Download Maths Workshop

Maths Workshop
Welcome and thank you for coming
Aims of the Workshop
To
To
raise standards in maths by working closely with parents.
provide parents with a clear outline of the key
features of maths teaching at St Peter’s School.
To outline the changes to the national curriculum for
mathematics.
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The government have given us a new
curriculum and made quite a lot of
significant changes for the teaching of
mathematics.
Increased the difficulty
More demanding of the children
Key changes are –
Mathematics – curriculum 2014
What’s gone ?
Data handling , describing patterns,
describing how to solve problems
 What’s new?
Counting and writing numerals to 100
Write numbers in words up to 20
Number bonds to 20 secure recall
Use vocabulary – equal to, more than, less
than, fewer etc
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Y1
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What’s gone ?
rounding to nearest 10, Halving and doubling,
Sorting
What’s new?
Solving problems with subtraction, finding fractions of
quantities and measures
Adding 2 digit numbers mentally,
adding 3 1 digit numbers,
understanding commutativity in addition and
subtraction,
describing properties of shapes,
measuring temperature,
telling the time to nearest 5 minutes,
using less than, greater than and equals signs and
symbols,
recognise £ and p.
Y2
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Our curriculum planning for maths has
changed
Cyclic curriculum still in place
Still want maths to be fun, focussed on
learning
Hard work this year but benefits later on
Abacus scheme
Assessment
What do these changes mean?
So how do children learn in
maths?
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Counting of objects and mental counting.
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Early stages of calculation with learning of addition and subtraction
number facts, with recording.
5+8=
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or
13 =
+5
Work with structured number lines
0 1 2 3 4 5 6 7 8 9 10
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Work with larger numbers, unstructured
number lines and informal jottings.
e.g. 47 + 26
+20
+3
73
47
50
+3
70
73
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Informal written methods, first with whole numbers and decimals.
Remember
to partition
76 + 47
=
76 + 40 +7 =
116 + 7
= 123
I must remember
to add the least
significant digit
first
(8+3)
(60+90)
(300+400)
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Formal written methods.
With any calculation, teach children to consider first whether a mental
method is appropriate and remembering to estimate first.
What does a maths lesson
look like?
Oh look, these
numbers make
a lovely
pattern.
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Mental recall of addition and subtraction facts
10 – 6 = 4
17 -  = 11
20 - 17 = 3
10 -  = 2
Find a small difference by counting up
82 – 79 = 3
Counting on or back in repeated steps of 1, 10, 100, 1000
86 - 52 = 34 (by counting back in tens and then in ones)
460 - 300 = 160 (by counting back in hundreds)
Subtract the nearest multiple of 10, 100 and 1000 and adjust
24 - 19 = 24 - 20 + 1 = 5
458 - 71 = 458 - 70 - 1 = 387
Use the relationship between addition and subtraction
36 + 19 = 55
19 + 36 = 55
55 – 19 = 36
55 – 36 = 19
MANY MENTAL CALCULATION STRATEGIES WILL CONTINUE TO BE USED.
THEY ARE NOT REPLACED BY WRITTEN METHODS.
Subtraction- mental methods
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Counting back along number lines
Drawing and removing – what’s left?
Using empty number lines
Jumping back in larger steps
Counting on/finding the difference
Partitioning without bridging first then
decomposition…
Towards written methods in
subtraction…
Decomposition expanded
method…
Decomposition
Addition
1. Practical addition of real objects.
2. Mental addition of number facts.
3. Use of a structured number line to add.
0 1 2 3 4 5 6 7 8 9 10
4. Partitioning to add.
100
203
+
=
5. Use of an unstructured number line.
Remember
37 + 48=
+
+10
+10
to put the
largest
number first
48
Note: the units jump can be
broken down to make it
easier to count on through a
multiple of 10
58
+10
68
+2
78
+5
80
85
Addition cont ………
6. Beginning to record vertically.
Adding the least significant digit first.
126 +57=
Estimate: 126 +57 is nearly 130 + 60 so estimate answer
should be near 190.
126
+ 57
13 (6+7)
70 (20+50)
100 (100+0)
183
Addition cont ………
7. Standard vertical method involving carrying.
When children are confident working with larger numbers using the
previous strategies, they will be introduced to ‘carrying’ digits.
