Transcript Maths_parents_evening KS2 updated 2015

How we teach Maths in school
Parents’ Information Evening
2014
Aims

To discuss a range of mental and written
calculation methods that your child will be
taught while they progress through St.
Leonard’s

To show you some of the types of recording
that your child will be introduced to in order
to support their written calculation methods.

To show you some possible activities and
resources that you may be able to make/use
to support your child/children at home.
Year 3
Year 4
• Number line
• Number square
• Counters
• Online games
• Place value cards
• Unifix sticks
Resources
Place Value
• We use place value cards in combination with unifix cubes
and 100 squares to recognize values of numbers.
i.e. make the number 245
Step 1: separate the number into its value
2 hundreds, 4 tens and 5 units
Step 2: make that number with either cubes or a value card.
Mental calculations
1)
2)
3)
4)
5)
6)
7)
8)
9)
1 more / 1 less
3 + 5 number bonds
10 more/ 10 less
6 + 6 doubles
6 + 7 near doubles
26 + 9 add 10 subtract 1
26 + 57 add to the nearest ten and adjust
48 + 25 partitioning
counting on/back
Written methods: 7 + 4
+1
7
+1
8
+1
9
+1
10
11
This relates to putting a number
into your head and count on
Written methods: 32 + 23
+ 10
32
+ 10
42
+3
52
55
By counting on or back in tens the
hundred square is used
The temperature is -80C. It increases by 150. What is the temperature now?
T.U.B Method
•
•
•
•
•
25 + 33= 58
Step 1: partition numbers ( tens 20 + 30) (units 5+3)
Step 2: add up the Tens (T) ( 20 + 30 = 50)
Step 3: add up the Units (U) ( 5+ 3 = 8)
Step 4: add both
(B) (50 + 8= 58)
• 55 + 26 ( T 50 + 20= 70) (U 5+6= 11)
• 70 + 11 = ( T70 +10= 80 ) (U 0+1=1)
• 80+1=81
Now try these!
73+24=
87+21=
44+37=
Subtraction
Mental methods: 35 - 22
a) as ‘take away’
− 10
−1
−1
13
− 10
14
15
25
35
b) as ‘difference’
+8
22
+5
30
35
Using complements to 10, 100
Subtraction
towards formal written methods
No ‘breaking down’ needed:
95 − 41
−
90
40
50
Leading to:
and
and
and
95
− 41
54
5
1
4
‘Exchange’
‘83 − 47’
80 and
− 40 and
3
7
Re-written as:
−
70 and 13
40 and
7
30 and
6
Now try these!
63-24=
87-23=
54-31=
Vertical calculation for subtraction can create real difficulties for both children and teachers.
It’s easy to think that teaching children to remember a process, perhaps developed through
the use of place value resources, will work. Some children may be able to remember this,
but, even if they do, learning without understanding is never a basis for future
development.
The following method, which can be used if you decide you have to teach a vertical
method,
is still mathematically ‘transparent’. There are no tricks, there is no need to swap 10 ones
for a ten or 10 tens for a hundred and it’s possible to keep track of the number you are
subtracting from all the way through. Having said that, don’t move to this method unless
children have a thorough grasp of subtraction with decimals on a number line and a real
understanding of place value. For the first time it’s possible, and necessary, to use
partitioning for subtraction.
Multiplication as
repeated addition
2+2+2+2=8
4 pairs of socks is 8 socks
4 groups of 2 is 8
(4 × 2 = 8)
Or show as 4 hops of 2 on a number line
(2 × 4 = 8)
2 multiplied by 4 is 8
0
1
2
3
4
5
6
7
8
Multiplication as
describing an array
5 x 7 = 35
7 x 5 = 35
Multiplying numbers by 10 and 100
If you can multiply by 1, then you can multiply by 10, 100 etc.
When multiplying by 10 we move the digits one place to the left
and add a zero if necessary
hundreds
tens
units
hundreds
tens
1 3
× 10
hundreds
tens
units
7
× 100
units
1 3 0
hundreds
tens
units
7 0 0
The grid method
23 × 8 =184
×
20
8
160
3
24
We had to know that 8 × 20 is the same as 8 × 2 × 10.
Add the numbers in the boxes together:
160 + 24 =184
We can extend this grid method to larger numbers.
From informal to formal
methods
23
x 8
(20 x 8) 160
( 3 x 8)
24
184
23
x 8
( 3 x 8)
24
(20 x 8) 160
184
23
x 8
184
2
Larger numbers can also be developed in this way.
These will eventually be extended to numbers with 2
decimal places.
Example 7.24 m × 14
(eg “12 ÷ 4”)
Division
EQUAL SHARES:
“12 sweets between 4 children”
GROUPING:
“12 sweets into groups of 4”
Written methods: 12÷4
-4
0
1
2
-4
3
4
5
6
-4
7
8
9
10
11
12
This relates to grouping
(chunking) or how many 4’s go into 12?
145 ÷ 6 = ?
Using a number line to divide
(with remainders)
60
(10 × 6)
24 (4 × 6 )
25
1
145 ÷ 6 = 24 r 1
85
145
120 (20 × 6 )
24 (4 × 6 )
1
60
(10 × 6)
25
145
Using a number line to divide
(with remainders)
The progression in written calculations

Establish mental methods, based on a good understanding of
place value in numbers.

Use number lines, and grid methods for multiplication.

Show the children how to set out written calculations
vertically, initially using expanded layouts.

Gradually refine the written method into a more compact
standard method.

Extend to larger numbers and decimals.
Online games
Children love games to engage their learning.