addition and subtraction calculating efficiently and accurately [ks1]
TRANSCRIPT
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Addition and Subtraction
Calculating efficiently and accurately
[KS1]
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Objectives
To explore the knowledge, skills and understanding required for children to add, subtract, multiply and divide efficiently and accurately
To explore the progression in recording and (some of) the teaching approaches used
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The Four RulesUnderstanding Mental
calculations
Rapid recall
Efficient written methods
Models, images & concrete materials
Stories / rhymesProblem solving and role play
Use of ICT
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Progression for addition and subtraction
• Counting
• One more / less
• Addition as combining two groups, then counting on
• Subtraction as take away or difference (eg how many more is … than …?)
• Ten more/less
• Recall of addition/subtraction facts to 10, 20 and beyond
• Understand that subtraction and addition are inverses
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Counting and estimation
There are 5 principles of counting:1. The stable order principle - understanding that the number
names must be used in that particular order when counting2. The one-to-one principle - understanding and ensuring that
the next item in a count corresponds to the next number3. The cardinal principle - knowing that the final number
represents the size of the set4. The abstraction principle - knowing that counting can be
applied to any collection, real or imagined5. The order irrelevance principle - knowing that the order in
which the items are counted is not relevant to the total value
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94 65 48 30 71
28 36 56 97 32
12 24 51 82 19
77 63 44 53 28
60 96 75 17 43
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2 + 3 =I buy 2 cakes and my friend buys 3 cakes.How many cakes did we buy altogether?
(Children could draw a picture to help them work out the answer)
8 + 5 = 8 people are on the bus. 5 more get on at the next stop. How many people are on the bus now?
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Addition
pictures
symbols
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Counting on – jumps of 1(modelled using bead strings) 18 + 5 = 23
18 19 20 21 22 23 24
+1 +1 +1 +1 +1
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47 77 80 82
(+ 2)(+ 3)(+ 30)
35 + 47 = 47 + 30 + 5= 77 + (3 + 2)
= 82
35 + 47 = 82
No number line
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374 + 248
Addition by partitioning
70 + 40 = 110 4 + 8 = 12
300 + 200 = 500
622
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1
Column addition
Extend to:
1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km
1
+ 248374
622
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31 14 20 1624 6 5 2530 29 18 3611 7 13 1
14 20 21 34 39 45 50Three in a row
Choose two numbers from the row of numbers above the grid.
Find the difference between these numbers.
If the answer is on the grid, cover that number with a counter.
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5 – 2 =I have five cakes. I eat two of them. How many do I have left?
A teddy bear costs £5 and a doll costs £2. How much more does the bear cost?
(Take away)
(Find the difference)
13 – 5 =Mum baked 13 biscuits. I ate 5. How many were left?
Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have?
Drawing a picture helps children to visualise the problem
Using dots or tally marks is quicker than drawing a detailed picture
(Take away)
(Find the difference)
Subtraction
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Taking away – jumps of 1(modelled using bead strings) 13 – 5 = 8
8 9 10 11 12 13
-1 -1 -1 -1 -1
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Counting on – jumps of 1(modelled using bead strings) 11 – 8 = 3
0 1 2 3 4 5 6 7 8 9 10 11
+1 +1 +1
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74 48 50 54
− 2− 4
− 20
Number lines - taking away
74 – 26 = 48
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Number lines - counting on
74 – 26 = 48
0 26 30 70 74
+ 4 + 4
+ 40
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Subtraction by partitioning
754 - 186
754 – 100 = 654654 – 80 = 574574 – 6 = 568
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Subtraction by decomposition