Maths in Key Stage 1
Aims
All pupils should:
solve problems
reason mathematically
become fluent in thefundamentals of mathematics
The aims require children of allages to make and justifydecisions in all areas ofmathematics. This requirementis at the centre of thisframework, putting talk at theheart of mathematics teachingand learning.
Mathematics can be experienced throughcontexts, language, mathematical images/picturesand symbols.
Symbols
Mathematicalimage/picture
Context
Language
Symbols
Mathematicalimage/picture
Context
Language
Topic Headings in NC
•Number – Number and Place Value
•Number – Addition and Subtraction
•Number – Multiplication and Division
•Number- Fractions (including decimals andpercentages)
•Ratio and Proportion
•Measurement
•Geometry – properties of shapes
•Geometry – position and direction
•Statistics
Four themes
•number sense
•additive reasoning
•multiplicativereasoning
•geometric reasoning
4 operations
Addition
Subtraction
Multiplication
Division
Need to develop anunderstanding of therelationship between theoperations
If I know3 +4= 7…….what else do I know?
3 +4= 7
7 = 3 +4
40 +30= 70
7 -3= 4
7 -4= 3
7 = 4 +3
3 = 7 -4
4 = 7 -3
4 +3= 7
70 -30= 40
70 -40= 30
30 = 70 -40
40 = 70 -30
700 = 300 +400
700 = 400 +300
400 +300= 700
And I can work out…
7 = +3
4 + = 7
+ 4 = 7
7 = 3 +
= 4 +3
= 40 +30
+ 40 = 70
70 = 30+
12 + 2 = 1412 - 2 = 1012 x 2 = 2412 ÷ 2 = 6
Language of addition
•plus
•more than
•add
•total
•sum
•make
•altogether
•make
•altogether
Addition
Starting with anumberednumber line…
Different ways ofrepresentingnumbers…
Combining setswith pictorialrepresentations oftheir calculations.
Counting on..
Using blanknumberlines…
Complementary addition.
Children should understand solvingword problems, such as ‘You need 10marbles, but you only have 6, howmany more do you need?’ Model onbead bar and number line… ‘How tofind the missing number’ e.g. 10 = 6 +__
6 7 8 9 10
Equals =
is the same as
makes
totals
Flexibility of recording
3 + 4 = 7
4 + 3 = 7
7 = 3 + 4
7 = 4 + 3
Language of Subtraction
•take away
•difference
•less than
•fewer
•minus
•leave
•left over
Subtraction
takingaway
finding the difference
Counting back
Counting on
Compensation
When subtracting 9, it is easier tosubtract 10 then add 1, (model on a beadbar)
37 - 9 =??
37 - 10 = 27 27 + 1 = 28
Flexibility of recording
3 + 4 = 7 7 – 4 = 3
4 + 3 = 7 7 – 3 = 4
7 = 3 + 43 = 7 – 4
7 = 4 + 34 = 7 – 4
Language of multiplication
•lots of
•times
•multiply
•multiplied by
•groups of
•multiples of
5 10 15 20
Images of multiplication..
They should begin to understandmultiplication as repeatedaddition…
5 times 3 = 5 x3 = 5 three times = three groups of 5 =
5 + 5 + 5 = 15
On a bead bar:
And on a number line:
Children should know that 3 x 5 has the same answer as 5 x 3.
This can also be shown on the number line.
15 = 5 x 3
15 = 3 x 5
…and as an array in context e.g.eggs in a box and cakes in a tin.
Children should be able to model a multiplication calculation using an array.
Children will need to be taught the language of ‘rows’ and ‘columns’.
2x5 = 10
5x2 = 10
Does it matter which way round?
•2 x50 or 50 x2?
Both equal 100 but when you put into acontext…
There are two jobs available, 2 days at £50/dayor 50 days at £2/day…
•£2 x50 or £50 x2?
Language of division
•shared between
•grouped into
•divided by
•double
•half
•share
•equal groups of
Children will understand equal groups and share items
out in play and problem solving.
They will count in 2s and 10s and later in 5s.
Children should experience halvingnumbers in a range of contexts. (Object,shape & quantity)
Children shouldexperience finding,recognising & namingone half as one of twoequal parts and onequarter as one of fourequal parts.
Make arrays to finddivision facts for ½ & ¼
Teacher to model therecording of finding half andquarter of an array, forexample 8 divided by 2 is 4.
Grouping and Sharing
Sharing ‘6 sweets sharedbetween 2 people, how many dothey each get?’
Grouping ‘There are 6 sweets,how many people can have 2sweets each?’
6 ÷ 2 = 3 “6 sweets shared between 2 people gives 3 sweets each”
6 ÷ 2 = 3 “6 sweets grouped into 2’s gives 3 groups”
6 ÷ 2 = 3
Repeated Subtraction
15 ÷ 5 = 15 – 5 – 5 – 5 =
(3 groups of 5)
Solve calculations usingsymbols to stand for unknownnumbers and completeequations using inverseoperations.
÷ 2 = 4 20 ÷ = 4 ÷ = 4