…… Primary School
Parents Meeting on:
Progression through
Calculations
Do I need
jottings ?
Can I do
it in my
head?
Shall I use a
pencil and
paper method?
Do I need to
use a
calculator?
Starter
•
•
•
•
•
(use a calculator!)
Think of a number between 1 and 9
Multiply by 2 (x 2)
Add 5 (+5)
Multiply by 50 (x50)
If you have had your birthday this year
add 1 760. If not add 1759.
• Subtract the year of your birth.
Aims
• To look at the ways in which the
teaching of mathematics has changed;
• To look at how children calculate;
• Try activities to develop calculation
strategies;
• To look at ways in which parents can
help their children
How has mathematics changed?
• Daily mathematics lesson;
• Emphasis on mental calculations;
• Interactive whole class and group
teaching;
• Enjoyable practical approaches;
• Mathematics with understanding
Calculations
Ways to help children to remember…
• Practice with just one fact a day, or try a ‘fact of the
week’
• Practice ‘fact families’, e.g. 6+8=14, 8+6+14, 14-6=8,
14-8=6
• Work from answers back to facts – how many facts
do you know with an answer of 12?
• Make an addition or multiplication table and cross out
all those facts you already know. Now focus on those
you need to learn.
• Encourage children to work out their own ways to
remember facts
• Draw pictures to accompany particular facts.
• Repeat it and repeat it!
Skills of mental calculation
• Remembering number facts and recalling them
without hesitation.
• Using facts that are known by heart to figure out new
facts.
• Applying understanding of place value and ability to
partition numbers into parts
• Understanding and using the laws of arithmetic and
relationships between the four operations to find
answers and check results
• Having a repertoire of mental strategies to do
calculations with some thinking time
• Solving word problems
Mental gymnastics
• Think of a number and keep doubling it. How
far can you go?
• Face the person next to you and alternate!
• In two’s – one person recites all the numbers
from 1 to 100
• The other person raises their hand at any
number that can be divided by 3 or …
• Divided by 4 or …
• Divided by 3 and 4 or …
• Divided by 5
You can use your number square to help you!
Mental calculations
Children are encouraged to
count in different ways and
to calculate mentally.
Number lines – Bead bar / number stick / individual number lines /
Number ladders
Calculations
The aim is that
children will always
be able to recognise
when calculations
can be done ‘ in their
heads’ and choose
effective and
efficient strategies
to work out the
answers.
Overview
Up to Year 3 the emphasis is on:
o working mentally,
o calculations recorded in horizontal number
sentences
o some jottings for more challenging numbers
o Models and Images
In Year 3-6 children will be gradually taught more
formal written methods of calculation but
they will still use mental methods and jottings
where appropriate.
Developing children’s mental
picture of number system
o DEMONSTRATE on a number line children’s
response to a calculation.
o DISPLAY number lines and washing lines
around the room for the children to access.
o MODEL the use of number lines and tracks to
aid calculation from YR and empty number
lines from Y2
o CONTINUE to demonstrate, display and
model use of a number line all the way to Y6!
Early Recording
So - how can we give children the
best foundations for success
with written calculations?
o We need to encourage children to use
mental calculation strategies for
smaller/ simpler numbers.
o We need to encourage children to
ask the question “Can I do it in my
head?” or “Can I do it in my head with
jottings/ a number line?”
Laying the foundations for
addition and subtraction
o Partitioning
o Rounding
o Compensating
o Counting on
o Bridging through 10s, 100s, 1000s boundaries
o Addition and subtraction facts
Laying the foundations for
multiplication and division
o Doubling/ Halving
o Grouping/ equal groups/ equal jumps
o Repeated addition/ subtraction
o Arrays
o Multiplication and division facts
Multiply
• Slap, clap, click (not as violent as it sounds!)
• ‘Show me’ –
1.The product of a multiplication
2.A multiple of 2, 3, 5, 10, 4, etc
3.A number that is exactly divisible by 3, 5, 2, 10,
4, etc
4.A common multiple of 2 and 3, 3 and 5, 3 and 10
1.In groups have a go at ‘Hot Seat’
You can use your number square or calculator to help
Common calculation errors!
99
+101
1901
158
+ 184
612
4 1
945
- 237
712
1 1
1
2000
108
902
Dartboard Activity
Rules: You have 3 darts. You can hit the
same section of the board more than once,
but all three must score. Show how you
could score each of these totals.
Demonstrate the first one
Work with a partner
Do you always make the totals in the same
way?
How might you differentiate this game?
