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Addition and Addition and SubtractionSubtraction
Calculating efficiently
and accurately
Objectives
To explore the knowledge, skills and understanding required for children to add / subtract efficiently and accurately
To explore the progression in recording and (some of) the teaching approaches used
Self-esteem
The Four RulesUnderstandinUnderstandin
gg
Mental Mental calculationcalculation
ss
Rapid Rapid recallrecall
Efficient Efficient written written
methodsmethods
Models, images & concrete materials
Stories / rhymesProblem solving and role play
Use of ICT
Progression in knowledge and understanding for + / -
• 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
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 counting
2. The one-to-one principle - understanding and ensuring that the next item in a count corresponds to the next number
3. The cardinal principle - knowing that the final number represents the size of the set
4. The abstraction principle - knowing that counting can be applied to any collection, real or imagined
5. The order irrelevance principle - knowing that the order in which the items are counted is not relevant to the total value
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
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
Counting on – jumps of 1(modelled using bead strings) 18 + 5 = 23
18 19 20 21 22 23 24
+1 +1 +1 +1 +1
47 77 80 82
(+ 2)
(+ 3)
(+ 30)
35 + 47 = 47 + 30 + 5= 77 + (3 + 2)
= 82
35 + 47 = 82
374 374
+ 248 + 248
12 622
110
500
622
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
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
Taking awayTaking away – jumps of 1(modelled using bead strings) 13 – 5 = 8
8 9 10 11 12 13
-1 -1 -1 -1 -1
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
74 48 50 54
− 2− 4
− 20
Number lines - taking taking awayaway 74 – 26 = 48
Number lines - counting on 74 – 26 = 48
0 26 30 70 74
+ 4 + 4
+ 40
3131 1414 2020 1616
2424 66 55 2525
3030 2929 1818 3636
1111 77 1313 11
14 20 21 34 39 45 50
Three 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.
Subtraction by decomposition
No breaking down needed:
563 − 241
500 + 60 + 3 − 200 + 40 + 1
300 + 20 + 2
Leading to:563
− 241322
Using red alerts:
563 − 248
500 and 60 and 3 − 200 and 40 and 8
Re-written as:
500 and 50 and 13 − 200 and 40 and 8
300 and 10 and 5
Leading to: 5 6 3 − 2 4 8
3 1 5
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