Maths in Key Stage 1

• WIM Day 1 Videos

AimsAll pupils should: solve problems reason mathematically become fluent in the fundamentals of mathematics

The aims require children of all ages to make and justify decisions in all areas of mathematics. This requirement is at the centre of this framework, putting talk at the heart of mathematics teaching and learning.

Mathematics can be experienced through contexts, language, mathematical

images/pictures and symbols.

Symbols

Mathematical

image/picture

Context

Language

Symbols

Mathematical

image/picture

Context

Language

Topic Headings in NC

• Number – Number and Place Value• Number – Addition and Subtraction• Number – Multiplication and Division• Number- Fractions (including decimals and

percentages)• Ratio and Proportion• Measurement• Geometry – properties of shapes• Geometry – position and direction• Statistics

Four themes• number sense • additive reasoning•multiplicative reasoning •geometric reasoning

4 operations

AdditionSubtraction

Multiplication Division

Need to develop an understanding of the relationship between the operations

If I know 3 +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 a numbered number

line…

Different ways of representing numbers…

Combining sets with pictorial

representations of their calculations.

Counting on..Using blank

number lines…

Complementary addition.

Children should understand solving word problems, such as ‘You need 10 marbles, but

you only have 6, how many more do you need?’ Model on bead bar and number

line… ‘How to find the missing number’ e.g. 10 = 6 + __

6 7 8 9 10

Equals =is the same as

makestotals

Flexibility of recording

3 + 4 = 74 + 3 = 77 = 3 + 47 = 4 + 3

Language of Subtraction• take

away• differenc

e • less than• fewer

• minus• leave • left over

Subtractiontaking away

finding the difference

Counting back

Counting on

Compensation

When subtracting 9, it is easier to subtract 10 then add 1, (model on a bead bar)

37 - 9 =?? 37 - 10 = 27 27 + 1 = 28

Flexibility of recording

3 + 4 = 7 7 – 4 = 34 + 3 = 7 7 – 3 = 47 = 3 + 4 3 = 7 – 47 = 4 + 3 4 = 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 understand multiplication as repeated addition…

5 times 3 = 5 x3 = 5 three times = three groups of 5 =5 + 5 + 5 = 15On 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 = 105x2 = 10

Does it matter which way round?

• 2 x50 or 50 x2?Both equal 100 but when you put into a context…There are two jobs available, 2 days at £50/day or 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 halving numbers in a range of contexts. (Object, shape & quantity)

Children should experience finding, recognising & naming one half as one of two equal parts and one quarter as one of four equal parts.

Make arrays to find division facts for ½ & ¼

Teacher to model the recording of finding half and quarter of an array, for example 8 divided by 2 is 4.

Grouping and Sharing

Sharing ‘6 sweets shared between 2 people, how many do they each get?’

Grouping ‘There are 6 sweets, how many people can have 2 sweets 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 Subtraction15 ÷ 5 = 15 – 5 – 5 – 5 =

(3 groups of 5)

Solve calculations using symbols to stand for unknown numbers and complete equations using inverse operations. ÷ 2 = 4 20 ÷ = 4 ÷ = 4