A1258608264xLSYc

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Strengthening Progress in Year 4
Louise Grattage Elizabeth Huggett Maths Team
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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

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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
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Y4 Learner
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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)

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Supporting material for mental calculation
booklets
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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

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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

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Interactive Essentials
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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

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Partitioning using multiples of 10 and 100

• 34 53

Gordons - Add vertical expanded with PV cards
Gordons Add number line
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Partitioning using multiples of 10 and 100
Gordon-Expanded addition
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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

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Partitioning bridging through multiples of 10
Working with larger numbers and informal jottings
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24 8
32
2
32
24
56 7
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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)
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www.topicbox.co.uk
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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

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Compensating
Equivalent calculations Gordons calculation
balance
Gordons Christmas
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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

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Using near doubles
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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

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When would bridging through numbers other than 10
be used in Y4?
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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

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Multiplying by 10 and 100

• Calculator space invaders

ITP- moving digits
Interactive Essentials
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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

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Halving and doubling
Gordons Function Machine
ITP Function Blocks
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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

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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

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From mental strategies to written calculations

• Session 2

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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.

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Bingo

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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.

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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
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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
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Why do children need to record a calculations?

• SUPPORT RECORD EXPLAIN

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• 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.

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

20
7
4
3
56
76
80
83
?
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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

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

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

• b) 734
• - 257
• 3 260
• 40 300
• 400 700
• 34 734
• 477

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96 7
a) Chunking up
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96 7
b) Chunking back
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c) Chunking back
7 )
96
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Which of these methods do you prefer? Why?
or
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www.learningclip.co.uk
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Interactive essentials

• Division by grouping

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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
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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.

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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.

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