Addition and Subtraction Oct 2016 SCITT Day 3 Addition and Subtraction Oct 2016

Day 3 - We will… •Study the NC2014 approach to addition and subtraction including using concrete manipulatives and/or recording of mental methods, informal jottings and formal written methods; •Consider how the use and complexity of number lines progress through the primary years Associated Issues for Teaching Review all aspects of own mental methods of calculation for addition and subtraction Developing different layers of understanding in calculation using the CPA approach Why and how do different strategies work? Making links - Measurement – measuring and reading scales.

Reading Firstly - share your own readings… Then discuss: Mental calculation methods Informal jottings Written methods …and what links were made for progressing between i, ii and iii? Were connections made between addition and subtraction ? Overall: Were there any key pedagogical messages for teaching and learning? GROUP READING: ‘Issues in Teaching Numeracy in Primary Schools’ [Second Edition] Chapter 13 - The empty number line Chapters 12/14 mental and written calculation; Ian Thompson ‘Mental Calculation’ ‘Deconstructing the PNS approach to addition Part 1’ ‘…subtraction Part 2’.

Write the Roman Numerals on the clock face…

+/- ‘fundamentals’ in ks1

+/- ‘fundamentals’ in Lks2

+/- ‘fundamentals’ in Uks2

Additive reasoning When to do a particular type of calculation How to carry out the calculation Knowing how and knowing when are not that simple! Q: Is the chosen method effective? Is it efficient?

Progression when calculating (+/-) Counting Early stages of mental calculation and learning number facts Working with larger numbers and informal jottings Non-standard expanded written methods Standard written methods What have you seen in your classroom so far?

NC2014– year by year NC2014 year group expectations... How does learning progress from EYFS to Ks2? Where does your year group fit in? What links to your reading? Is progression clear: mental with jottings  expanded  written? Keep these age-related expectations in mind to adopt/ adapt today’s key messages

Why teach mental arithmetic? Real life done in the head Creates creative and independent thinking Develops better problem solving skills Develops number sense Basis for estimation skills Progression of informal to formal written

Ian Thompson - 1999 “One of the reasons why teachers should discuss children’s mental strategies in the classroom and get them to try out each other’s methods is to legitimate the use of personal (as opposed to ‘school approved’) strategies. Teachers need to be aware of the range of available methods, not so they can formally teach them, but to enable them to support children who are developing proficiency with a particular strategy…” http://www.ianthompson.pi.dsl.pipex.com/index_files

Research - ‘Collective knowledge’ Bruner ‘CPA’ Enactive  Concrete Iconic  Pictorial Symbolic  Abstract Moyer (2001) ‘Through active manipulation of objects, children are able to build a repertoire of mental images that can be used when dealing with abstract concepts’.

M Askew 2016 “The best way for pupils to get to grips with number is through track and dice games. Research shows that children entering school with limited experience of mathematical activity can close the gap between them and their peers in only a few weeks playing games on straight number lines.”

Number Track Games 9 8 7 6 5 4 3 2 1 Player A rolls ‘3’ Race to the Moon 9 8 Player A rolls ‘3’ Player B rolls ‘2’ 7 6 5 4 3 2 Once you’ve played the game, consider how you might adapt it 1

Number lines - Order! You need: One number line (0-100) between 2 or 3 players (marked in divisions, age-appropriate) Turn over 2 arrow cards to make a two-digit number. Write that number where it ‘lives’ on the number line. 32 0 10 20 30 40 50 60 70 80 90 100 3 0 2 How many numbers can you place correctly in 3 minutes?

Mike Askew – Models and Images ‘Models of’ [the teacher using a number line to model 3+4 to her class] ‘Models for’ [children begin to use it for themselves – allowing the underlying mathematics to be explained to all] ‘Tools for’ [Research ‘tools for thinking’ – without making actual marks on paper] Dutch Realistic Mathematics education (1999) “Models that are used effectively by teachers become more than just a model to show a solution, but rather develop into a mental image within a child’s mind that they can use to help support their mathematical understanding .” “This movement takes time and not all children will move through these stages at the same rate.”

Progression i +/- with nos to 10 ‘Magic 10’ Simple resources Eleflip Hanger and pegs 10 green bottles Language: “If 10 is the whole, 4 is a part and 6 is a part” Q: How are these images connected?

Progression ii Addition e.g. 2 + 3 = Subtraction e.g. 9 – 3 = On your table - talk through your understanding of these mental methods/ strategies that could be used… +/- with nos to 20 Addition e.g. 2 + 3 = Subtraction e.g. 9 – 3 = Addition Subtraction Count all Count out Count on from first number Count back from Count on from largest no Count back to Use known facts Count up Use derived fact Use known and derived facts

Progression iii +/- 20 to 100 - Main methods… Split method - partitioning into 10’s and 1’s [1010 procedure] Sequencing, cumulative or jump method– keep one number whole then split one into 10’s and 1’s and adjust [N10] Links to Place Value - Day 2 Number sense – where numbers live on a number line Partitioning numbers

Use the ‘split’ method and the ‘jump’ method to calculate… Progression iii +/- 20 to 100 - Main methods… Split method - partitioning into 10’s and 1’s [1010 procedure] Sequencing, cumulative or jump method– keep one number whole then split one into 10’s and 1’s and adjust [N10] 36 + 35 = 72 – 38 = 245 + 137 = 563 – 486 = Use the ‘split’ method and the ‘jump’ method to calculate… Are there ‘other’ methods?

White Rose Calculation Guidance http://tinyurl.com/z26lags White Rose Calculation Guidance Go through the examples from ‘bare principles’ to ‘written methods’… How are concrete resources used to model +/- ? How do the different images link? What support does this provide?

Teaching and learning ideas for your year group +/- Visit NCETM Dulux Paint chart from Home Page Explore TABS: Subject Knowledge Activities Exemplification Videos Teaching for Mastery What are the Big Ideas? Do the Maths! Mastery Videos A Year 1 lesson on difference as a form of subtraction A Year 4 lesson on place value with decimal numbers https://www.ncetm.org.uk/resources/41211 https://www.ncetm.org.uk/resources/48209

What is the length of the key in mm? Which jug holds the most? How much more? Explain how you worked it out.

Teaching and learning ideas for measure Teaching for Mastery What are the Big Ideas? Do the Maths!

GROUP READING: for day 4 1.‘Issues in Teaching Numeracy in Primary Schools’ [Second Edition] a. Chapter 11 Errors and Misconceptions b. Chapter 15 Progression in the teaching of multiplication c. Chapter 16 Progression in the teaching of division 2.Google - ‘Ian Thompson Maths’ a. ‘Deconstructing the PNS approach to multiplication Part 3’ ‘…division Part 4’ 3. D Haylock ‘Mathematics Explained for Primary Teachers’ Chapters 7, 8 and 9