box
• using the till receipt to check the shopping
• calculating the cost of the family going to the cinema, swimming baths, etc
Multiplication and Division
Understanding multiplication as repeated addition
5 added together 3 times is 5 + 5 + 5
or
3 lots of 5
or
5x3
Multiple Representations of a multiplication fact
How might this support children’s conceptual
understanding of multiplication?
The importance of arrays
5 x 2
2 x 5
Number facts Triangle
4 x 6 = 24
24
÷
÷
6 x 4 = 24
24 ÷ 4 = 6
4
6
x
24 ÷ 6 = 4
Multiplication Challenge
How many eyes can you see around the room?
How many fingers?
How many thumbs and heads?
Learning Facts
Let’s learn to count in multiples of 17
What facts can we use to help us?
Rehearsing facts
Applying Facts
•
•
•
•
•
•
Two even numbers - with a product of 32 and a sum of 12
Two odd numbers - with a product of 35 and a sum of 12
Two odd numbers - with a product of 63 and a sum of 16
Two prime numbers - with a product of 14 and a sum of 9
Two consecutive numbers - with a product of 30 and a sum of 11
Two consecutive numbers - with a product of 56 and a sum of 15
Applying tables facts
Progression in multiplication TU x U
14x7=
10
4
7
70 + 28 = 98
x
10
4
7
70
28
14
14
x 7
x 7
28 (4x7)
98
70 (10x7)
2
98
98
Progression in multiplication TU x TU
17 x 14 =
10
10
4
100
40
7
70
28
17
17
x 14
x 14
100 (10x10)
170 (17 x 10)
70 (7x10)
68 (17 x 4)
40 (10x4)
28 (7x4)
238
238
What’s the same? What’s different?
Intelligent Practice
Division as Sharing
12 ÷ 2 = 6
Repeated subtraction of one
There are 12 sweets and 2 children. They share the sweets
equally, how many sweets does each child have?
Each child has 6 sweets
Division as Grouping
12 ÷ 2 = 6
Repeated subtraction of groups
There are 12 sweets and each party bag needs two sweets.
How many party bags can be made?
There are 6 party bags
The Empty Number Line: Division using Chunking
63 ÷ 4
= 15 r 3
rem 3
0
10 x 4
5x4
3
23
63
Division: Using Chunking
63 ÷ 4
= 15 r 3
4 63
40
10 x 4
23
20
3
5x4
Division: Chunking with larger multiples
• 412 ÷ 7 = 58 r 6
7 412
- 350
62
50 x 7
- 56
8x7
6
Things I know about 7:
7x1=7
 7x10=70
7x2=14
 7x20=140
7x5=35
 7x50=350
Short Division – Formal Method
Long Division – Formal Method
Multiplication and division activities at home
• Hanging out the washing – decide how many pegs are needed
• Calculating discounts e.g. 20% reduction, 50% sale price
• Calculating the cost of a meal using a menu – How much would it be for three people
to eat?
• Calculating the cost of the family going to the cinema, swimming baths, etc
• Measuring weights of ingredients for baking – this recipe is for two people, how
much flour would we need if we were baking cakes for six people?
• Recording the growth of a special plant in the garden – How long do you think it will
be until it doubles in size?
• Making orange squash – how many cups can you get from one bottle, two bottles?
• Counting house numbers but emphasising odd and even
• Counting up to 10, 20, 100 – backwards and forwards – Try counting in twos, threes.
• Laying the table for four people – count the cutlery as you go
• Matching pairs of socks, gloves, shoes
Vocabulary for Calculation
Addition
add
more
plus
increase
sum
total
altogether
how many more
double
how many less
Subtraction
subtract
take away
minus
decrease
leave
how many left
difference
how many fewer
Multiplication
lots of
times
groups of
product
multiply
multiplied by
multiple of
repeated addition
… times as big
double
row
column
array
product
multiplier
Division
divide
share
share equally
equal groups of
divided by
divided into
divisible by
what is remaining
halve, half
remainder
dividend
divisor
quotient