1. Mental and Written Calculation Multiplication and Division
SCITT Day
Mental and Written Calculation
Multiplication and Division

2. Today we will…
Review the National Curriculum approach to multiplication and division using mental methods, informal jottings, written methods and calculators;
Review aspects of measures – conversion of units x and ÷ by 10, 100, 1000;
Explore the role of calculators in the primary classroom.

3. Associated Issues
Review all aspects of your own mental methods of calculation for multiplication and division
Why and how do the different methods work?
Assess which calculation methods are accurate, reliable and efficient.
Differentiation in mathematics

4. ‘Differentiation’ What does ‘differentiation’ mean?
‘Constitute a difference between’
‘Render unlike’
(Penguin English Dictionary)
How would you define it in educational terms? Different types?

5. ‘Mathematical’ Differentiation
By Number
Boxes 100
By Operation
Using digits 1, 2, 4 and 8, what number sentences can you make using addition?
By Rules
Magimixers
By Parameters/ Criteria
‘Card tricks’ Challenge

7. Exchange Boards - decimals
To review our learning of using exchange boards…
Can you:
= – 2.7 =
= – 1.78 =
What are the concepts of PV we are highlighting?

8. National Curriculum Expectations
What are the expectations for x and ÷ in your year group?
Language?

9. Multiplication Julia Anghileri (2009):
“Children’s first experiences of multiplication arise when they make groups with equal numbers of objects and recognise the possibility of counting groups rather than counting individual items.”

10. Words/ phrases x and ÷ dividend divisor quotient product divisible by
groups/ sets/ lots of
Divided into
divided by
multiple
factor
‘timesed’ by
remainder / left over
sharing
sharing equally
how many times…
array
row
column
repeated addition/ subtraction
Double/ half
one/ two/ three… each
inverse

11. Learning Tables
What have you already seen being done in class to support the learning of times tables?
The following ideas are from:
‘Teaching Children to Calculate Mentally’ DfE 2010

12. Six two’s… 2, 4, 6, 8, 10, 12
12 dots can be represented as…
Make cards showing calculation on one side, the answer on the other

13. Times tables grid & games!!
Models and images
How could you use equipment to develop understanding in multiplication?
What have you (seen) used successfully?
What language would you use?
Times tables grid & games!!

14. Multiplication - Repeated Addition
‘5 groups of 3’
or 3 x 5
We read 3 x 5 as ‘3 multiplied by 5’
(since the 5 is operating on the 3)

15. Multiplication - Scaling
Increasing a quantity by a scale factor.
Multiplication by 5 makes it 5 times as big.
‘Scaling 3 by a factor of 5’
‘Scaling 3 by a factor of 0.5’

16. Pictures of x tables “6 times 7” “6 groups of 7” “6 lots of 7”
Let’s consider… “6 x 7 =”
“6 times 7” “6 groups of 7”
“6 lots of 7”
“6 multiplied by 7”
“the product of 6 and 7”

17. Other facts! 5 x 7 = 35 6 x 7 = 35 ÷ ? = 7 7 x 5 = 35 35 ÷ 7 =
35 ÷ 5 = =

18. Secrets for Cheating at x tables
Secret 1: If you know one fact, then you know a second. Secret 2 X tables always give you a buy one, get three free offer. Secret 3: If you can double, then you can multiply by 2, 4 and 8. Secret 4: If you can multiply by 1, then you can multiply by 10. Secret 5: If you can halve, then you can multiply by 5. Secret 6: If you use fingers, then you can multiply by 9 Nines in your head: Multiply by 10 and then adjust Secret 7: If you know the 3 times table, then you know the 6 times table.

19. You Tube http://www.youtube.com/watch?v=yXdHGBfoqfw
Search: ‘Times tables in 10 mins’

20. Maths Appendix NC2014
Look at the formal written methods of multiplication.
Talk through the first example of short multiplication…

21. What skills are required for written methods of multiplication?
Recognise the size and position of numbers
Count on in different steps 2s, 5s, 10s
Double numbers up to 10
Recognise multiplication as repeated addition
Quick recall of multiplication facts
Use known facts to derive associated facts
Multiplying by 10, 100, 1000 and understanding the effect
Multiplying by other multiples of 10 (e.g. 20, 30…)

22. Multiplication x 13 = 10 3 60 18
= 78 6
so 6 x 13 = 78

23. Division – Equal Sharing
This corresponds to finding a fraction…
Each group is 1/3 of 12
So ⅓ of 12 Ξ 12 ÷ 3
‘Divide 12 into 3 equal parts or groups’

24. Division - Grouping How many groups of a given size…
‘How many groups of 3 are there in 12?’

25. Division - Grouping ‘How many 3’s make 12?’
How many groups of a given size…
‘How many groups of 3 are there in 12?’
This grouping model may involve repeated addition or repeated subtraction
‘How many 3’s make 12?’

26. The language of division
Should always use the language ‘divided’
18 ÷ 3 = “18 divided by 3”
Sharing – “18 divided between 3”
Fraction – “18 divided into 3 equal parts” (or groups)
Grouping – “18 divided into 3’s”
With a partner, agree a range of models you could use for each example.
Are there any limitations with each method?

27. ?! How would you say ‘6 ÷ ½’? “Share 6 between ½”
“How many ½’s make 6?”

28. Maths Appendix – Division examples
Can you talk through the examples for Division?
What language would you use?

29. Short Division
How could Exchange Boards help us?
94 ÷ 4 =

30. Task 2: Hand in Day 4
Work with a group of children on a task involving calculation (examples from relevant year group expectations).
What different calculation strategies/ methods are they familiar with?
Discuss with pupils different models & images they utilise to explain HOW they did the calculations? (With KS2 children you might be able to explore alternative methods and discuss ‘efficiency’.)

31. Task 2: WILF OUTCOMES
be aware of the range of calculations that children might do mentally and/or with paper and pencil recording
listen to children’s explanations/ reasoning
annotate children’s work to show their thinking
consider next steps (including other models and images you could/would introduce)
show an awareness of any errors/ misconceptions and how they may be addressed