1. Lower School Curriculum evening
Mathematics
Mastery
Maths for all
Active
Engaging
Fun
Need whiteboards and pens, a4 paper with tens frame, pot of double sided counters, pot of 5 tens and 2 ones

2. Where’s the maths in that?
Interesting maths facts
Da vinvi code –way flowers grow?

3. Attitudes Towards Maths
Maths is everywhere
Noticing patterns
Not just number crunching
Everyone is a mathematician!
A can do attitude
Value the importance of maths and a positive attitude towards maths learning

4. What is mastery?
If you drive a car, imagine the process you went through…
The very first drive, lacking the knowledge of what to do to get moving
The practice, gaining confidence that you are able to drive
The driving test, fairly competent but maybe not fully confident
A few years on, it’s automatic, you don’t have to think about how to change gears or use the brake
Later still, you could teach someone else how to drive or drive in any situation

5. What is mastery of mathematics?
Mastery in mathematics is similar.
It involves:
Deep and sustainable learning
Ability to build on something already mastered
Ability to reason about a concept and make connections to other concepts
Procedural and conceptual fluency (can’t solve problems without these)
The understanding of how and why it all works
Mastery is a continuum… mastery at a particular point of time that is sufficient mastery for that stage of learning and then built on at a later stage

6. Concrete Pictorial Abstract (CPA)
These stages are continuous
Some children may need all stages
Some children may go through all stages quickly
Vary through topics 
Therefore, it is important that a variety of representations are available for children to use at all times.
Sometimes children will need to touch and manipulate, but at other times simply seeing or imagining the representation will be enough.
Using objects that can be moved, grouped and rearranged to help them make sense of a problem (plastic fruit, counters, cubes etc.)
Meaningful pictures/ drawing them
Numbers or symbols

7. Resources and Representations of Mathematics
Resources to help build concepts

8. Teaching for mastery Factual knowledge Conceptual Understanding
Procedural fluency
Language and communication
Thinking mathematically

9. 1. Factual knowledge Number bonds Doubles and halves Times tables
5 + 3 = 8
6 + 4 = 10
Doubles and halves
Times tables
Being fluent with this knowledge
Quick recall
Using known facts to work out others

10. 2. Conceptual Understanding

11. 3. Procedural fluency

12. 4. Language and communication

13. 5. Mathematical thinking

14. Addition lesson Use your tens frame to help you
How did you work it out?
Can you find a different way?
Word problem adding three numbers maths no problem
Add on tens frames
How many different ways?
Use your ten frame
Write you answers.
Demonstrate number line
Demonstrate related facts –
Two digit
Inverse
Parents need an A4 sheet with 3 tens frames on it and a pot of two sided counters

15. Count all the counters
Any other ways?

16. Partitioning How many different ways can you partition 52?
Parents to have 5 tens and 2 ones in a pot beneath chair
Exlpain how paritioning then leads into more formal written calculation – ability to manipulate number is really important

17. Partitioning to help with division
52 =
40 ÷ 4 = 10
12 ÷ 4 = 3
52 ÷ 4 = 13

18. Mastery Maths Mastery curriculum
Going deeper and broader
Concrete – Pictorial – Abstract (CPA) approach
Contextualising and making deep connections in maths
Demonstrating different ways to solve the same problem
Reasoning and explaining
Making generalisations
“I can see a pattern!” – the excitement they have when they can prove and explain a concept
Messy maths – giving children the skills to explore and discover patterns for themselves
All say – we always talk in full sentences
Spot the mistake
Odd one out
Concept and non concept

19. Making Generalisations

20. Number blocks

21. Whole part part

22. The bar model… • It is a mathematical representation of a word problem
• It is a representation that reveals the structure of a word problem
• A way of ‘acting’ out a problem
• It is not a calculating tool, it is a visulising tool a b c

23. The relationship between addition and subtraction
a = b + c
a = c + b
a – b = c
a – c = b
Part / whole relationships

24. Using a bar model £84 Spiky has 3 times as much money as Curly
Together they have £84
Ask parents to use strips of paper to show a picture of the problem so far
£84

25. How much more money does Spiky have than Curly?
What do we need to work out?
84 ÷ 4 = 21
40 ÷ 4 = ÷ 4 = ÷ 4 = 1
£84

26. How much more money does Spiky have than Curly?
Each part is worth £21
£21
£21
£21
£84
£21
Spiky has £63 and Curly has £21
£63 - £21 = £42 OR £21 + £21 = 42
Spiky has £42 more than Curly

27. Mathematical skills in Primary aged children
Fluency
Reasoning
Problem solving
Procedural and conceptual mathematical understanding
Pupils are encouraged to explain their thinking, prove why an answer is right or wrong, find more than one way to solve a problem and convince their peers that their answer is correct

28. Cross curricular maths
Maths is everywhere!
Early Years PE
Topic
Science
Computing
Art
Just as we teach literacy across the curriculum, we teach maths across the curriculum too!

29. Your turn!

30. How can you support at home?
Maths learning can happen anywhere
Look for maths problems you can solve together
Some examples:
Follow a recipe
Talk about the weather forecast
Going shopping
Planning an outing
Maths is all around us and problem solving is at the heart of the mastery approach.

31. Think and talk like a mathematician
Mathematics language often uses common words in a new way. For example, ‘difference’, ‘right’, ‘product’, ‘table’.
Always encourage your child to explain how they have gone about solving a problem, and work with them to test, prove, explain, reflect and spot patterns.
Communicating and discussing maths problems (in a way that others can understand) demonstrates depth of understanding
Questioning and prompts can be powerful tools to boost your child’s mathematical thinking: ‘What do you think…?’ ‘Why …?’ ‘What will happen if…?’ ‘What do you notice about…?’ ‘Can you see a pattern between…?’ ‘What if we try…?’

32. Questions?

33. For handout How can you support at home?
Maths learning can happen anywhere. Maths is all around us and problem solving is at the heart of the mastery approach. Look for maths problems you can solve together, making connections between what your child has been learning at school and the world around them.
Follow a recipe: work together to find out the quantities needed, ask your child to weigh the ingredients, discuss how you’d halve or double the recipe and discuss the ratio of ingredients.
Talk about the weather forecast: is today’s temperature higher or lower than yesterday’s? What do the numbers mean?
Going shopping: talk about the cost of items and how the cost changes if you buy two items instead of one. Let your child count out the coins when paying and discuss the change you get back. Use coins to explore addition, subtraction, multiplication and division.
Planning an outing: discuss how long it takes to get to the park, and so work out what time you need to leave the house. Encourage your child to work out the best solution based on the time and distances. Discuss what shapes you see when you get there.

34. For handout Think and talk like a mathematician
Mathematics language often uses common words in a new way. For example, ‘difference’, ‘right’, ‘product’, ‘table’.
Always encourage your child to explain how they have gone about solving a problem, and work with them to test, prove, explain, reflect and spot patterns. Questioning and prompts can be powerful tools to boost your child’s mathematical thinking: ‘What do you think…?’ ‘Why …?’ ‘What will happen if…?’ ‘What do you notice about…?’ ‘Can you see a pattern between…?’ ‘What if we try…?’
Communicating and discussing maths problems (in a way that others can understand) demonstrates depth of understanding – another fundamental aspect of mastering mathematics.