Transcript Parents maths presentation Nov 15

Aims:
 to provide an overview for parents of how mathematics is taught
within our school,
 to explain the expectations of the National Curriculum
To demonstrate the differences between written and mental
methods in maths
 to model and demonstrate the pencil and paper procedures for
the four main operations +, –, ×, ÷ as they look throughout the
school
The current national curriculum has
been statutory from September 2014.
It is now in its third year of use at St
Mary’s, as we began using it in 201314.
General points about the national curriculum for
maths
Expectations are higher than ever. Pupils are benchmarked
against age-related expectations. “Levels” are a thing of the
past.
Number, calculation and arithmetic are the most important
areas. Shape, space and measure are secondary.
Pupils are learning to manipulate and calculate with
fractions in more depth than ever.
All pupils are expected to build firm foundations. They are a
no longer accelerated to content expected in secondary
school.
Expectations
Pupils must learn their tables to 12 x 12 by the end of
year 4.
Maths has become more “old fashioned” in approaches to
calculations. Children must master their written methods
(more on this in a minute.)
There is an earlier and more challenging requirement for
fractions and decimals.
By Year 6, pupils must use formulae and be familiar with
algebraic equations (for example, for volume and to
calculate the area of shapes other than squares and
rectangles.)
Points to note
The use of calculators is restricted until the later
years of primary.
Roman numerals are taught from Year 3.
There is a focus on counting beyond whole
numbers, that is, decimals, fractions and
percentages.
Financial education is emphasised, with focus
on essential numeracy skills, using money and
working with percentages.
Our approach at St Mary’s
We aim to make maths fun and interactive
wherever possible.
We use our learning powers – collaboration,
determination, curiosity, creativity and
independence – to support our learning.
We ask children to be self-reflective through
peer-marking and self-evaluation.
Homework is used to support and reinforce
classroom learning.
Written vs. mental methods
A “mental method” is one which gets to the answer
without writing anything down.
A “written method” involves writing – which can include
jottings and notes.
Mental methods are nevertheless formal and taught
explicitly. For example:
- Doing 13 + 40 by counting on in tens in your head.
- Doing 116 – 99 by taking away 100 and adding 1.
- Doing 8 x 4 by doubling and doubling again.
The methods shown in this presentation will be about
written methods specifically.
Place value
Children must gain an understanding of place value alongside learning
calculation methods.
For example:
24 =
20
2 tens
+
4
= 24
4 units
To teach this we use a variety of resources such as arrow cards, dienes
blocks, mini-flips, etc.
Addition and subtraction
Drawings & visual representations
3+2=
+
=
-
=
4–3=
Addition and subtraction
Number lines
8+5=
8
9
10
11
12
13
Using knowledge of round numbers to jump on in units other than ones
18 + 7 =
+5
+2
18
20
25
Addition and subtraction
12 – 8 =
+1
Starting with the smallest
number at the start of the
numberline
8
18 – 7 =
+1
9
+1
10
+3
7
58 - 25 =
11
12
18
+ 20
30
Place the largest
number at the end
+8
10
+5
25
+1
+8
50
58
Addition and subtraction
Addition and subtraction in columns
13 + 6
TU
13
+ 6
18 – 15
TU
18
-1 5
“Recording addition and
subtraction in columns
supports place value
and prepares for formal
written methods with
larger numbers” –
National Curriculum, Y2
Fractions
In the late KS1 the children begin to add and subtract fractions.
For example:
¼ + ¼ = 2/4 = ½
3/5 – 2/5 = 1/5
Addition
Below is an example of the vertical method and crossing the tens, a ten must
be carried over to the tens column.
145 + 37 =
HTU
145
+ 37
182
1
Subtraction
HTU
358
- 134
224
H T U
3 4123 12
- 2 4 5
1 8 7
Th H T
9
1 1 1
2 0 2
- 7 5
1 2 7
U
8
1
7
Multiplication
By the beginning of KS2 the children should have confident and quick recall of the 2,
10, 3, 4 and 5 times tables.
Children should know rules for multiplying by 10 and 100.
In early KS2 we introduce the grid method for multiplication.
For example: 26 X 7 = 182
X
20
6
7
140
42
140 + 42 = 182
The idea of partitioning is used in this
method to break the numbers down
into more manageable chunks which
are recombined in the final stages of
the method.
Multiplication
The grid method is then used to assist the children when multiplying 2 and 3 digit
numbers.
For example: 25 X 132 =
X
100
30
20
2000 600
40
5
500
10
150
2
2000 + 600 + 40 = 2640
First the children will add the first row.
500 + 150 + 10 = 660
Then move on to the second.
2640 + 660 = 3300
Finally they will add the totals to reach
their final answer.
Multiplication
The grid method moves on to the written column method
H T U
2 1 4
x
6
1 2 8 4
2
Upper KS2
The written column method becomes the method for long multiplication
x
3
4
1
H T
3 2
1
9 7
1
2 5
2 2
1
U
5
3
5
0
5
Tth Th H
4
x
1 8
2
9 1
1 1
1 0 9
1
T
5
2
2
2
4
U
7
4
8
6
8
0
Division
Written bus stop method, using Does Macdonald’s Sell Burgers (Division,
Multiplication, Subtraction, Bring down)
0
3 2
0
2
2
0
7 5 r 1
2 6
2
1
1 6
0
5 3
0
3
3
0
7 0 5 r 4
5 2 9
5
5
0 2
0
2 9
Long Division
0
15 4
0
4
4
0
3 1 1 r 11
6 7 6
6
5
1 7
1 5
0 2 6
1 5
1 1
0
13 8
0
78
7
0
6 5 5 r4
5 3 9
15
8
6
7 11
6 5
0 6 9
6 5
4
Fractions
Children begin to add and subtract with fractions containing
non-common denominators:
1 + 3 = 13 =
3
4
12
1 1
12
Eventually they learn to multiply by a fraction
4
6
x
1
2
=
4
12
=
1
3
I hope this has proven useful for you, and that
you will feel more able to help your children
with their maths at home.