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Title: A1258608264xLSYc


1
Strengthening Progress in Year 4
Louise Grattage Elizabeth Huggett Maths Team
2
Session 1
  • To develop awareness of the range of mental
    strategies used in Y4
  • To strengthen progress and achievement in Y4 with
    a focus on Ma2
  • To consider a range of models and images to
    support the teaching and learning of mental
    calculations

3
Strands in the Renewed Framework
7 Strands 1.Using Applying Mathematics 2.Countin
g Understanding No 3.Knowing Using No
facts 4.Calculating 5.Understanding shape
6.Measuring 7.Handling data
4
Y4 Learner
5
Key aspects of learning
  • The introduction of written methods that build
    on earlier practical, mental and visual work, and
    consideration of why some calculation methods are
    more efficient than others, helps children to
    develop their evaluation skills.
  • (pg7 Y4 The Learner)

6
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7
Supporting material for mental calculation
booklets
8
Mental calculation strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

9
Counting forwards and backwards
Childrens counting skills should always be
slightly more advanced than their calculating
skills. If children are not confident with
counting higher numbers they may find it
difficult to calculate with such numbers.
  • Counting Joe
  • Interactive Essentials

10
Interactive Essentials
11
Mental calculation strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

12
Partitioning using multiples of 10 and 100
  • 34 53

Gordons - Add vertical expanded with PV cards
Gordons Add number line
13
Partitioning using multiples of 10 and 100
Gordon-Expanded addition
14
Mental Calculation Strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

15
Partitioning bridging through multiples of 10
Working with larger numbers and informal jottings
6
24 8
32
2
32
24
56 7
16
Partitioning bridging through multiples of 10
  • Children need to recall facts within 20 as a
    pre-requisite skill for adding or subtracting
    efficiently

Bridging Shuttle (Topic Box)
17
www.topicbox.co.uk
18
Mental Calculation Strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

19
Compensating
Equivalent calculations Gordons calculation
balance
Gordons Christmas
20
Mental Calculation Strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

21
Using near doubles
22
Mental Calculation Strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

23
When would bridging through numbers other than 10
be used in Y4?
24
Mental Calculation Strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

25
Multiplying by 10 and 100
  • Calculator space invaders

ITP- moving digits
Interactive Essentials
26
Mental Calculation Strategies
  • Counting forwards and backwards
  • Reordering
  • Partitioning using multiples of 10 and 100
  • Partitioning bridging through multiples of 10
  • Compensating
  • Using near doubles
  • Bridging through numbers other than 10
  • Multiplying by 10 and 100
  • Halving and doubling

27
Halving and doubling
Gordons Function Machine
ITP Function Blocks
28
Year 4 The Learner Knowing and using number
facts
  • Children use their knowledge of halves of
    2digit multiples of 10 and of even numbers to 20
    to calculate half of any even 2digit number.
  • eg. half of 58 half of 50 plus half of 8
  • or half of 40 plus half of 18

29
In conclusion
  • Being aware of the range of strategies should
    ensure teachers
  • Choose appropriate numbers with which to model
    and then use
  • Encourage children to consider efficiency of
    calculations
  • Develop childrens confidence and fluency with a
    range of strategies

30
From mental strategies to written calculations
  • Session 2

31
Warm up - Bingo Caller
  • www.bingo-caller.com
  • Write 10 different multiples of 10 numbers
    ranging from 0 to 180.
  • As each number is called, double it, round to the
    nearest 10, and cross it off your grid.
  • First to get 5 crossed off wins.


32
Bingo

33
Aims
  • To consider the progression in calculations
    towards an efficient written method
  • To explore the more difficult to learn,
    difficult to teach strategies
  • To introduce a gap task focusing on identifying
    strengths and development areas in particular
    calculations.

34
Strands in the Renewed Framework
7 Strands 1.Using Applying Mathematics 2.Countin
g Understanding No 3.Knowing Using No
facts 4.Calculating 5.Understanding shape
6.Measuring 7.Handling data
35
Calculating Y3
  • Develop and use written methods to record,
    support or explain addition and subtraction of
    two-digit and three-digit numbers

Calculating Y4
Refine and use efficient written methods to add
and subtract two-digit and three-digit whole
numbers and .p
36
Why do children need to record a calculations?
  • SUPPORT RECORD EXPLAIN

37
  • Children just recording a written answer only
    allows us to see whether an answer is right or
    wrong, it doesnt allow us to see the strategies
    used.
  • Encouraging children to explain their strategies
    verbally is a strength, however modelling
    childrens explanations is an important step.
  • For calculations that children cant do in their
    heads or with jottings they will need the support
    of an efficient written method.

38
Progression in Addition
Working with larger numbers and informal jottings
83
56
27
20
7
56

20
7
4
3
56
76
80
83
?
39
237 185
Children use the skills of partitioning to
support the expanded method of calculation
  • 200 30 7
  • 100 80 5
  • 300 110 12 422

40
  • As children become more confident in using
    expanded methods, recording as much detail
    becomes less essential.

237 185 422 1 1
41
Progression in Subtraction
a) Working with larger numbers
734 - 257
477
400
34
40
3
734
257
700
300
260
42
734 - 257
or a)
  • b) 734
  • - 257
  • 3 260
  • 40 300
  • 400 700
  • 34 734
  • 477

43
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44
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45
96 7
a) Chunking up
46
96 7
b) Chunking back
47
c) Chunking back
7 )
96
48
Which of these methods do you prefer? Why?
or
49
www.learningclip.co.uk
50
Interactive essentials
  • Division by grouping

51
Progression in addition UA
Problem. If 25 people in Florence are waiting for the bus, another 7 people join the queue. How many people are waiting for the bus altogether?
Calculation needed
Jottings
Answer to the problem
25 7
5
2
32
25
32
52
In summary
  • Year 4 children need to build on their
    understanding of place value and partitioning to
    refine written methods of recording for addition
    and subtraction.
  • They should first see if they can do the
    calculations in their heads.
  • Children need to develop their written methods
    for efficient multiplication and division
    calculations and need to apply this knowledge for
    calculations involving money, measures and time.

53
Gap Task
  • Choose 2 children who are just below national
    expectations who should just be able to do these
    calculations. Encourage the children to explain
    how they arrived at their answers. The children
    may need to write the calculation down and do
    some jottings or record using more efficient
    methods.

54
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