The New Primary Curriculum for
mathematics: what does it mean to you?
22.03.14
Aims:
• How to teach calculation within the remit of
the National Curriculum
• The importance of manipulatives to help
develop the children’s conceptual
understanding
• The usefulness of the bar model
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.
3
The expectation is that the majority of pupils will move
through the programmes of study at broadly the same
pace. However, decisions about when to progress should
always be based on the security of pupils’ understanding
and their readiness to progress to the next stage. Pupils
who grasp concepts rapidly should be challenged through
being offered rich and sophisticated problems before any
acceleration through new content. Those who are not
sufficiently fluent with earlier material should consolidate
their understanding, including through additional practice,
before moving on.
What is Place Value?
•
•
•
•
Positional
Base 10
Multiplicative
Additive
1000 100 10 1
2 3 4 5
(Ross 1989)
5
Does this represent
understanding of place value?
JULIA ANGHILERI1, MEINDERT BEISHUIZEN2 and KEES VAN PUTTEN (2001)
FROM INFORMAL STRATEGIES TO STRUCTURED
PROCEDURES: MIND THE GAP! Educational Studies in Mathematics 49: 149–170, 2002.
6
Common errors and
misconceptions
36
+48
111
45
- 37
12
4
35
 3
915
2
18
216
248
 25
1240
496
1736
A sledgehammer to crack a nut
0
1
9 19 1
0 1
1000
- 997
3
16
- 9
7
08
7 56
0
5
97
x 100
00
000
9700
9700
Well known mental calculation strategies
•
•
•
•
•
•
•
•
•
•
•
•
Partition and recombine
Doubles and near doubles
Use number pairs to 10 and 100
Adding near multiples of ten and adjusting
Using patterns of similar calculations
Using known number facts
Bridging though ten, hundred, tenth
Use relationships between operations
Counting on
x4 by doubling and doubling again
x5 by x10 and halving
x20 by x10 and doubling
45 + 77
10
45 + 77
11
45 + 77
45
+77
122
1 1
12
182 - 147
13
182 - 147
14
182 - 147
17 81 2
-1 47
3 5
15
30
8
3
3
30
8
90
24
38
x 3
114
2
Hundreds
Tens
Ones
20
3
01 1
6 138
23
6
138
17
The bar model (Singapore Bar)
This has been extremely successful in helping
children to make sense of problems in Singapore
and Japan.
It is increasingly being used in the UK.
David spent 2/5 of his money on a book.
The book cost £10.
How much money did he start off with?
£10
What if the book cost…..
£20?
£6?
£5?
Peter has 4 books.
Harry has five times as many books as
Peter. How many more books has Harry?
Peter’s books
Harry’s books
19
Sam had 5 times as many marbles as Tom. If Sam gives 26
marbles to Tom, the two friends will have exactly the same
amount. How many marbles do they have altogether?
A computer game was reduced in a sale by
20% and it now costs £48. What was the original price?
A gardener plants tulip bulbs in a flower bed.
She plants 3 red bulbs for every 4 white bulbs.
She plants 60 red bulbs.
How many white bulbs does she plant?
Generalisation
This can then help the children solve, for example, missing
number problems:
45 + ? = 93, ? – 62 = 13, 146 - ? = 79, ? + 82 = 147
KS2 2012