Title: A1258608264xLSYc
1Strengthening Progress in Year 4
Louise Grattage Elizabeth Huggett Maths Team
2Session 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
3Strands 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
4Y4 Learner
5Key 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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7Supporting material for mental calculation
booklets
8Mental 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
9Counting 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
10Interactive Essentials
11Mental 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
12Partitioning using multiples of 10 and 100
Gordons - Add vertical expanded with PV cards
Gordons Add number line
13Partitioning using multiples of 10 and 100
Gordon-Expanded addition
14Mental 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
15Partitioning bridging through multiples of 10
Working with larger numbers and informal jottings
6
24 8
32
2
32
24
56 7
16Partitioning 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)
17www.topicbox.co.uk
18Mental 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
19Compensating
Equivalent calculations Gordons calculation
balance
Gordons Christmas
20Mental 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
21Using near doubles
22Mental 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
23When would bridging through numbers other than 10
be used in Y4?
24Mental 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
25Multiplying by 10 and 100
- Calculator space invaders
ITP- moving digits
Interactive Essentials
26Mental 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
27Halving and doubling
Gordons Function Machine
ITP Function Blocks
28Year 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
29In 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
30From mental strategies to written calculations
31Warm 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.
32Bingo
33Aims
- 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.
34Strands 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
35Calculating 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
36Why do children need to record a calculations?
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.
38Progression in Addition
Working with larger numbers and informal jottings
83
56
27
20
7
56
20
7
4
3
56
76
80
83
?
39237 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
41Progression in Subtraction
a) Working with larger numbers
734 - 257
477
400
34
40
3
734
257
700
300
260
42734 - 257
or a)
- b) 734
- - 257
- 3 260
- 40 300
- 400 700
- 34 734
- 477
-
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4596 7
a) Chunking up
4696 7
b) Chunking back
47c) Chunking back
7 )
96
48Which of these methods do you prefer? Why?
or
49www.learningclip.co.uk
50Interactive essentials
51Progression 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
52In 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.
53Gap 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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