Do you wish you knew more about the waywe teach maths in school?

Then come along to our Parents’ and Carers’ Workshops to find out about themethods, terminology and resources we use in the classroom in our daily

maths lessons. Session 1: Adding and SubtractingWednesday 12th November 2014

KS1: 6.00-7.00pmKS2: 7.30-8.30pm

Session 2: Multiplication and DivisionWednesday 4th February 2015

KS1: 6.00-7.00pmKS2: 7.30-8.30pm

Please sign up with Hayley in Reception to secure your place. Unfortunately we are unable to offer Crèche facilities for theseevents.

Mathematics Workshops for Parents and Carers

S

2nd February 2015

An Introduction toMultiplication and Division

KS2

Let’s warm up!

The Ladder Game – new for 2015!

The National Curriculum for Mathematicsaims to ensure that all pupils:

become fluent in the fundamentals of mathematics, includingthrough varied and frequent practice with increasingly complexproblems over time, so that pupils have conceptual understandingand are able to recall and apply their knowledge rapidly andaccurately to problems

reason mathematically by following a line of enquiry, conjecturingrelationships and generalisations, and developing an argument,justification or proof using mathematical language

can solve problems by applying their mathematics to a variety ofroutine and non-routine problems with increasing sophistication,including breaking down problems into a series of simpler steps andpersevering in seeking solutions. 4

Where have your children comefrom?

Concrete and pictorialrepresentations

5 lots of 44 x 5 = 20

4 lots of 55 x 4 = 20

Multiplication Year 3

recall and use multiplication and division facts for the 3, 4and 8 multiplication tables (and 2, 5 and 10 multiplicationtables from Y2)

write and calculate mathematical statements formultiplication using the multiplication tables that theyknow, including for two‐digit numbers times one‐digitnumbers, progressing to formal written methods

Place Value Counters

24 x 6

Place Value Counters

Towards column methode.g. 24 x 6

Factor x factor = product

Your turn…

34 x 7 =Place value countersGrid methodExpanded written method

Multiplication Year 4

recall multiplication and division facts for multiplication tables up to 12 × 12

use place value, known and derived facts to multiply and divide mentally, including:

• multiplying by 0 and 1;

• dividing by 1;

• multiplying together three numbers e.g. 7 x 8 x 4

recognise and use factor pairs and commutativity in mental calculations

multiply two‐digit and three‐digit numbers by a one‐digit number using formalwritten layout eg 64 x 7 and 321 x 4

Consolidation of written methodsand the formal written method

Your turn…

34 x 7Grid methodExpanded written methodCompact written method

Multiplication Year 5

Multiply and divide numbers mentally drawing upon known facts

Multiply and divide whole numbers and those involving decimals,by 10, 100 & 1000

Recognise and use square & cube numbers (& notation)

Multiply numbers up to 4 digits by a one‐ or two‐digit numberusing a formal written method, including long multiplication fortwo‐digit numbers 2345 x 3 or 2345 x 23

Children need to know all their times tables up to 12 x 12

10 1 . 10th

3 . 23 2 . 0

Place value charts

Multiplying by 10(we don’t just add a zero!)

3.2 x 10

Three digit number x two digit numbers

When multiplying bythe digit in the tenscolumn we add a placeholder.

Your turn… 137 x 27

Multiplication Year 6

Perform mental calculations, including with mixed operations and large numbers(increasingly large numbers & more complex calculations)

use all the multiplication tables to calculate mathematical statements in order to maintainfluency.

use estimation to check answers to calculations & determine, in the context of a problem,an appropriate degree of accuracy.

multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimalplaces.

multiply multi‐digit numbers up to 4 digits by a two‐digit whole number using the formalwritten method of long multiplication (short & long multiplication) e.g. 1234 x 12

multiply one‐digit numbers with up to two decimal places by whole numbers e.g. 1.23 x12

How many differentx/÷ facts can

you make using 72?7.2? 0.72?

