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**Numeracy Methods at SMA**

How , what and why we teach what we teach

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**Four cornerstones to effective numeracy learning**

A sense of number Times tables Place value Patterns

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A sense of number What is ten?

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**Times Tables MUST be learnt! Increase confidence**

Form the foundation of many other skills (division)

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**Place value What do the numbers mean?**

Includes a knowledge of multiplying and dividing by 10, 100, 1000 etc.

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Place Value Place value allows children to partition, which is an essential skill needed in the development of techniques to solve all four number operations 34 = 30 +4 456= 3456=

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**Place Value X 10 DOES NOT simply mean add a zero!**

X 10 means move to the left ÷ 10 DOES NOT mean remove a zero! ÷ 10 means move to the right!

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**Patterns Patterns in sequences and tables and shape**

An ability to see patterns makes a lot of numeracy more accessible and indeed more enjoyable! Fibonnaci sequence; patterns between tables, within tables

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**Lots of methods and techniques**

Idea is to provide children with a tool box of methods that also ensure children maintain a sense of number and place value By year five, children should be able to choose from these ‘tools’ and to choose their EAR method Efficient Appropriate Reliable The only correct method is the one that gets the right answer No point slaving at a technique if a child does not understand it and gets the wrong answer!

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Only one answer Whilst making mistakes and discussing mistakes and misconceptions is essential to the learning process, the right answer is essential! ‘I was almost right!’ is not good enough An engineer who miscalculates the width of a bridge is no use to anyone!

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**Attitude of parents is essential if children are to become effective learners in numeracy**

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The four operations

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Addition

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**Mental Strategies for Addition**

Secure mental addition requires the ability to: recall key number facts instantly (number bonds to 10, 20 & 100, doubles etc) and to apply these to similar calculations recognise that addition can be done in any order and use this to add mentally different combinations of one and two digit numbers partition two-digit numbers in different ways, including adding the tens and units separately before recombining understand the language of addition including more than, sum, plus, greater than, total, altogether etc)

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Addition – Year 5 Consolidate and use an effective written method when adding: Expanded form of addition, starting with the hundreds column first, then moving on to ones.. Using the words 'carry ten' or 'carry one hundred', not 'carry one‘

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Addition – Year 5 Consolidate and use an effective written method when adding. Moving onto compacted form of addition, where addition is started in the ones column and the carried number is shown at the top. Moving up to adding whole numbers with up to 5 digits. Using the words 'carry ten' or 'carry one hundred', not 'carry one‘ These same strategies can be used when adding decimals, lining up all columns and the decimal point.

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Subtraction

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Subtraction – Year 5

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Subtraction – Year 5 Consolidate written methods of subtraction: Moving onto compacted form of subtraction, where subtraction is started in the ones column and the borrowed number is shown at the top. Moving up to subtracting whole numbers with up to 5 digits. These same strategies can be used when subtracting decimals, lining up all columns and the decimal point.

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Multiplication

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**Multiplication – Year 5 Factors of numbers**

Children understand that the factors of a number are all the numbers that divide it exactly giving no remainder. For example, 4 is a factor of 12 because 12 can be divided by 4 with no remainder. The other factors of 12 are 1, 2, 3, 6 and 12. All the pairs of numbers that give the product 60. Take feedback. Establish that 60 has 12 factors:

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Multiplication – Year 5 Multiplication/Division. ‘Buy one – get three free’ Children rehearse multiplication facts to 12 × 12 and the related division facts. They discuss the facts that they can recall rapidly and strategies to help them derive those they struggle to recall, for example doubling 4 times-table facts to work out 8 times table facts. They respond to questions such as: The product of Two numbers is 24. What could the numbers be?