Usually this is during Year 5 and 6. 2856+1095
Estimate: 2900+1100 =4000 Answer should be less as I have
rounded up.
2856
+1095
3951
11
Addition cont ………
8. Adding decimals
This is first introduced through money and measures. As
with all vertical methods, children should know how to line
up place value columns and the decimal point under each
other.
£5.75 + £3.18 =
Estimate: £6.00 + £3.00 = £9.00
£5.75
+ £3.18
0. 13 (0.05+0.08)
0. 80 (0.70+0.10)
8. 00 (5.00+3.00)
£8.93
£5.75
+£3.18
£8.93
1
• These are a selection of mental calculation
strategies:
• Doubling and halving
• Using multiplication facts
• Using and applying division facts
• Use closely related facts already known
• Multiplying by 10 or 100
• Partitioning
• MANY MENTAL CALCULATION STRATEGIES
WILL CONTINUE TO BE USED. THEY ARE
NOT REPLACED BY WRITTEN METHODS.
Multiplication – mental strategies
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Repeated addition
Commutivity
Arrays
x
10
4
(6 x 10) + (6 x 4)
6
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60
24
60
+
24
84
Leading to grid method…
Multiplication towards written
methods…
Grid method
Stage 1
Children are encouraged to develop a mental
image of the number system in their heads to
use for calculation. They should experience
practical calculation opportunities involving
equal groups and equal sharing.
 They may develop ways of recording
calculations using pictures.
 A child’s jotting showing halving six spots
between two sides of a ladybird.
 They could show how they shared the apples
at snack time between two groups.
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Towards division…
Stage 2
 Children explore practical contexts where they
share equally and group equally. 6 ÷ 2 = ?
 Equal sharing (6 shared equally between 2)
 6 football stickers are shared equally between 2
people, how many do they each get? Children
may solve this by using a ‘one for you, one for
me’ strategy until all of the stickers have been
given out.
 Equal grouping (How many groups of 2 are
there in 6?)
 There are 6 football stickers, how many people
can have 2 stickers each?
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Developing division…
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Children are also taught …
Doubling and halving
Knowing that halving is dividing by 2
Deriving and recalling division facts
Tables should be taught from Y2
onwards, either as part of the mental
oral starter or other times as
appropriate within the day.
Mental strategies for division
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Stage 3
Children continue to use practical equipment to
represent division calculations as grouping (repeated
subtraction) and use jottings to support their
calculation. Children are taught that division is the
inverse of multiplication and that tables facts can be
used to calculate..
12 ÷ 3 = ? Children begin to read this calculation
as,
‘How many groups of 3 are there in 12?’
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At this stage, children will also be introduced to
division calculations that result in remainders.
13 ÷ 4 = 3 remainder 1
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Division next steps
Children will develop their use of repeated subtraction to be able to subtract multiples of
the divisor. Initially, these should be multiples of 10s, 5s, 2s and 1s – numbers with which
the children are more familiar.
72 ÷ 5
-2
0
-5
2
-5
7
-5
12
17
-5
-5
22
-5
-5
-5
27 32 37
-5
42
-5
47
52
-5
-5
57 62
-5
67
-5
72
Moving onto:
-50
-5
-5
-5
-5
r2
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1
1
1
1
10
02
7
12
17
22
72
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Stage 4
43 ÷ 8
43 ÷ 8 = 5 remainder 3
At this stage, children also learn if the remainder
should be rounded up or down e.g. 62 ÷ 8 = 7
remainder 6
I have 62p. Sweets are 8p each. How many can I
buy?
Answer: 7 (the remaining 6p is not enough for
another sweet)
Apples are packed into boxes of 8. There are 62
apples. How many boxes do I need?
Answer: 8 (the remaining 6 apples still need to be
placed into a box)
Division the remainder
Stage 5
 The previous method of
repeated subtraction on
a number line is
continued, but using a
vertical number line
alongside practical
equipment.
 The repeated
subtraction is made
more efficient by
subtracting ‘chunks’ of
the divisor.
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Stage 6
This is the final stage, in which children use the ‘chunking’ method.
Then onto the vertical method:
Short division TU ÷ U
72 ÷ 3
3 ) 72
- 30
42
- 30
12
- 6
6
- 6
0
Answer :
24
10x
10x
2x
2x