Transcript Maths Information Evening Presentation

Calculation Policy
Parent’s Evening
Wednesday 22nd January 2014
7pm
Order of Evening
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Principles of Numicon
Sequence of teaching addition
Sequence of teaching subtraction
Sequence of teaching multiplication
Sequence of teaching division
Time for questions and discussion
Numicon Kits
Firm Foundations (Reception)
Kit 1 (End of Reception, start of Year 1)
Kit 2 (Year 1 and Start of Year 2)
Kit 3 (End of Year 2 and Year 3)
Early Stages
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Counting objects
Counting forwards and backwards
Counting on from a given number
Number games
Counting stories
Counting songs
Real life role play
Writing numerals
• Not formally asked to write numerals until
they can order images of number.
• Necessary hand control needed.
• Modelling of writing numerals daily.
• Making numerals practically.
• Making their own number lines.
Beginning to record
Introduced when children can:
• Describe verbally what they have made with
Numicon apparatus.
• Use signs practically with bodies.
• Find numerals and words using cards.
• Match signs and number sentences to what
they are describing.
Informal Jottings
• Need to move on to bigger numbers and so it
becomes harder to calculate mentally.
• Informal jottings become part of mental
strategies.
• May begin independently then should be
explained to avoid misconceptions.
• When ready, move onto progression of
written calculations.
Addition
Stage 1
Partitioning and recombining:
25 + 31
20 +30 = 50 (tens)
5 + 1 = 6 (units)
50 + 6 = 56 (recombining)
Introduce the blank number line:
25 +31
+10
+ 10
+ 10
+1
25
35
45
55
56
Stage 2
Continue blank number lines, adding whole
numbers:
35 +52
+50
35
+2
85
87
Move onto larger numbers:
121 +243
+200
121
+40
321
+3
361
364
Begin to use the expanded written method
using a horizontal layout:
67 + 24
60 + 7
20 + 4
80 + 11 = 91
Stage 3
Extending to vertical layout
• Once children understand the place value of the
numbers through using the expanded method they
should begin to work vertically, and with larger
numbers. For example:
264 + 48
264
+ 48
12
100
200
312
 total of the units
total of the tens
total of the hundreds
•When working with this stage, estimation
should always be encouraged first.
•This layout should be used for adding amounts
of money and decimals.
Stage 4
Progression from the vertical layout to the
compact written method
• Continued use of estimation before
calculating.
• Carrying should now be shown below the line.
For example:
783 + 135
783
+ 135
918
1
This method should continue to be used for larger
numbers, where there is more than one need to carry a
number and when adding decimals, including amounts
of money, weight and length.
If the children show any misconceptions at this stage
then they should refer back to stage 3.
Subtraction
Stage 1
Begin to understand the use of an empty
number line to count back:
32-22
-1
-1
-10 -10
12
13
14
24
34
Stage 2
• Counting on using multiples of 10 on the blank
number line:
67-22
+10 +10 +10 +10
+5
22
32
42
52
62
67
Stage 3
Move on to larger numbers using the empty
number lines; introduce the concept of the
unknown number.
• Counting on or back using partitioning:
• 324-113
-3
211
-10
214
-100
224
324
Introduce the concept of the unknown number:
62-
= 27
Stage 4
• Expand written methods showing vertical
layout with calculations where no exchanging
needs to occur.
67-25
60 7
-20 5
40 2
• Expanded decomposition
Extend to larger numbers using the same
method
• When exchanging, it is important to show the
children what has actually been exchanged
each time. When the children are aware that
tens or hundreds are brought across, they can
cross numbers out and write the adjusted
amount in each column, to make the method
more efficient:
Stage 5
• Compact written methods involving
decomposition
• Move on to borrowing in a compact method
where exchanged numbers are written above
the calculation.
• Ensure calculations are worked on where 0
acts as a place holder to teach how to
exchange in this situation.
• Extend written methods for subtraction to
include decimal numbers with up to 2 decimal
places and larger numbers up to 10,000.
• Children should now be able to choose the
most efficient and appropriate method for
each calculation.
Multiplication
Stage 1
Draw pictures to show equal sets – grouping
pictures:
3 x 2 = 3 groups of 2
Stage 2
• Repeated addition on an empty number line:
• 3 x 5 = 3 jumps of 5
+5
+5
+5
0
5
10
15
Stage 3
• Multiplication as an array:
3 x 4 = 3 rows of 4
Stage 4
• Use knowledge of partitioning to multiply:
32 x 3
32 x 3 = (30 x 3) + (2 x 3)
= 90 + 6
=96
Stage 5
Develop the extended written method of the
grid method for tens and units.
• Partition 2 digit numbers into tens and units and
multiply across the grid.
37 x 4
X 30 7
4 120 28
• When the concept of the grid method is
understood, move on to multiply 2 digit
numbers by 2 digit numbers.
37 x 23
X
20
3
30 7
600 140
90 21
• Continue the use of this method to multiply 3
digit numbers and decimals.
• Continue to develop the use of estimation
throughout the use of multiplication
calculations.
Stage 6
Move on to written vertical methods
• All vertical methods should be taught
alongside the grid method to ensure
understanding. For example:
38
X 7
210 (30 x 7 = 210)
56 (8 x 7 = 56)
266
X 30 8
7 210 56 = 266
• Extend the use of vertical methods for larger
calculations.
Stage 7
• Extend written methods for multiplication,
encouraging estimation first.
• Continue to use the same methods as in stage
6, ensuring the grid method is used alongside
vertical methods.
• Begin to develop short multiplication:
625 x 6
625
X
6
3750
13
• When appropriate, use the same method
moving on to numbers with one decimal place
and then extend to two decimal places.
Division
Stage 1
• Draw pictures to show sharing:
9 ÷ 3 = 9 shared between 3
Stage 2
• Repeated subtraction on a number line:
6÷2
-2
0
-2
2
-2
4
6
Stage 3
• Repeated subtraction as chunking.
• Subtract chunks of the larger number, such as
multiples of 10. 148 ÷ 4 =
148
-40
108
-40
68
-40
28
-28
0
(10 x 4)
(10 x 4)
(10 x 4)
(7 x 4)
148 ÷ 4 = 10 + 10 + 10 + 7 = 37
Stage 4
• Extend written method, encouraging
estimation first.
• Move on to using the bus stop method,
recording as long division first. For example:
196 ÷ 6
32 remainder 4
6)196
-60 (10 x 6)
136
-60 (10 x 6)
76
-60 (10 x 6)
16
-12 ( 2 x 6)
4
• This then contracts to the more compact form
of repeated subtraction.
196 ÷6
32 remainder 4
6)196
-180 (30 x 6)
16
-12 ( 2 x 6)
4
Stage 5
• Extend written methods with larger numbers
and decimals.
• When children have fully understood the
concept of the bus stop method for dividing
by one digit, extend to divide by 2 and 3 digits.
Then move on to dividing decimals using the
same method.