1. Maths at St. Bons

3. Mastery Maths Lesson structure Concrete -> pictorial -> abstract
New equipment – double sided counters
- place value counters
- abacus
Marking policy

4. Bruner, Dienes and Skemp
Jerome Brunner – Concrete, Pictorial and Abstract
Zoltan Dienes – inventor of Base 10 materials and believer that we learn best through manipulatives, games story and dance
Richard Skemp – you have to have conceptual understanding of a principle before you can use it in practice

5. Lesson Structure

6. What does a ‘ping pong’ lesson look like?
Model how to create a maths lesson with all working using concrete material, then stop/start

7. What do ‘tiny steps’ look like?

8. What time is this, in the 12 hour clock?
B 10:2
C 10:10
D 2:10

9. What does ‘greater depth’ look like?
Year 1

10. What does ‘greater depth’ look like?
Year 2

11. What does ‘greater depth’ look like?
Year 3

12. What does ‘greater depth’ look like?
Year 4

13. What does ‘greater depth’ look like?
Year 5

14. What does ‘greater depth’ look like?
Year 6

15. Representation of concepts
Part part whole
Bar model
Set out 5 counters any way you want to……

17. KS1 Draw part part wholes to represent the mathematics in these:
Where is the whole? Where are the two parts?
SAT questions or practice SAT
Assume about ½ participants will not have come across PPW model

18. KS2 SATs 6 1 (Measures) (Money) (Number) (Statistics) (Geometry)
Find the structure of the maths questions – in each question the problem is in fact whole and then 3 different parts – where it is the third part which is unknown
Three numbers have a mean of 5.
One number is 6, one number is 1.
What is the third number? 6 1
(Statistics)
(Geometry)

19. Part part part whole
£20.00
£5.45
£7.50 ? 4m
150
1.28m
1.65m ? 90 40 ?
Three numbers have a mean of 5.
One number is 6, one number is 1.
What is the third number? 5 5 5 6 1 15
180 6 ? 1 38 38 a
Exposes structural similarities in questions which appear quite different at first glance

20. The Bar Model

21. Laura had $240. She spent 5/8 of it. How much money did she have left?
Overall percent correct:
Singapore: 78%,
United States: 25%
This is taken from a research article, which can be accessed on the web
Reference: Beckman, Sybilla. (2004). Solving algebra and other story problems with simple diagrams: A method demonstrated in grade 4–6 texts used in Singapore. The Mathematics Educator, 14(1), 42–46.
Ask participants to solve the problem any way they wanted.
Why were Singapore so successful?
They used a particular representation which
enabled pupils to access the structure of the
mathematics

22. Adam had 2 oranges for every 6 oranges that Ben had
Adam had 2 oranges for every 6 oranges that Ben had. If they had a total of 72 oranges between them how many did Ben have?

23. Adam had 2 oranges for every 6 oranges that Ben had
Adam had 2 oranges for every 6 oranges that Ben had. If they had a total of 72 oranges between them, how many did Ben have?
Adam 72
Ben

24. What other questions could you find the answer to easily?
How many did Adam have?
How many more did Ben have than Adam?
How many would Ben need to give to Adam to make them have an equal amount?

25. Problems to solve with your partner

26. 1) In a school, there are 240 children.
A quarter of the children are girls.
Altogether, how many boys are there in the school?
4) A computer game is £24 in the sale. This is one quarter off its original price. How much did it cost before the sale?
2) Amy had £24.
1/6 of her money was spent on a dress. ½ of her money was spent on a pair of shoes. How much money was left?
3) Peter has 4 books
Harry has five times as many books as Peter.
a) How many books has Harry?
b) How many books do they have in total?
c) How many more books does Harry have than Peter?

27. Proportion In a school, there are 240 children.
A quarter of the children are girls.
Altogether, how many boys are there in the school?
The whole school
240 children 60
Girls 60 60 60
???? Boys
240 ÷ 4 = 60 children
= 180 boys in the school

28. Proportion
Amy had £24.
1/6 of her money was spent on a dress. ½ of her money was spent on a pair of shoes. How much money was left?
£24
£24 ÷ 6 = £4 £4 £4 £4 £4 £4 £4
dress
Shoes ??

29. Multiplication Peter has 4 books
Harry has five times as many books as Peter.
How many books has Harry?
This image can also answer the harder questions such as:
How many books do they have in total?
How many more books does Harry have than Peter?

30. Fractions
A computer game is £24 in the sale. This is one quarter off its original price. How much did it cost before the sale?

31. Useful websites Thinking Blocks

32. The Bar Model