How could you adapt these for your year group? What skills / knowledge does this activity help practice? How could you use this activity to teach a different skill? What resources could you provide pupils with to help them tackle this problem? addition subtraction resources

What is mastery in mathematics? What do some of the key principals look like in the classroom? How can we move towards mastery teaching?

What does it mean to master something?

I know how to do it It becomes automatic and I don’t need to think about it – riding a bike I’m really good at doing it – painting a room I can show someone else how to do it

Mastery in mathematics means more… Deep and sustainable learning The ability to build on something that has already been sufficiently mastered The ability to reason about a concept and make connections Conceptual and procedural fluency

What are the principals of primary mathematics teaching for mastery? Based on NCETM research of East Asian primary mathematics teaching Read some of the key principals on the cards. Discuss with colleagues whether you consider them to be: – Challenges – Opportunities or – Existing practice

Reasoning Full sentences Mathematical vocabulary

paper tapes were broken, can you guess which original paper tape is longer? Why? How do you get your answer?

If the rectangle is the whole, the shaded part is one third of the whole. I say, you say, you say, we all say

Which line is longer? First ： Second ：

Whole class Continual formative assessment Rapid intervention Questioning Additional practice

What are the challenges of teaching the whole class the same thing?

When should interventions and extra practice take place?

‘Every lesson, every activity, every question should be seen as assessment.’

Plan enough time for depth Sequence content carefully Focused, sharp learning objectives

Maths curriculum planning: Suggested time allocation YEAR 4 term 1 term 2 term 3 term 4 term 5 term 6 week 1 place value assessment + position and direction addition and subtraction assessment + measurement multiplication and division assessment + time fractions, decimals, percentages assessment + position and direction fractions, decimals, percentages assessment + time assessment week 2 number: place value calculation: + and - calculation: x and ÷ fractions, decimals and percentages revision of all content week 3 number: place value calculation: + and - calculation: x and ÷ fractions, decimals and percentages revision of all content week 4 number: place value calculation: + and - calculation: x and ÷ fractions, decimals and percentages revision of all content week 5 number: place value calculation: + and - calculation: x and ÷ fractions, decimals and percentages revision of all content week 6 place value assessment + properties of shape addition and subtraction assessment + properties of shape multiplication and division assessment + properties of shape fractions, decimals, percentages assessment + properties of shape fractions, decimals, percentages assessment + properties of shape assessment + properties of shape homework focus reading, writing, ordering numbers number bonds mental recall of + - facts mental recall of x and ÷ facts mental recall of fractions, decimals and percentage facts mental recall of x and ÷ facts as applicable to revise / consolidate areas of study to be used as contexts measurement statistics perimeter (KS2) measurement area (KS2) volume (KS2) measurement as applicable to revise / consolidate

How would we break this learning down? What would be the best sequence to teach it? StrandContent domain reference Number: Addition and subtraction 3C1 add and subtract numbers mentally, including:  a three-digit number and ones  a three-digit number and tens  a three-digit number and hundreds 3C2 add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction 3C3 estimate the answer to a calculation and use inverse operations to check answers 3C4 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

Intelligent practice Variation Structures Representations Making connections

Intelligent practice ‘avoid mechanical repetition and create an appropriate path for practising the thinking process with increasing creativity’ [Gu, 1991] facts, concepts, procedures taught in an integrated way develops and embeds fluency promotes deep, sustainable learning mix of ideas in contexts and the abstract / symbolic comparisons are key plan for misconceptions – teach, learn, confuse!

Take a number ending in 7 and add 6 Repeat for another and another………. What do you notice? Answer the following: = 1, =

3 + □ = □ = □ = □ = 11

25

Seeing pattern and structure is important in a mastery curriculum

Make = = = = = = = 7

Part Part Whole

= = = = Identification of relationships and making connections supports depth and sustainable learning and paves the way for later learning 35

>

Structures of addition AggregationAugmentation

Structures of subtraction PartitionDifferenceTake away 12 8

Maths mastery = Fluency What does it look like? efficient accurate flexible appropriate How do we achieve it? DEPTH intelligent practice variation time structures knowledge reasoning connections

Teaching for Mastery

TASK 1 Look at your year group expectations for addition and subtraction Make a plan for how you are going to break these down over the 4/5 weeks allocated for this Think about the best sequence and what you expect all pupils to be able to do by the end TASK 2 Design an assessment activity to be used both formatively and summatively for the addition and subtraction expectations for your year group Remember to include variation, different contexts and opportunities to check for depth of understanding Use resources suggested