Maths in Key Stage 1

WIM Day 1 Videos

Aims All 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. Symbol s Mathematica l image/pictur e Context Language Symbol s Mathematica l image/pictur e 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 Addition Subtraction 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 7 = = = = = = = = = = = 700

And I can work out… 7 =   = 7  + 4 = 7 7 = 3 +   = 4 +3  =  + 40 = = 

= = x 2 = ÷ 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 + __

Equals = is the same as makes totals

Flexibility of recording = = 7 7 = = 4 + 3

Language of Subtraction take away difference less than fewer minus leave left over

Subtraction taking 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) =?? = = 28

Flexibility of recording = 7 7 – 4 = = 7 7 – 3 = 4 7 = = 7 – 4 7 = = 7 – 4

Language of multiplication lots of times multiply multiplied by groups of multiples of

Images of multiplication..

They should begin to understand multiplication as repeated addition… 5 times 3 = 5 x3 = 5 three times = three groups of 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 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 Subtraction 15 ÷ 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