Primary Mathematics Key Stages 1 and 2 Multiplication and Division

Aims of the Session To consider the stages of early multiplication and division. To look at the calculations strategies for X and ÷ at Ks1 and KS2. To look at strategies for teaching both at KS2. Especially the written methods.. HAYLOCK

Multiplication from EY Reception: Counting in groups of 1,2’s,5’s and 10’s.

Multiplication from NC Year 1: Counting on and back in groups of 1,2,5 and 10. Doubles of numbers to 10. Combining groups of 2,5 and 10. Doubling and halving in context.

Multiplication from NC Year 2: BIG focus on X and interlinking that division is the inverse. Doubles of numbers to 20 Tables for at least 2,5,10. Multiplication as repeated addition and arrays. Using the symbols accurately. Knowledge of multiples of 10.

Vocabulary Multiply/multiplication/multiple Times Lots of Groups of Double Product of

Practical Activities - Reception Using Number lines/objects Counting in 2’s,5’s and 10s Counting and sorting objects in 2’s. Confidence in place value and counting skills are ESSENTIAL to build foundations for X and division. Lots of practice adding on and counting back…

Practical Activities - Reception Fingers: Show me 2 fingers on one hand. Show me 2 fingers on the other hand. How many fingers altogether? Fingers are good for doubles from 1+1 to 5+5 Rhymes: Learn nursery rhymes and number pattern rhymes, 2,4,6,8, Mary at the kitchen gate. 1,2,3,4,5, once I caught a fish alive. etc

Practical Activities - Year 1 Individual number lines for counting on in regular intervals. Use number squares to identify simple multiples. Look at ITP and charts and individual number squares. Chanting simple patterns to focus on the rhythm of multiples, 2,4,6,8,10, etc. Use actions, claps, clicks to reinforce the connection between rhythm and patterning. Use number fans and dice to practice doubling and halving.

Practical Activities - Year 2 Use arrays to organise thinking about multiplication. 3x2=6, demonstrate with symbols, dots, counters etc

Multiplication Begin teaching formal multiplication by showing links between repeated addition and multiplication, explain that Mathematicians are ‘lazy’ and like to take short cuts so rather than writing 3+3+3+3=12, they would write 4 lots of 3=12 and even quicker, 4x3=12. 2+2+2+2=8 so 4x2=8 etc

Multiplication Use number squares and lines or arrays to reinforce. Remember the commutative law is relevant to x (can swap numbers around, 3x2=2x3) Talk, talk, talk about methods and ways to calculate-NOT teacher-children! Learn doubles and how to x4/8/10/20/25 etc will really help with division.

Multiplication Methods at KS2 Horizontal and informal from end of Y2 Y3. Introduce more formal methods in Y3 and up. BY Y5 and 6 all should be using ‘grid’ methods or shorter and more efficient methods-refer to sheet. Remember-some ‘drill and practise’ is necessary but majority should be put into problem solving contexts.

Multiplication Common problems: Confusion of addition and multiplication. Removal of practical equipment too soon, keep using it for as long as the children need it, not for as long as you deem it useful! Introducing formal written strategies too soon, there is no requirement to do vertical x until they are in KS2. Horizontal strategies are best to gain confidence and skills.

Division Children seem to find division harder than multiplication-WHY? Have a discussion with your neighbour-did you find one more difficult than the other-why?

Division Vocabulary Share Group Divide Lots of Groups of Halve Split/equal

Division in the NC Reception: Share objects into equal groups and count how many in a group. Year 1: Sharing in equal groups. Using halves and quarters in context. Halving numbers and money. Year 2: Division as halving and repeated subtraction. Using the division symbol. Remainers with most able. Year 3: Remainders in context and using informal written methods. Ability to divide 2 digit numbers by 10.

Practical Activities - Reception Practise sharing in real life situations; cutting up cakes/pizza/apples and giving pieces out, sharing fruit/sweets etc. Practise grouping; by size, shape, colour etc. Rehearse concept of equal, use child’s innate sense of fairness, offer unequal halves, children will quickly point out that it is not a ‘fair share’.

Practical Activities - Year 1 Lots of halving using practical equipment, food, money etc. Develop through role play but with greater accuracy than in Reception. Learn doubles and corresponding halves to 10 or more, use games, number lines, dice, counters and cubes to reinforce this.

Practical Activities Year 2 Use of hundred squares and number lines plus practical equipment. Use arrays-demo to show how to divide. Teach it as the inverse of multiplication. Use the ‘lazy mathematician’ to show how subtraction does the same thing- 12-3-3-3-3=0 is the same as 12 divided by 4 lots of 3. Actually take groups of 3 away each time, using cubes/counters etc. Put problems in a context, I have 3 children and 12 sweets, how many should they each get?

X and ÷ KS2 Multiply 1 digit and 2 digit numbers by 10 or 100 and describe its effect. Derive and recall X facts for 2,3,4,5,6 and 10 times table. Recognise multiples of 2,5 or 10 up to 1000. Use practical and INFORMAL written methods to x and ÷ 2 digit numbers and round remainders up or down depending on context. Understand that division is the inverse of x and vice versa. Derive and record number sentences for x and ÷.

Division Division as sharing Division as grouping Demonstrate as arrays/groups etc-demo on whiteboard.

. Division methods at KS2 Start using remainders consistently Y3. Y4 - start introducing more formal methods. Y5 and Y6 more formal methods and the dreaded ‘long division’ in Y6 Again some ‘drill and practise’ but problem solving all the way. Check answers using the inverse-use a calculator! (but don't tell anyone!)

Common Problems with Division Remember like subtraction, it is NOT commutative, 14÷7 is not 7÷14! Practical, practical, practical… Do not take away visual or practical support too early. Confusing between sharing and grouping-can you grasp the difference? 12 sweets shared by three children, is it different to using groups of 3 to ‘make’ 12? Care with moving from the practical to the written, use horizontal methods with missing numbers etc, * ÷ 2=5 etc. Don’t use the ‘funny box’ shape until top end Y2 or Y3. Remainders can confuse, try doing practical problems, 9 children need to travel by car, can put 4 people in each car, how many cars do we need etc.

Primary Mathematics Key Stages 1 and 2 Multiplication and Division