Transcript Slide 1

Mathematical Language
Words linked to +
Words linked to -
add, addition, and, count
on, plus, sum, more,
altogether, increase
take away, subtract,
subtraction, count back,
minus, less, decrease,
difference between
Words linked to x
multiply, multiplication,
multiple, double, array,
times, lots of
Words linked to =
Words linked to ÷
group, divide, division,
divided by, divisible,
factor, share, half,
halve, remainder,
quotient
equals, makes, same as
Number sentence
e.g. 2 + 4, 5 – 3, 6 x 3 or 12 ÷ 3
Partition
splitting a number up
e.g. 123 … 100 + 20 + 3
Recombine
putting a number back together
e.g. 100 + 20 + 3 … 123
Bridging
crossing over 10 or 100 etc
Exchanging
e.g. swapping a 10 for 10 ones
Place value
the value of each digit in a
number e.g. hundreds, tens and
ones (units)
÷
All children will develop efficient methods of
calculation with all four operations choosing an
appropriate method (mental, mental with jottings or
formal written method) to solve a range of different
problems.
Children develop at different rates. The onus is on
developing mathematical understanding, a feel for
number NOT just learning a mechanical method that
is prone to error in order to develop learners for
life.
The Basics
Recognise, read
and write numbers
Know what
numbers mean
and understand
place value
Did you know that if you bend
a number line around it could
make the face of a clock or
the dial on a pair of scales?
Count on and
back in steps
of the same
size
Put numbers in
order
40
8
Partition a
number and
recombine it
Addition
Know your number
bonds.
Pairs of numbers that
make 10 or 20
HEADS first!
Estimate.
Don’t move
on until you
understand.
In Years 1 and 2
Know that addition is counting on
and that it can be done in any order
Go back if
you need to.
3 7
Number Bonds
1 + 9 = 10
9 + 1 = 10
2 + 8 = 10
8 + 2 = 10
3 + 7 = 10
7 + 3 = 10
4 + 6 = 10
Add single digit numbers
• below 10
• then crossing over (bridging) 10
+3
3+5
8 + 7 = 15
8
5
8
+2
+5
10
6 + 4 = 10
5 + 5 = 10
BIGGEST number first
15
In Year 2, children add two 2-digit
numbers:
• without crossing (bridging)
the tens boundary
• the crossing over (bridging)
the tens boundary
+30
48
+2
78
+2
48
40
Partitioning up to
two 3-digit
numbers is a
stepping stone to
the column
method.
T
U
+4
48 + 36
84
80
+34
U
40 + 8
84
50
8
T
30
30 + 6
6
+
40 + 30 + 8 + 6
40 + 30 = 70
8 + 6 = 14
70 + 14 = 84
48
80 + 4
36
10
Column
Method
THINK!
Is the
answer
sensible?
4 8
+ 3 6
8 4
1
Subtraction
Know subtraction
facts for numbers
up to 10 and 20
Number Bonds
10 - 1 = 9
HEADS first!
Estimate.
Don’t move
on until you
understand.
In Years 1 and 2
Find the difference
between numbers
Go back if
you need to.
Subtract single digit numbers
• below 10
• then crossing through (bridging)
10
10 - 9 = 1
10 - 2 = 8
10 - 8 = 2
10 - 3 = 7
10 - 7 = 3
15 - 7 = 8
10 - 4 = 6
10 - 6 = 4
10 - 5 = 5
Biggest number FIRST
Children use partitioning as
a stepping stone to using the
column method.
In Year 2, children subtract two
2-digit numbers
• without crossing (bridging) the
tens boundary
• then crossing through
(bridging) the tens boundary
43 - 27 =16
to subtract 7 units
we need to exchange
a ten for ten units
43 – 23
-3
- 10
20
23
- 10
33
T
43
U
13
30
43 - 27 =16
4 3
20
43 – 20 = 2 3
23 – 7 = 1 6
7
- 2
7
Column Method
is also used
without and with
exchanging.
40
and
3
- 20
and
7
and
6
10
3
4 13
- 2 7
1 6
Multiplication
HEADS first!
Estimate.
Don’t move
on until you
understand.
Go back if
you need to.
2 x 5 =10
2 + 2 + 2 + 2 =
8
4 x 2 = 8
Do you know your
multiplication facts
to 12 x 12?
Learn them they’re
really useful!
x5
4 x 5 =20
6 x 5 =30
3 x 5 =15
10 x 5 = 50
8 x 5 =40
5 x 5 =25
2 multiplied by 4
Know that
multiplication is
repeated
addition
4 lots of 2
Set out multiplication as an
array
Use place value apparatus to
support multiplication of
U x TU
Compact method for
TU x U
10
3
23 x 3
4 x 13
4
Use place value apparatus to
support multiplication of U x TU
alongside the grid method
10
3
40
12
10
3
4 x 13
4
x
4
40
12
40 + 12 = 52
Column method
for TU x TU
56
×
27
1120
392
1512
1
(56 × 20)
(56 × 7)
÷
Division
Go back if
you need to.
Do you know your
division facts?
Learn them they’re
really useful!
10
20
÷
÷5
50
÷
÷ 5
5 = 2
30
÷
6
15
÷
5 = 10
40
÷5
÷
5 = 5
Group objects to divide them and
show this on a number line
5 =
= 4
25
Share things out equally
then begin to understand
remainders
HEADS first!
Estimate.
Don’t move
on until you
understand.
18 divided into groups of 3
5 = 3
= 8
18  3 = 6
0
3
6
9
18  3 = 6
12
15
18
In Year 3
7
2 4
4
916
The ‘bus stop’
method using
known facts.
Year 6 expectation:
2
In Year 4
This is then extended to dividing a 2-digit number by
a 1-digit number with remainders (using known facts).
Children will use long division
for dividing a 3-digit number by
a 2-digit number, extending to
larger numbers and remainders
expressed in different forms
e.g. fractions.
558 ÷ 24 = 23 ¼ or 23.25
33 ÷ 4 = 8 r 1
558 ÷ 24
Children will also divide a 1-digit or 2-digit whole
number and those involving decimals by 10 and 100
(supported by apparatus and place value indicators).
26 ÷ 10 = 2.6
2 3 r6
Long division,
Using
repeated
subtraction
24
5 6 0
- 4 8 0
7 8
-
7 2
6