BSJ Maths Workshop - Progression in Skills

Thursday 22nd October 2015Inspire , Challenge and Nurture for Excellence

Mathematics at BSJAims of the workshop:

1. An introduction to the written Calculation Hierarchy document and progression of written calculation methods.

2. Supporting your children with the basics - finding gaps in learning and bridging them.

3. Resources for use at home to support with Mathematics.

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Mathematics at BSJ

Part 1

An introduction to the written Calculation Hierarchy document and progression of written calculation methods.

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Calculation Hierarchy Document

Format for the progression of written calculation methodsHas clear progression for the 4 operations – split into phases.

Emphasis on developing mental methods that can then support and move on to written methods.

It is an aid and helpful guide.

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Calculation Hierarchy

These are the steps for addition:

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Calculation HierarchyThere are diagrams and explanations for each step and how it should be

done.

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Calculation Hierarchy

◻Number lines are an aid for calculations with the aim that these written methods becoming mental methods.◻It is at this point where key number facts also become very

important to aid the efficiency of mental methods.◻Children need to know with speed simple number facts.

This then allows them to do more complex calculations mentally.

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Calculation Hierarchy

Other steps after that are to use vertical algorithms to allow larger and more complex calculations to be done. However, their mental methods are still

important.

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Example: steps for additionHow do children learn to add? ◻Combining sets of objects◻Counting on the amount they are adding from a starting

number.◻Recalling and using number facts.◻Extending bridging, partitioning and using and recognising

patterns. Commutative relationships.◻Column addition

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Video demonstrating expanded bridging.

Partitioning to add◻Partitioning is an incredibly useful tool that can be used for

solving addition and multiplication calculations.◻It also helps children to consolidate their understanding of

place value.◻In addition it can be used before the vertical column

method like so:38+79=117

30+70=100

8+9=17

100+17=117

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What are steps for subtraction?

◻Taking away from a set or hiding part of the set.

◻Counting back from a starting number with a number given.

◻Recalling and using number facts including inversing addition facts.

◻Bridging, partitioning (although a sound knowledge of place value is needed) and looking for patterns.

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Video demonstrating subtraction using the expanded column method

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What are the steps for multiplication.

◻Counting up sets of objects.

◻Counting on in groups, repeated addition.

◻Using knowledge of counting in groups such as counting in

twos (times tables).

◻Recognising patterns and applying them.

◻Partitioning and recombining to solve larger multiplications.

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Partitioning to multiply

In multiplication partitioning is useful when solving 1dx2d calculations. Whilst it can be used to solve 2dx2d it’s better to use the grid or vertical methods.

23x6=

20x6=120

3x6=18

120+18=138

This is one example of where basic facts knowledge is really important. If the children have at least some of these facts to hand they will be quicker in their calculations.

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What are the steps for division◻Finding groups of the same size in a given number, sharing out

and sorting objects equally.◻Counting back in groups from a given number and working out

how many groups you counted and if there are any remainders left. ◻Understanding multiplication is the inverse of division and

apply this knowledge to solve calculations.◻Using knowledge of doubles and halves, fractions and

timetables to support understanding and speed.◻Partitioning and recombining to solve larger division problems.

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Video demonstrating division using the short division method

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Calculation Hierarchy Challenge

Use the addition calculation hierarchy to solve the following calculations:

7+2 = (use pictures and marks)

11+13 = (use a number line)

34+58 = (use column by column addition)

132+254 = (use pure column addition)

Explain to a partner how you solved these problems.

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Calculation Hierarchy

The Calculation Hierarchy can be found on the bsj.sch.id website

by following the path below:

Our School>Primary>Curriculum>Y1-6>Maths

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Manipulatives that could be used

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Part 2Supporting children with the basics, finding gaps in learning and bridging them.

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We Will Cover:

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The importance of meaning and language

The importance of meaning and language

Understanding the language of mathematics and then applying the correct process to solve a problem is vital.

As adults we often make the assumption that children will know or just understand the basic concepts. This often leads to us missing gaps in their learning.

Never assume they will just know it!

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Using questioning and discussion with children to find out what they are thinking.

◻6+5 = 10◻How do you respond to this?◻‘That’s great, but how did you work it out?’◻‘I counted on from 6, oh I got it wrong’ – can they self

correct? ◻What do you do if they still think they are right? Go back

to what they can do and find the next step. Steps are important for each operation.

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Take a moment to familiarise yourself with the Key Knowledge Ladder

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A word of caution

◻Key knowledge is important, for example, key number facts.◻But, prior understanding is crucial to success

‘They may be able to say all the time tables by rote in Year 2 but they are only useful if they can apply them correctly or know

what they are doing.’

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Part 3: Supporting at Home

Other areas of Math’s that children find difficult - how could you help?

Think about the basics and the language: do you need to take some steps back? What are the gaps in their learning or areas they are finding particularly difficult?

Discuss for 5 minutes, feedback and questions.

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A word about Kumon

◻Focuses on calculation strategies◻Formal delivery style◻Benefits some children ◻Tends not to develop wider mathematical skills

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Resources for support at home

Securing Maths Levels Guidance

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Questions and Feedback

◻You will be emailed a link to the feedback form. Please do take a moment to offer feedback.◻There is a maths trolley that you are welcome to look

through to give you some ideas of the resources we use to teach Maths. ◻Please come and ask us questions.

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Mathematics at BSJ

Thank you for comingMr Karl Prudhoe and Mrs Clara Buckley

karl_prudhoe@bsj.sch.id

clara_buckley@bsj.sch.id

Thank you

Bintaro Sektor 9Jl. Raya Jombang-Ciledug, Pondok ArenTangerang 15227. JAKARTA - INDONESIATel. +62 (21) 745 1670 • Fax. +62 (21) 745 1671www.bsj.sch.id

Inspire, Challenge and Nurture for Excellence

Bintaro Jaya Sektor 9Jl. Raya Jombang Ciledug, Pondok Aren

Tangerang 15227 – JAKARTA – INDONESIA Telp. 021 745 1670 Fax. 021 745 1671

www.bsj.sch.id