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**Multiplication – Year 5 Use strategies previously taught to help:**

Children use known multiplication facts and place value to find related facts. For example, they use 8 × 4 = 32 to find the answer to 80 × 4, explaining that 80 is ten times as big as 8 so the answer will be ten times 32, or 320. They predict the answer to 80 × 40, explaining how they worked this out. They find related division facts, e.g. recognising that ÷ 400 = 8 because 8 × 400 = Children use similar strategies and their understanding of inverse operations to find the missing numbers in calculations= such as: 20 × = 600 2800 ÷ 70 = ÷ 50 = 300

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Multiplication – Year 5 Children multiply whole numbers by 10, 100 and They answer questions like: How many times bigger than 60 is 6000? What did I multiply 6 by to get 600?

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Multiplication – Year 5 Inverse operations and finding patterns between the operations. Multiplication Division 4 × 80 = ÷ 80 = 4 4 × 800 = ÷ 800 = 4 40 × 8 = ÷ 8 = 40 40 × 80 = ÷ 80 = 40 40 × 800 = ÷ 800 = 40 400 × 8 = ÷ 8 = 400 400 × 80 = ÷ 80 = 400

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Multiplication – Year 5 Multiply two-digit by one-digit numbers mentally by using partitioning. 26 × 7 = 20 × 7 and 6 × 7 = 140 and 42 = then putting the answers together to get 182. They use factors where appropriate to help them to multiply numbers efficiently, for example calculating 35 × 6 by working out 35 × 2 × 3.

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Multiplication – Year 5 Children develop and refine written methods for multiplication. They move from expanded layouts (such as the grid method) towards a compact layout for HTU × U and TU × TU calculations. They suggest what they expect the approximate answer to be before starting a calculation and use this to check that their Answer sounds sensible. For example, 56 × 27 is approximately 60 × 30 =

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Multiplication – Year 5 Develop written methods of Multiplication: HTU × U, TU × TU x x 27 x 20 = x 20 120 6 x 20 = x 7 x 7 = 42 6 x 7 = 1512 x 50 6 = 392

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Multiplication – Year 5 Develop written methods of Multiplication: HTU × U, TU × TU x x

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Division

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**Division – Year 5 Multiplication/Division. Buy one, get three free**

Children rehearse multiplication facts to 12 × 12 and the related division facts. They discuss the facts that they can recall rapidly and strategies to help them derive those they struggle to recall, for example doubling 4 times-table facts to work out 8 times table facts. They respond to questions such as: The product of Two numbers is 24. What could the numbers be?

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**Division – Year 5 Children divide whole numbers by 10, 100 and 1 000.**

They answer questions like: How many times smaller than 5000 is 5? What did I divide by to get 75?

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Division – Year 5 Inverse operations and finding patterns between the operations. Multiplication Division 4 × 80 = ÷ 80 = 4 4 × 800 = ÷ 800 = 4 40 × 8 = ÷ 8 = 40 40 × 80 = ÷ 80 = 40 40 × 800 = ÷ 800 = 40 400 × 8 = ÷ 8 = 400 400 × 80 = ÷ 80 = 400

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Division – Year 5 Children understand that 6 ÷ 3 gives a different answer from 3 ÷ 6. They divide two-digit by one-digit numbers mentally also by using partitioning, finding 51 ÷ 3 by splitting 51 into 30 and 21, dividing each part by 3 and then putting the answers back together to get 17. They use factors where appropriate; for example, they work out 90 ÷ 6 by dividing 90 by 3 and then dividing the answer by 2..

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Division – Year 5 Children extend their knowledge of division to short division of HTU by U, by repeated subtraction of multiples of the divisor (taking away chunks), aiming to subtract as few chunks as necessary. 84 ÷ ÷ 7 (7x10) (7x10) (7x2) (7 x 3) = = 13 R 5

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**Division – Year 5 7 959 - 700 (7 x 100) 259 - 210 (7 x 30) 49**

7 959 - 700 (7 x 100) 259 - 210 (7 x 30) 49 (7 x 7) = 137

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Numeracy at home Essential that numeracy is seen as something that is happening all the time all around us. Talking and listening to your child about their work in maths- parents are not expected to teach their child maths but rather be engaged in it with them. Shopping, time, measurement, money, games and cooking all provide excellent opportunities for maths

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**Useful websites www.maths-games.org**

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