maths in key stage 1. wim day 1 videos aims all pupils should: solve problems reason...
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Maths in Key Stage 1
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AimsAll pupils should: solve problems reason mathematically become fluent in the fundamentals of mathematics
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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.
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Mathematics can be experienced through contexts, language, mathematical
images/pictures and symbols.
Symbols
Mathematical
image/picture
Context
Language
Symbols
Mathematical
image/picture
Context
Language
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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
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Four themes• number sense • additive reasoning•multiplicative reasoning •geometric reasoning
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4 operations
AdditionSubtraction
Multiplication Division
Need to develop an understanding of the relationship between the operations
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If I know 3 +4= 7…
….what else do I know?
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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
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And I can work out…
7 = +3
4 + = 7 + 4 = 7
7 = 3 +
= 4 +3
= 40 +30
+ 40 = 70
70 = 30+
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12 + 2 = 1412 - 2 = 1012 x 2 = 2412 ÷ 2 = 6
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Language of addition
• plus • more than• add• total
• sum• make• altogether• make• altogether
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Addition
Starting with a numbered number
line…
Different ways of representing numbers…
Combining sets with pictorial
representations of their calculations.
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Counting on..Using blank
number lines…
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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
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Equals =is the same as
makestotals
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Flexibility of recording
3 + 4 = 74 + 3 = 77 = 3 + 47 = 4 + 3
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Language of Subtraction• take
away• differenc
e • less than• fewer
• minus• leave • left over
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Subtractiontaking away
finding the difference
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Counting back
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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
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Flexibility of recording
3 + 4 = 7 7 – 4 = 34 + 3 = 7 7 – 3 = 47 = 3 + 4 3 = 7 – 47 = 4 + 3 4 = 7 – 4
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Language of multiplication
• lots of• times• multiply• multiplied by• groups of• multiples of
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5 10 15 20
Images of multiplication..
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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
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…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
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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?
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Language of division
• shared between• grouped into• divided by• double• half• share• equal groups of
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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)
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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.
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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
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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