Transcript KS2 Parent Workshop

Key Stage 2 Maths
What and how do we teach it?
Aims of the meeting tonight



To help you to understand more
of what we do in maths at Key
Stage 2
To enable you to support your
child more confidently in maths
To give you more information
about what we teach and how
we teach maths at Key Stage 2
By the end of Key stage 2 we
hope that children will….









Develop a reliable, accurate method to calculate in
all 4 operations
Be able to record their working in a compact way
Apply basic maths skills to calculations
Apply the maths they know to new situations
Make links between different areas of maths
Develop their own strategies for problem solving,
choosing the maths they need to use and how they
will record their working.
Key stage 2 maths moves from using concrete
apparatus to more abstract working and formal
recording
To do this successfully, children need a firm grasp
of basic mental maths skills and the concept of the
number system.
The key to a good understanding of written methods
of calculations is based on mental strategies.
Basic skills in maths











Use of the number line and 100 square
Counting – forwards, backwards, different
steps, decimals
Complements
Crossing over ‘boundaries’
Multiplication facts and linked division facts
Use of money, finding change
Time
Doubling halving
Multiplying and dividing by 10, 100, 1000
Use of calculator
Measures – conversion and practical
reading of scales
Using number lines
“The number line is a powerful
and sophisticated linear model of
the number system. It embodies
all learning styles; visual, auditory
and kinaesthetic. It evolves into
an internalised mental
representation which can be used
when children are able to
dispense with the actual line.”
Numeracy Team 2002

The four kinds of track or line
Number tracks
1
2
3
4
5
6
11
12
7
8
9
10
Numbered lines
5
6
7
8
9
10
13
Partly numbered line
5
10
The empty number line
15
14
15
16
Number lines used in Tests at KS2
Time lines
I started walking at 08:45 and finished at
12:25. How long did my walk take me?
Written methods for the 4
operations


The key to a good understanding of written
methods of calculations is based on mental
strategies. Each of the four operations
builds on mental skills which provide the
foundation for jottings and informal written
methods of recording. These skills lead on
to more formal written methods.
The transition between stages depends on
a child’s understanding of the method. Not
all children will be ready to move on to
the next stage at the same time and
should not be hurried until they have a
secure understanding of the method.
Subtraction
43 – 26
This calculation can be modelled two
ways.
How can we model subtraction?
Both understandings of subtraction (take away
and difference) can
be modelled on number lines.
43 – 26 = 17
-3
+4
26
33
20 23
17
30
43
-3
-10
+ 10
-10
+3
40
43
Number lines with more complex calculations
624 – 381 =
+19
+200
400
381
+24
600
624
6.24 – 3.81 =
+0.19
3.81
4.00
+2.00
+0.24
6.00
6.24
Complementary addition vertically
Complementary addition can also be represented
vertically.
624 – 381
43 - 26
4 (30)
10 (40)
3 (43)
17
19 (400)
200 (600)
24 (624)
243
Multiplication
Arrays
Arrays are important because they provide
a good visual image of the calculation that
links closely to the concept of repeated
addition.
4x2=8
2x4=8
Other good images – number lines
2
0
+
2
2
+
4
2
+
6
2
+
8
2
10
This image can be expressed as 2 multiplied by 5,
two five times, 5 groups of 2, 5 lots of 2 and 5
hops of 2 on a number line.
 
5
0
+
5
5
10
This image can be expressed as 5 multiplied by 2,
five two times, 2 groups of 5, 2 lots of 5 and 2 hops of 5 on
a number line. It is also double 5 (5 x 2).
Partitioning
7 x 14 = (7 x 10) + (7 x 4) = 70 + 28 = 98
0
+70
+28
7x10
7x4
70
98
Partitioning - continued
18 x 8
10
8



8
80
64





18 x 8 =144
8
10
80
8
64
Grid method of multiplication
38 x 27
20
30
8
600
160
760
7
210
810
56
+
216 =
+ 266
1026
Skills needed
Skills needed to be able to carry out the grid
method of multiplication when multiplying 2 twodigit numbers.
• partition numbers into tens and units/ones
• recall multiplication facts
• multiply by ten
• multiply by multiples of ten
• add together two and three-digit numbers
• decide whether the answer is sensible
Multiplying by 10
It is important that multiplying by 10 is not thought of as a
case of ‘adding zeros’. It in an inappropriate expression
because adding zero actually leaves a number unchanged
and the ‘add a zero rule’ fails when, for example, 0.2 is
multiplied by 10 (‘adding a zero’ results in 0.20).
Children need to understand that when you multiply by 10
the digits move one place to the left, leaving an empty
space which is filled by zero (a place holder).
Multiplication facts
Children will struggle with multiplication if they can’t recall
multiplication facts.
Knowing a multiplication table is much more than being able
to recite it in order. It also means children should be able to
respond quickly to oral or written questions phrased in a
variety of ways, e.g.
• What are six fives?
• What is 3 times five?
• 5 multiplied by 3 is…
• How many fives in 35?
•What would I multiply by five to get 30?
Division
In Year 3 and 4 children need to know that:
• 16  2 does not equal 2  16
• division reverses multiplication (the inverse)
– this allows
them to solve division calculations by using
multiplication strategies (18  3 by counting
the hops
of 3 to 18)
•there will be remainders for some division
calculations (to be expressed as wholenumber remainders).
• relate division and fractions
• use a written method for division
(chunking).
Teaching chunking - number line
72 ÷ 5 =
Grouping - How many 5’s are there in 72?
Adding groups of 5
5 x 10 or
5 x 4 or
10 groups of 5
0
5
10
15
20
25
30
4 groups of 5
35
40
45
50
55
60
65
70 72
Teaching chunking - vertical
5x1 =5
5 x 2 = 10
5 x 5 = 25
5 x 10 = 50
72  5 =
72
50
(5 x 10)
22
20
2
Answer: 14 remainder 2
(5 x 4)
Teaching chunking - larger numbers
256  7 =
7x1=7
7 x 2 = 14
7 x 5 = 35
256
210
46
42
4
(7 x 30)
(7 x 6)
7 x 10 = 70
Answer: 36 remainder 4
Real Life Problems
To make a box pieces of wood 135mm long
have to be cut from a 2.5m length. How many
lengths of wood can be cut?
Train fares cost £14.50. I have £52. How
many people can I take on the journey?
Teach do we teach maths in
school?





Abacus Maths scheme
Real life problems
Maths in context – links made
with topics
Open ended investigations
Maths during CIL
How can you help at home?




Use information on our school
website for ideas for support.
Refer to the calculation policy on the
website
Support children with their homework
– ask them to explain what they are
doing and how
Reinforce the basic skills mentioned
earlier – these will often be reflected
in the targets set by teachers
Any Questions?

Please spend some time looking
at the resources around the hall
– and have a go at some of the
problems!