Mathematics Kings Worthy Primary School

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MathematicsKings Worthy Primary School

• Friday 20th September

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Aims of the session

• To develop an understanding of how calculation
  strategies are developed from Key Stage 1 to Key
  Stage 2
• To experience examples of Key Stage 2 maths
  investigations
• To gain an understanding of age-related
  expectations in maths at Key Stage 2
• To give examples of home-learning activities

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When you were at school..

• How did you feel about maths?
• What were your experiences of maths like?
• How do you feel about maths now?

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Maths in school today.

• Maths is fun!
• Children are encouraged to have a go!
• They are not afraid to be wrong mistakes are
  part of the learning
• Maths is made purposeful and interesting

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Why has maths changed?

• Children used to learn standard methods we
  were shown what to do before understanding was
  consolidated
• If you couldnt remember, or hadnt understood
  the methodsyou went wrong
• Today, we teach methods that help children to
  understand the underlying maths and the basic
  concepts involved
• Children need to develop number sense more
  insight into mathematics

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Todays techniques

• are not just about getting the right answer
  but about knowing and understanding how you got
  there
• are not new many pre-date the techniques you
  learned
• eventually join up with the ones you did in
  school but the children understand them
  thoroughly
• reduce the chance of mistakes being made
• build a firm foundation for understanding more
  complicated mathematics later on

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A balanced mathematical diet

• Using and applying mathematics
• Counting and understanding number
• Knowing and using number facts
• Calculating
• Understanding shape
• Measuring
• Handling data

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Place Value

• Our number system consists of ten digits
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• The place of each digit determines its value.
• For example, the 6 digit can represent for 6,
  sixty, six hundred. It depends where we place it
• 6.65.653
• Game

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Counting

• We expect children at the start of Yr3 to be able
  to
• count, read, write and order whole numbers to at
  least 100 know what each digit represents
  (including 0 as a place holder)
• partition 2 digit and some 3 digit numbers in
  different ways and use this to help solve
  problems
• know by heart all addition and subtraction facts
  for each number to at least 10, all pairs with
  totals to 20, all pairs of multiples of 10 with
  totals up to 100
• add or subtract mentally a one digit number or a
  multiple of 10 to or from any two digit number
• begin to bridge through tens numbers using known
  number facts when adding and subtracting
• understand multiplication as repeated addition or
  as an array, solve simple x and problems by
  pictorial or abstract methods
• derive and recall facts for the 2, 5 and 10
  multiplication tables
• use and interpret the symbols /-/x/ and in
  number sentences
•  

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Counting

• We expect children at the start of Yr5 to be able
  to
• read, write and order whole numbers to 10 and
  100s of thousands, know what each digit
  represents and can partition 4 and 5 digit
  numbers into multiples of 1000, 100, 10 and 1 in
  different ways
• use diagrams to identify equivalent fractions
  interpret mixed numbers and position them on a
  number line
• round fractions or decimals to the nearest and/or
  next whole number
• use mental recall of addition and subtraction
  facts up to 20 in solving problems involving
  larger numbers
• use informal methods to add two numbers together
  that have one decimal place
• use efficient written methods are used to add and
  subtract three digit and four digit whole numbers
  and .p.
• know by heart 2,3,4,5,and 10X tables, use them to
  solve multiplication and division problems and
  begin to know 6,7,8 and 9X
• find pairs of factors of any number to 30
• recognise two digit multiples of 2,5, 10 and
  three digit multiples of 2, 5, 10, 50 and 100
• find remainders after division and round up or
  down after depending upon the context

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Number Lines

• They help to develop an ability to order numbers,
  and give children a sense of where numbers sit in
  our number system
• They allow children to draw a picture or model
  in their heads when calculating
• Can be used in a range of aspects of mathematics
  numbers and the number system, fractions,
  decimals, percentages, addition, subtraction,
  multiplication, division, measures, handling data

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The four types of number tracks or number lines

• Number tracks
• Numbered lines

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The four types of number tracks or number lines

• Partly numbered line
• The empty number line

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Partitioning

• This means breaking up numbers into smaller
  numbers
• All numbers can be partitioned in many different
  ways
• If children understand about partitioning numbers
  in different ways, they will calculate more
  efficiently and with understanding.

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Jump 10s first Typical at end of Yr 1/start
of Yr 2
26 23
10
10
1
1
1
26
36
49
48

46
47
-10
-10
44 - 25
34
44
23
21
20
19
24
22



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Jump and adjust 26 9
Compensating
10
26
35


36

-1
44 - 9
-10

44

34
35
1
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Mental skills and strategies

• We constantly draw upon mental strategies that
  we know and have internalized when we carry out
  calculations
• doubling
• adding multiples of ten
• Partitioning
• compensating
• applying known facts
• Children need to learn and understand these
  strategies and know how and when to apply them.
  

