maths – the strategies we use in school calculation
TRANSCRIPT
Maths – The strategies we use in school
Calculation
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.
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.
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
Early YearsCounting
• Count reliably to 20 • Count backwards from 10
Number Recognition
• Recognise numbers to 20• Order numbers to 20
Calculation• One more and one less than a given number• Add and subtract two single digit numbers practically
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
Adding
We then move on to using number lines and counting up in ones.
14 + 5 = 19
+1 +1 +1 +1 +1
14 19
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
Adding by Partitioning
Now we can add by partitioning –
86 + 57 =
+50 +4 +3
86 136 140 143
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
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
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
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
Column Method for multiplication
4346
x 8
48
320
2400
32000
34768
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?
Subtracting (number lines)
We can use a number line to count back.
22 – 7 =
-5 -2
15 20 22
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
Subtracting with ‘exchanging’
5 13 1
6 4 6 7
- 2 6 8 4
3 7 8 3
Th H T U
Dividing
Division starts with practical sharing of objects again -
If I share my 9 sweets between 3 people, how many do they each get?
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
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
SATs KS1• Typical questions:
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.
Key Stage 2 SATsSample Questions:
Key Stage 2 SATsSample Questions:
Extra support for NumeracyExtra support for Numeracy
• EYS and KS1 – Numicon
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
Year 4
Mental/Oral Starter Activities
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