Children should know the square numbers upto 12 × 12 & derive the corresponding squares

of multiples of 10 e.g. 80 × 80 = 6400

Use mental strategies to solveproblems

e.g. x4 by doubling and doublingagain

x5 by x10 and halvingx20 by x10 and doubling

x9 by multiplying by 10 andadjusting

x6 by multiplying by 3 anddoubling

Factors, Multiples and PrimeNumbers

Your turn…

Decimal Multiplication

Your turn… 1.37 x 27

Division Year 3

recall and use multiplication and division facts for the 3, 4 and 8multiplication tables.

write and calculate mathematical statements for multiplicationand division using the multiplication tables that they know,including for two‐digit numbers times one‐digit numbers, usingmental and progressing to formal written methods.

solve problems, including missing number problems, involvingmultiplication and division, including positive integer scalingproblems and correspondence problems in which n objects areconnected to m objects

How it starts

Repeated subtraction 20 -5 -5 -5 -5

Using tables facts 72 ÷ 8 = 9

Remainders using tables facts 75 ÷ 8 = 9 remainder 3

Division in Year 4

recall multiplication and division facts for multiplication tables upto 12 × 12

use place value, known and derived facts to multiply and dividementally, including: multiplying by 0 and 1; dividing by 1;multiplying together three numbers

recognise and use factor pairs and commutativity in mentalcalculations

Pupils practise to become fluent in the formal written method ofshort multiplication and short division with exact answers

63 ÷ 3 =

Representations to support mentaland written calculations

Short division

Your turn…

95 ÷ 5 =

Division Year 5

Multiply and divide whole numbers and those involving decimals by10, 100 and 1000

Multiply and divide numbers mentally drawing upon known facts

Identify multiples and factors, including finding all factor pairs of anumber, and common factors of two numbers

Pupils practise and extend their use of the formal written methodsof short multiplication and short division.

Divide numbers up to 4 digits by a one‐digit number using theformal written method of short division and interpret remaindersappropriately for the context. e.g. 1234 ÷ 3

Division with remainders322 ÷ 8 =

Division in Year 6

perform mental calculations, including with mixed operations and largenumbers.

use their knowledge of the order of operations to carry out calculationsinvolving the four operations.

identify common factors, common multiples and prime numbers.

divide numbers up to 4 digits by a two‐digit whole number using the formal writtenmethod of long division, and interpret remainders as whole number remainders,fractions, or by rounding, as appropriate for the context e.g. 1234 ÷ 23

divide numbers up to 4 digits by a two‐digit number using the formal writtenmethod of short division where appropriate, interpreting remainders according tothe context e.g. 1234 ÷ 23

Pupils practise division for larger numbers, using the formal written methods ofshort and long division.

BODMAS

3 + 3 x 6

(3 + 3) x 6

Your turn…

Long division322 ÷ 8 =

Peter has 4 books.

Harry has five times as manybooks a Peter. How manymore books has Harry?

36

Problem Solving

Issues in problem solving…

RUCSAC

1. Read

2. Underline

3. Calculate

4. Solve

5. Answer

6. Check

Peter has 4 books.

Harry has 5 times as manybooks as Peter.

How many more books hasHarry?

Peter has 4 books.

Harry has five times as many books as

Peter. How many more books has Harry?

38

Peter’s books

Harry’s books

What is the bar model?

A mathematical representation of a wordproblem

A representation that reveals the structure of aword problem

Not a calculating tool

Josie had 7 times as many sweets as Abi.

Josie gave Abi some of her sweets.They now each have 20.

How many sweets did Josie have before sharingthem with Abi?

Try this using double sided counters

80% 20%

crisps

chocolate

20% 20% 20% 20%

Sam had 5 times as many marbles as Tom. IfSam gives 26 marbles to Tom, the two friendswill have exactly the same amount. How manymarbles do they have altogether?

Your turn…

Fractions

Children use a variety of images to support theirunderstanding of multiplication with fractions.

Your turn…

Scaling up and Scaling down

Thank you for coming!

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