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Partitioning

• 47 76 40 70 110
• 7 6 13
• 110 13 123
• 40 7
• 70 6
• -------
• 110 13 123

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Column

• 47
• 76 Adding 1s first
• ----
• 110 (7040) then 47
• 13 ( 7 6) 76
• ---- -----
• 123 13
• 110
• 123

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Column and exchange

• h t u
• 4 7 7 6 13 which is 1 ten
  and
• 71 6
  3 units
• --------
• 1 2 3 We exchange 1 group
  of ten for ten units

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Subtraction

• Expanded by partitioning
• 563 241
• then 563-
• 500 60 3 241
• 200 40 1 ------
• ------------- 322
• 300 20 2 322

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Subtraction with exchange

• The previous method does not always work
• 74 27 2 313411 -
• 2 6 8
• 670 14 ------
• 20 7 0 7 3
• -------
• 40 7 47

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Multiplication in KS1
Arrays are important because they provide a good
visual image of the multiplication that links
closely to the concept of repeated addition.
2 2 2 2
4 x 2 8
2 x 4 8
They are the visual image which leads directly
into grid multiplication a key strategy in KS2
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Arrays

• They show the link between multiplication and
  division these are not concepts taught in
  isolation

2 x 4 8 4 x 2 8 8 2 4 8 4 2
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Number lines for multiplication
2 2 2 2
2
0 2 4 6 8 10
This image can be expressed as 2 multiplied by 5,
two, five times, 5 groups of 2, 5 lots of 2 and
5 hops of 2 on a number line.
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Multiplication on a number line
There are 5 cakes in one box. How many cakes in 4
boxes?
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Grid (2digit x 1digit)

• Encourage estimation first
• 38 x 7 (approx 40 x 7 280)
• x 7
• 30 210 210 56 266
• 8 56

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Expanded short

• Column but showing working
• 38 x 7
• then h t
  u
• 30 8 3
  8
• 7
  7
• ---------
  -------
• 56 (7 x 8) 5
  6
• 210 (7 x 30) 2 1
  0
• 
  2 6 6

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Short

• 38 x 7
• grid
  for 2dp x 2dp
• 38 x then
• 7 x 20
  7
• 266 50 1000
  350 1350
• 5
  6
  120 42 162
• 
  1 5 1 2

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Compact long (end of KS2)

• Children find this tricky!

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Division in Key Stage 1
Division can be GROUPING or SHARING Sharing We
have 20 marbles in the marble run to share
between 4 children. How many marbles do they get
each? 5 marbles Grouping We have 25 marbles
and they come in packets of 5. How many packets
were there? Putting 20 into groups of 5. Answer
is how many in each group 4 I have
20 cakes, I can fit 5 cakes in a box. How many
boxes will I need?
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KS1 strategies for division

• I have 12 lollipops and I share them among 4
  people. How many lollipops will they have each?
• I have 12 lollipops and I want to put 4 lollipops
  in each bag. How many bags will I need?

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Linking to tables

• Chunking
• 345 3
• 300 (100 x 3)
• 45 (15 x 3) 115
• 45
• 00

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Short division

• See progression in calculation document

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Long division

• http//www.mathsisfun.com/numbers/long-division-an
  imation.html
• 425 25
• 200 - (8 x 25) 17
• 225- (8 x 25)
• 200
• 25 (1 x 25)
• 25-
• 00

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Why are images important?

• Resources, models and images help children to
  visualise and understand mathematical concepts
• They build up and remember - the mental
  picture in their minds
• They should be available throughout the primary
  years. Children will rely on them less and less
• TABLES!

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When tackling a mathematical problem, children
will ask themselves

• What do I know about these numbers?
• Can I do this in my head?
• Do I know the approximate size of the answer?
• If I cant do it all in my head, what do I need
  to write down to help me?

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• Above all have fun! Children often say that
  maths is their favourite subject and they get
  quicker and better at it when they understand
  what they are doing. Theres no need for you to
  teach your child you help by helping them to
  explain their thinking and their understanding
• From Count on me 200 ways to help with
  mathematics

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• Its the schools job to provide the structured
  learning.Your role is to nurture and support
  your childs mathematical knowledge away from
  school, to bring it into their real lives and,
  most important of all, to turn it into an
  exciting adventure
• From Maths for Mums and Dads Rob Eastaway and
  Mike Askew

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Have your questions been answered?