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

Where’s the maths in that? https://nrich.maths.org/7414 Interesting maths facts Da vinvi code –way flowers grow?

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

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

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

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

Resources and Representations of Mathematics Resources to help build concepts

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

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

2. Conceptual Understanding

3. Procedural fluency

4. Language and communication

5. Mathematical thinking

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 8 + 5 on tens frames How many different ways? Use your ten frame Write you answers. Demonstrate number line Demonstrate related facts – 80 + 50 Two digit 48 + 35 Inverse Parents need an A4 sheet with 3 tens frames on it and a pot of two sided counters

Count all the counters Any other ways?

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

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

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

Making Generalisations

Number blocks https://www.bbc.co.uk/iplayer/episode/b08dr1l3/numberblocks-series-1-the-whole-of-me

Whole part part

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

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

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

How much more money does Spiky have than Curly? What do we need to work out? 84 ÷ 4 = 21 40 ÷ 4 = 10 80 ÷ 4 = 20 4 ÷ 4 = 1 £84

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

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

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!

Your turn!

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.

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…?’

Questions?

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.

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.