1. Mathematics
Workshop
2013

2. and why we’ve changed some things
What we’ve learnt,
and why we’ve changed some things

3. As part of our regular assessments within mathematics we identify;
How we found out..
As part of our regular assessments within mathematics we identify;
- Children making ‘above’ expected progress within a particular mathematical area
This helps us to identify how we can stretch their knowledge and understanding (for example, the child might have mastered a concept and be able to apply the skill. We then move the child carefully on to the next step).
Children making ‘average’ progress within a particular mathematical area
Children making ‘below’ expected progress within a particular mathematical area
We can then investigate the cause of this and, as appropriate, alter how these strategies are addressed

4. How we found out.. To find this out we….
Carry out informal assessments by;
- observing what children do without our help
- question them to identify how far their understanding reaches
- ask ‘how’ they know
Through;
- what they normally do in class
- monitoring by myself and external organisations/people
- the recording within their books

5. We identified... That some children answer questions literally
That some children struggle with understanding a lot of different approaches to a problem
- That some children were slow at calculating mentally

6. and what children do too
What you do,
and what children do too

7. Question 1
I have 28 apples in one hand and 57 apples in the other. What have I got..?
Big hands

8. Question 2
Find x.
Here it is!
4cm
3cm x

9. Answer 3
Write the number
one hundred and two
in digits.
1002

10. Place Value Simply – recognizing that the value of a digit is determined by its place in a number.
TH H T U Tenths Hundredths

11. Common mistakes… - Writing ‘one hundred and thirty six’ as 10036.
- Thinking that 6,000 is one more than 5099.
- Thinking that must be larger than 3.35 because it has more digits in it.
- Thinking that 0.75 is smaller than because 75 is smaller than 203.

12. Question 4
Sam has £1 in his pocket and apples cost 30p each.
How many apples can Sam buy? Show how you got your answer. 3.
Sam told me.

13. What we’ve changed,
and what we haven’t

14. How can you prove to someone that the answer to 9+6 is 15?
Some problems...
How can you prove to someone that the answer to 9+6 is 15?
Which is bigger… 23 or 32?
How do you know?
What is ?

15. How things develop across the school

16. Addition

17. Addition Counting using objects.
Jumping on a number line (of increasing size).
Using a hundred square to add 10. …

18. Addition Partitioning two digit numbers
Adding two digit numbers together (using any equipment, normally hundred squares)
Adding two digit numbers together (without equipment)
Adding three digit numbers together using above strategy.

19. Addition Using ‘empty’ number lines. More formal methods of addition.…
= 30
= 5
= 35

20. Addition Problems which do NOT involve the need to ‘carry’.
Problems which do involve ‘carrying’.
= (8 + 1) = (8 + 8)
( ) ( )
( ) ( )
= = 496

21. Addition
Further condensation of method.

22. Addition Adding decimals. Adding problems including brackets.
Algebra.
(4 + 7) x 3 =

23. Addition Condensing algebra. 4f + 7 = f + 16
4f + 7 – 7 = f + 16 – take 7 off both sides
4f = f + 94f – f = f + 9 – f take f off both sides
3f = 9f = divide both sides by 3

24. Subtraction

25. Subtraction Using songs and rhymes. Using pictures to take away.
Using number lines: ‘11 take away 7 is…’
Finding the difference between quantities.
Using number lines: ‘What is the difference between 11 and 7?’

26. Subtraction
Using hundred squares.
Subtraction as the inverse to addition.
Finding missing numbers, e.g. =
= 9
= 9
= 9
9 – 7 = 2
9 – 2 = 7

27. Subtraction Taking away using tens and units. 23 – 12 =
Using number lines.
47 – 11 =
22 – 7 =
16 – 9 =

28. Subtraction More formal representations.
87 – 32 = 55 because – 30 = 57
57 – 2 = 55
Formal written methods.
‘Borrowing’.

