Maths at Cawood School September 2016

What does it mean to master something? Deep and sustainable Conceptual and procedural fluency Ability to build on knowledge Ability to reason and make connections Be flexible thinkers – think about things in different ways

Maths mastery – what is it? Teachers reinforce an expectation that all pupils are capable of achieving high standards in mathematics

Teaching is supported by carefully planned lessons and resources to develop deep conceptual and procedural knowledge

The large majority of pupils progress through the curriculum content at the same pace. Differentiation is achieved by emphasising deep knowledge and through individual support and intervention

Sally knows all her tables up to 12 x 12 When asked what is 13 x 4, she looks blank - Does she have fluency and conceptual understanding?

High quality materials to support classroom teaching include the use of textbooks. Maths No Problem had been trialled by Maths Hubs around the country with very positive results and last year we invested in the programme.

Teachers also use their subject knowledge and experience, alongside guidance from e.g. NCETM to plan and teach lessons precisely

Mastery Approach to lesson design Pupils work on the same tasks and engage in common discussions. Precise questioning enables children to develop fluency and think about underlying mathematical concepts. Differentiation occurs in the support and intervention provided – not in the topics taught.

https://www.youtube.com/watch?v=PfPcn3SohrI Singapore maths Dr Ban HarYeap

Giza NOT Pisa

5 3 2 Use of number bonds and the number bond diagram make number bonds on tens frames 3 2

Making number bonds Lesson 1 Lesson 1 In focus Do as an anchor task How many cupcakes are there on each plate? Is there another way to put the cupcakes on the two plates?

Making number bonds Let’s Learn 2 5 3 1 2 and 3 make 5 This is a number bond

Making number bonds

Making number bonds

Making number bonds Do this one. Discuss using egg boxes and buttons at home

Making number bonds Guided Practice What do they notice - talk about variation

Depth at Y1 5+2=7 2+5=7 7-5=2 7-2=5 7 5 2

Addition Drop counters into a container. Add on or take away counters. Reception Children are encouraged to: Find one more than a given number Relate addition to combining two groups Start to put ‘largest number in head’ and count on All exploration is encouraged through play. Lots of counting in different contexts takes place Drop counters into a container. Add on or take away counters.

Use coat hangers and pegs to model addition and subtraction to 10

As children’s experience grows of using numbers to 20 and beyond, they begin to understand place value in two-digit numbers. For example, they count 17 straws, use an elastic band to group together a bundle of ten and identify that they have one bundle of ten and seven single straws. children’s experience grows

Children are encouraged to ‘decompose’ and recombine numbers to find the answer

Children learn number bonds – the numbers that add together to make 10, 20 etc. 10 + 0 = 10, 9 + 1 =10, 8 + 2 = 10

Lesson Objective: To be able to add a single-digit number to a 2-digit number without regrouping the ones. Lesson Approach: Use baskets or ten frames to replicate the problem found in the anchor task. Ask pupils to add 3 more into one of the baskets. In which basket should we put the 3 extra apples? Discuss why it is more useful to add the 3 apples into the basket that has 3 apples rather than the baskets that have 10. Show how we add 3 more by using a number line with 25. Explain that in this question the only part of the number 25 that changes is the units and not the tens. Show how we can add 3 to 25 by using ten blocks and unit cubes and the standard column method. Make sure the concrete element is simultaneously modelled with the column method. National Curriculum: Add numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones.

Subtraction   Children explore subtraction as ‘take away’, keeping all items visible e.g. 5 ladybirds on a leaf and two fly away.

Multiplication Children count in repeated groups of the same size -making use of repeated addition in real life examples, e.g. there are four teddies in a row; pick out the pattern in eyes 2 + 2 + 2 + 2 Use of counting games in 2s

Models for multiplication Lots of the ‘same thing’ Bead Bar Number Line 6 9 12 3 “12” “3” “6” “9” Fingers

Children have lots of practice doubling and halving numbers and relate this to the 2x table Children use arrays (a picture representing a number) and repeated addition 2 x 4 = 2 + 2 + 2 + 2

They then extend to different numbers and show examples of division facts 5 x 4 = 20, 4 x 5 = 20, 20 ÷ 5 = 4, 20 ÷ 4 = 5

Division Children use real life examples of division as sharing – sharing objects into equal groups Children begin to use examples of division as grouping e.g. putting wellies into pairs, pairing socks, putting two smarties on a cake etc.

Children begin with halving and relate this to dividing by 2 Children begin with halving and relate this to dividing by 2. They may also use number lines and count the number of hops that make a number, making the links clear between multiplication and division

Children understand division as grouping. They use practical examples e.g. putting items into a bowl. How many groups of 2, 3, 4 etc can I make from 12? Count back into the bowl – one group of 3, two groups of 3 etc. There are 6 sweets. How many people can have 2 each? How many groups of 2 make 6?

Take every opportunity to count! in 1s, 2s, 10s, 100s forwards and backwards and starting from a different number e.g. 3,5,7,9… 11,9,7,5,3… Counting activities are very important and feature as part of our maths work throughout school. T Try looking at house numbers when you are out walking – what do they notice about the numbers? Can they guess which number might come next? Count how many steps there are between your house and school. Count on car journeys – start at different numbers, count forwards and backwards. Can you start at 50 and count on/back in 5s?

Talking through ideas Talking and sharing our thinking and reasoning is very important support that we can all give to children in their maths work, e.g. “That’s a triangle because it’s got three sides.” “ I know that... Because...”

Maths at home through play Try playing number games with playing cards, dominoes and board games such as snakes and ladders or Lotto. Useful materials would include dice, counters e.g. pennies or buttons, uncooked pasta or building bricks. When playing cards you can vary the games e.g. taking cards from the centre – first to 20, finding pairs, adding pairs. Dominoes – play traditionally or try spreading them face down - each player chooses a domino at the same time. Add the two numbers on the domino together. Whoever has the largest number gets to keep both dominoes. The person with most dominoes wins

Time Children needs lots and lots of experience looking at clocks and telling the time – far more than we can devote to it at school O’clock, then half past, then quarter past and quarter to How much time has gone by/ how long is it to...

Money Lots of experience in handling money is needed: Value of different coins Which has the most/least value How many pennies = 2p, 5p,10p, 20p? Etc How much change will they get? Use real money – play shops Talk about the cost of items when shopping Let children hand over money and receive change when shopping