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

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

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

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

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.

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)

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.

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)

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.

Children can only explain their reasoning if they have the words. https://www.ncetm.org.uk/resources/49824

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.

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.

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

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.

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

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 7 + 5 rather than 7 + 4 (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

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

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)

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 …

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?

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.

Venn Diagram of CPA here 5 minutes – Collaborative

Next slide resources -

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

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

Organisation & Displays

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

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 …

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

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

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.