Addition- Progression
o Mental calculation supported by:
Modelling of method by teacher
Jottings
Number lines
o Expanded method using partitioning
o Compact ‘carrying’ method
Jottings
When do children still use
jottings/ number lines??
• When they can calculate mentally and
need a little support.
• When they are not completely secure
with ‘carrying’.
• When they are dealing with addition of
decimals, negative numbers, time,
measurement scales, etc.
• Stage 1: Mental method using partitioning:
47 + 76 = (40 + 70) + (7 + 6) = 110 + 13 = 123
• Stage 2/3: Use an expanded layout
47
+ 76
110
13
123
47
+ 76
13
110
123
Subtraction - Progression
• Mental calculations supported by:
Modelling of method by teacher
Jottings
Number line
• Expanded decomposition using partitioning
• Compact decomposition
78 – 12?
How do you
work out….
74 – 57?
Using a Number line for
Subtraction
• Counting Back
78 – 12
-10
-2
66 68
78
• Counting on to find the Difference
74 – 57
+10
57
+3
67
+4
70
74
When do children still use
jottings/ number lines??
o When they can calculate mentally and need a little
support.
o When they are calculating the difference between
two numbers relatively close together.
o When not completely secure with decomposition
o When calculating with decimals.
o When decomposition is made difficult by ‘trapped
zeroes’.
Stage 1: Mental method using partitioning.
76 – 32 = (70 – 30) + (6– 2) = 44
Stage 2: Expanded vertical layout
Stage 3: Compact decomposition
Ongoing
methods:
mental
methods and
subtraction
using a
number line
Multiplication - Progression
o Mental calculation supported by:
Jottings
Number lines
Modelling of method by teacher
o Understanding of multiplication as:
an array
repeated addition
scaling
o Grid method
Multiplication facts ITP
Multiplication Facts ITP
Using a number line
0
6
12
18
24
30
36
42
48
54
60
0
1
2
3
4
5
6
7
8
9
10
Grid method of multiplication
6
10
3
60
18
so 6 x 13 = 78
60 + 18 = 78
Grid ITP
Division - Progression
o Mental calculations supported by:
Jottings
Number lines
Modelling of method by teacher
o Understanding division as sharing and grouping.
o Visualising division using:
arrays
repeated subtraction
This child has used a strategy of
grouping tallies to find the answer.
This child has used a strategy of
counting equal groups to find the answer.
Table Trios and Multiplication
Clocks!
Division - Progression
Chunking
Step 1:
Demonstrate practically by repeatedly subtracting
groups of objects and keeping count
Step 2:
Model on a number line
Step 3:
Model vertical method
•Stage 1: Short division. i.e. TU ÷ U, HTU ÷ U
Known as the ‘chunking’ method.
6
72
- 60
x 10
12
- 6
x1
6
- 6
x1
0
Answer = 12
9
97
- 90
x 10
7
Answer = 10 r 7
Stage 3 Long division (HTU ÷ TU)
15
432
- 150
282
- 150
132
- 60
72
- 60
12
x 10
x 10
x4
x4
Answer = 28 r 12
15 432
- 300
132
120
12
x 20
x8
Answer = 28 r 12
How to help your child with
mathematics!
Visual maths
• Number lines
1
2
3
• Noticing numbers
23
4
5
6
Rhymes/songs
• 5 little speckled frogs;
• 10 huge dinosaurs (bottles);
• 1, 2, 3, 4, 5 once I caught a fish alive;
Sorting
• Socks
• Cars
• Shoes
Measures
• Keep a record of your child's growth;
• Scales and balances e.g. see-saws
• Capacity – different containers to play
with in the sink or bath;
Rectangle
Spot the Shape 1 and 2
Shape and space
• Recognising shapes around them e.g.
doors, windows, cans, boxes etc
• Construction sets, Lego,
• Shapes of cakes, biscuits, sandwiches.
How can parents help?
• Count with their child
• Play number games
• Involve children in shopping activities
• Involve children when taking measurements or weighing
items
• Take note of numbers in real life e.g. telephone numbers,
bus numbers, lottery numbers etc
• Give children opportunities to use money to shop, check
change etc
•Talking about the mathematics in football e.g.. How many
points does your favourite team need to catch the next
team in the division?
• When helping their children calculate use the method that
they have been taught.
Key Messages
To develop written calculation strategies, children need:
o Secure mental strategies from YR.
o A solid understanding of the number system.
o Practical, hands on experience including counters and base 10
apparatus.
o Visual images including number lines and arrays.
o Experience of expanded methods to develop understanding
and avoid rote learning.
o Secure understanding of each stage before moving onto the
next.
o The questions at the forefront of their minds:
‘Can I do it in my head? If not which method will help me?’