29. Subtraction
Decimal numbers
34.8 – 26.4 =

30. Multiplication

31. Multiplication Adding groups of equipment.
Understanding X as ‘lots of’.
Arrays.

32. Multiplication Partitioning numbers. Grid method.
6 x 124 = books were sold. Each book cost £6.
How much money was taken?

33. Multiplication Vertical method 124 x 6 24 (6 x4) 120 (6 x 20)
744
Grid method for larger numbers.

34. Multiplication
‘Short’ multiplication.
4 6 x

35. Multiplication
‘Long’ multiplication
Making it shorter…

36. Using multiplication facts
·It is vital that children know their times tables as all the work higher up the school relies on them knowing their tables.
·Tables should be learned at least 2-3 times a week.
What is expected
Year 2 2 times table
5 times table
10 times table
Year 3 2 times table
3 times table
4 times table
6 times table
Year 4 Derive and recall all multiplication facts up to 10 x 10 (5 second recall)
Years 5 & 6 Derive and recall quickly all multiplication facts up to 10 x 10 (5 second recall)

37. Division

38. Division
Practical sharing.
Counting on in ‘groups’.

39. Division
Introducing sharing.

40. Division
More complex grouping. and sharing.

41. Division Using number lines.
Knowing division as the inverse of multiplication.

42. Division
Remainders.
Using number lines confidently.

43. Division
Formal method.

44. Division
Remainders as a fraction.
Division of larger numbers.

45. Division
Division including decimals.
‘Bus Shelter’ method.

46. The models that we use, and why we use them

47. Partitioning
Children need to understand that in 102 there is one lot of one hundred, zero lots of ten and two units. Zero ‘holds’ the place of the tens.

48. 3276 3000+200+70+6 Partitioning So 52 x 3 becomes 50+50+50 and 2+2+2 …
Breaking a number up according to its place value. (typically to make addition and multiplication easier).
3276
So 52 x 3 becomes and …

49. How you can support mathematics learning at home

50. What can I do at home?
As well as looking at these strategies at home (in this order), you could…
Play number games.
Recognise numbers around shops and the environment.
Ask for an amount of something.
Make number patterns (e.g. one apple, two oranges, three bananas)
Use dice – count the dots quickly, predict bottom number on die, difference between two rolls…
Which number is missing?
Guess the number (it’s one more than 5, it’s between 100 and 150)
Share an amount between 2, 3, 4 people.
Count backwards and forwards from a given two-digit number.
Estimate total of something by rounding to 10, 100, etc.
Experiment with shapes through painting, ‘spot the shape’, patterns

51. What can I do at home? Measures. Cooking!
Count up money to find a total. Work out change from shop.
Telling the time.
What time will it be one hour from now?
How long have you spent doing something?
What can you do in one minute?
Times tables!

52. What can I do at home?
A prominent clock in the kitchen – ideally analogue and digital.
Display a traditional calendar, and refer to it.
Board games that involve dice and spinners – helps not only with counting but with the concepts of chance.
Traditional playing cards – simple games such as snap are a natural way of learning about sorting and chance.
Dominoes – to help with number combinations.
Using a calculator, for example when shopping. This shouldn’t be seen as a way of ‘cheating’ – just a way to save time. We use these in class to save time to focus on what is really happening.
Measuring jugs with scales / kitchen scales.
Dried pasta…or Smarties! – useful for counting large collections to investigate remainders etc.
Tape measure and ruler – involve your child in ‘real life’ situations.
An indoor / outdoor thermometer.

53. What can I do at home? www.funwithspot.com
Great interactive maths games for KS1
Counting, matching etc for KS1
Challenging activities for KS1
Great site for learning time, includes an interactive clock
Learning basic maths skills
Maths games, puzzles and activities
General websites:
Lots of problem solving activities  
A tool for making and customising maths puzzles   
Fun maths games
Good KS1 maths site
Maths games, quizzes ,and problem solving activities

54. Any questions?