1. Concrete Pictorial Abstract Key Stage 1 Mathematics Session 2
Lyne & Longcross
Concrete Pictorial Abstract Key Stage 1 Mathematics Session 2

2. Make bonds for 10 using the maths resources on your table.
How many different representations can you show?
Make bonds for 10 using the maths resources on your table.
Playing cards, dice, rods, double sided counters, numicon, bead strings, pegs, ten frame, number lines, part-part whole, objects (bus)

3. Concrete Pictorial Abstract Key Stage 1 Mathematics Session 2
Lyne & Longcross
Concrete Pictorial Abstract Key Stage 1 Mathematics Session 2

4. Aims of the session Revise theory underpinning CPA
Moving through the different stages
Steps to mastery
Planning and structuring lessons
Importance of reasoning
Organisational tips

5. What happens if? Children get stuck … How do you know they are stuck?
How do you help them?
Discussion and share ideas
Think of a child in your class. Why are they reliant on concrete? Have they been exposed to other representations?
relate concrete to pictorial and abstract representations?
Stuck in concrete, stuck in pictorial, stuck in abstract
Relationship between various representations

6. What happens if? Do they know the way out? CPA is not linear
C to P to A should not be a “leap of faith”
Must model and not make assumptions
When first introducing a topic show concrete and explore understanding
Then model pictorial and how that relates to the concrete
Verbalise your thinking using the correct terminology and a range of terminology
Finally link to abstract however constantly refer back to and show various representations and how they link
Students should be confident moving between and be able to relate various representations to one another
if children are exposed to different representations the whole time, their journey is mapped out for them.

7. My experience is the limit of my world.
If you have provide one view, that is the only way the students will see it.
My experience is the limit of my world.
Provide lots of different representations
Piaget (Showing lots of ways for deeper understanding)

8. They will be “stuck” in that representation.
If you have provided one view, that is the only way the students will see it.
Provide lots of different representations
They will be “stuck” in that representation.

9. My language is the limit of my world.
If you have provide one view, that is the only way the students will see it.
My language is the limit of my world.
Provide lots of different representations
Piaget (Showing lots of ways for deeper understanding)

10. Children can only explain their reasoning if they have the words.
National Numeracy Strategy (1999)
Vocabulary books – By year group
Model the full range of language – maths talk.

11. Children can only explain their reasoning if they have the words.

12. I can … Build it Draw it Write it … and explain it.
Reasoning and depth of understanding
Using a range of resources – prove understanding
… and explain it.

13. What do they know? Both of these look the same from the surface.
At first it may appear as if a children does understanding when showing in only one representation.
When expressing understanding using a different representation, depth of understanding is uncovered.
‘Can you show me another way?’
Unless you ask the right question you wont know until they move on to something new.

14. Lucy and Layla place value
Lucy and Layla – Year 2 this year (Autumn term)
Lucy – Blonde hair
Both working below –
Have strengths in different areas
In SATS achieved age related but unsure where to plot them
Watch both children at the start and notice how they are ordering

15. What do they know?
Unless you ask the right question and use a range of concrete materials you wont know.
What questions could we ask?
The difference between a superficial understanding and mastery is their depth of knowledge.

16. Avoiding getting stuck…
Not linear / in isolation
Represent alternatives
Model language
Plan questioning to spot misconceptions / gaps.
What story does that tell?
Prove it!
How do you know?
Concrete
Pictoral
Abstract

17. Planning: Big Picture - Little Steps
Assessment and observation Use assessment to drive planning.
Careful questioning (reasoning)
How? Why? Why not? What if? Can you prove it? Show me. Did anyone find another way? (Little Teacher)
Remember to use complete sentences
Plan for misconceptions, for example
Build on known number facts (4 x 2 rather than 3 x 8)
Use every opportunity: - ask rather than (if the total is 11 you lose an opportunity to check place value understanding) - avoid questions like 8 – 4 (the same digit appears twice)
Assessment eg links to Lucy and Layla video on next slide

18. Anne’s little steps for ordering numbers to 100
1. Compare 2 numbers and say which is the greatest/smallest
Firstly, with the same number of tens eg 46 and 48
Then with a different number of tens but the same units eg 38 and 48
Then with different tens and different units eg 34 and 42
Make the numbers with resources (numicon or place value) and explain why it is greater or
smaller Eg 42 is greater than 34 because it has more tens or 40 is greater than 30
2. Order numbers when all the numbers are given between 2 multiples of 10
Eg 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50
4. Give some 2 digit numbers between 2 multiples of 10 and then order
Eg 40, 42, 44, 45, 48, 49
5. Order numbers when given all the numbers in a range when crossing the tens
Eg 47, 48, 49, 50, 51, 52, 53
6. Order numbers when they have a different number of tens but the same units
Eg 8, 18, 28, 38, 48, 58, 68, 78, 88, 98
7. Order numbers when they have a different number of tens and different units
Eg 4, 12, 27, 36, 48, 52, 63, 75, 87, 93
8. Repeat step number 8 with some tricky numbers
Eg 4, 14, 27, 36, 41, 52, 63, 70, 87, 93
9. Repeat the above and this time give them one number with the same number of tens to put in
the correct order eg where would 57 go?
10. Order a selection of 2 digit numbers with any number of tens or units
Lucy and Layla video

19. Planning: Big Picture - Little Steps
Don’t always work towards the “answer” Work back from the total. How did I get there?
… in fact, how did you get here?
Freddies video (Working forwards and backwards)

20. Unpick your own reasoning
How did you get here today? What route did you take? What resources did you use? What was your reasoning? Discuss with your partner …

21. Unpick your own reasoning
How did you get here today? Did you use the same method as your partner? You are both here, so are you both right? Did you use a map/Google? Were you just following instructions or did you internalise and learn the route? Could you teach someone else how to get here? How deep is your knowledge?

22. Bonds to 10
Your turn ...
Use the Venn template to outline what you could use to teach bonds to 10.
Annotate with questions and ideas.

23. Venn Diagram of CPA here
5 minutes – Collaborative

24. Next slide resources -

25. Organisation of resources
Planning and organisation go hand in hand
You can have the best lesson but without organisation time is spent finding and putting away resources instead of learning.
Expectation and responsibility (shared)
Students need to have ownership
Every classroom will look different depending on the needs of the children
Good organisation keeps up the pace and engagement
Role play/hands on area
Table layout
Games and activities

26. How do I store digit cards without them getting muddled up?!
Organisation
Write the sticky notes
One wish – for organising your classroom
One top tip to share
One challenge you struggle with
How do I store digit cards without them getting muddled up?!
Sharing one wish, top tips, challenge
Discuss with people around you
Share top tips

27. Organisation & Displays

29. Organisation top tips
Labelling/photos (see through containers if possible)
Grouping resources together
Plastic bags and small containers
Enough resources (don’t plan for what you don’t have!)
Quality resources
Whiteboard with photo is corner
Laminate once, use often
Have post it and sticky notes ready
Next session: Online resources and FREE internet sources

30. Classroom Visuals What are the visuals for? Referred to often
Children's work and children's talk
Sign posting
Printed out/personalised (Twinkl et al) and real class examples
Child height
Must haves: numbers in order, hundred chart …

31. Classroom Visuals Not wall paper / working walls
Learning objective visible
Big paper to show working (save it, don’t wipe it out!)
Interactive displays
Photocopy whiteboards
Print screen Notebook

32. Planning time
Teachers have time to plan a lesson to teach before the next session

33. And finally … Next week please bring:
Examples from the lesson you started today; photos, resources, books etc.
Bring 3 student maths books.
Your school Calculations Policy.