Maths – The strategies we use in school Calculation.
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Transcript of Maths – The strategies we use in school Calculation.
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Maths – The strategies we use in school
Calculation
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The 4 strands of Maths
• Number
• Shape, Space and Measures
• Data Handling
• Using and Applying Maths
Using and Applying Maths occurs in all 3 other strands, as well as in other lessons, such as Science.
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Number
We are going to focus solely number.
• The four operations (+, -, x and ÷)
We are going to talk you through methods we teach children to use to add, subtract, multiply and divide and how build on each stage.
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The Four Operations
• The four operations in calculations are grouped into
Adding and Multiplying – where the answer gets bigger
Subtracting and dividing – where the answer gets smaller
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Early YearsCounting
• Count reliably to 20 • Count backwards from 10
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Number Recognition
• Recognise numbers to 20• Order numbers to 20
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Calculation• One more and one less than a given number• Add and subtract two single digit numbers practically
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Number Lines
We use number lines in all four operations.
We start with numbered lines like this one –
0 1 2 3 4 5 6 7 8 9 10
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Adding
We then move on to using number lines and counting up in ones.
14 + 5 = 19
+1 +1 +1 +1 +1
14 19
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Partitioning
Next we learn to partition – splitting the number into tens and units – to add.
What is 72 + 14?T U70 210 4 70+10= 80
2+4= 6 80+6=86
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Adding by Partitioning
Now we can add by partitioning –
86 + 57 =
+50 +4 +3
86 136 140 143
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Adding by Partitioning
Or by rounding then adjusting, taking it to the nearest 10 and then subtracting
754 + 96 (rounding and adjusting)
+100
-4 754 850 854
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Column Addition
Finally, we move on to adding in columns, using place value.
HTU ThHTU 597 7648+ 475 and + 1486 12 160 9134 900 1 1 1
1072
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MultiplyingNow we use the number line for repeated
addition.4 x 5 is the same as 5 + 5 + 5 + 5 = 20I have four 5p coins, how much is that?
+5 +5 +5 +5 0 5p 10p 15p 20p
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The Grid Method
We can partition to multiply using a grid, like this, this looks more complicated than it actually is –
72 x 38 = 70 2
30 2100 60
8 560 16
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Column Method for multiplication
4346
x 8
48
320
2400
32000
34768
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Subtracting
We begin by ‘taking away’, ‘counting back’ and seeing ‘how many left.’
We have 6 teddies in the shop. We sold 2. How many teddies are left?
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Subtracting (number lines)
We can use a number line to count back.
22 – 7 =
-5 -2
15 20 22
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Subtracting (number lines)
In Key Stage 2, we count UP the number line to find the difference.
What is the difference between 34 and 72?
+30 +8
34 64 72
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Subtracting with ‘exchanging’
5 13 1
6 4 6 7
- 2 6 8 4
3 7 8 3
Th H T U
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Dividing
Division starts with practical sharing of objects again -
If I share my 9 sweets between 3 people, how many do they each get?
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Division with number lines
Number lines are also used to count up in division.
A baker bakes 24 buns. She puts 6 in every box. How many boxes can she fill?
x1 x2 x3 x4
0 6 12 18 24
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Division with remainders
Finally, we can jump in groups and record remainders on the number line.
What is 42 divided by 4? 10 groups (Remainders)
x10 +1 +1
0 40 41 42
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SATs KS1• Typical questions:
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Key Stage 2 SATs• Key Stage 2 SATS are held in May.
• These are statutory, externally marked tests.
• The children sit three papers: Paper A - non-calculator paper Paper B - calculator paper Mental arithmetic paper
• The paper assesses children working between level 3 and level 5. Children will receive a test mark and a teacher assessment.
A minority of children will be entered for the level 6 test.
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Key Stage 2 SATsSample Questions:
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Key Stage 2 SATsSample Questions:
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Extra support for NumeracyExtra support for Numeracy
• EYS and KS1 – Numicon
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Key Stage 2
• Booster programme• Linked to numeracy lessons• Targeted at children who, with support, will reach level 4
• Sessions run three times a week for 30 minutes
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Year 4
Mental/Oral Starter Activities
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Cracking Times Tables•Is a scheme designed to support high standards in mathematics•Is a consistent approach to learning and testing tables across the school•Is based on a series of levels that the children work through at their own pace•Is motivating to children. They receive certificates for each level achieved