Addition and Subtraction Oct 2017 SCITT Day 3 Addition and Subtraction Oct 2017

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.

Roman Numerals – An aspect of Place Value Later abbreviations were made… 8 IIIIΛIII Λ implies four ‘prior’ marks VIII 4 IIII Quicker to write ‘one before five’ IV IIIIΛIIII X ‘One before ten’ IX Roman numerals appear to have started out as notches on tally sticks. These continued to be used by some Italian shepherds into the 19th century. IIIIΛIIIIXIIIIΛIIIIXII NB Different symbols for 5 and 10 Λ a hand - five fingers X two hands - ten fingers

Jordan’s Activity Yr4 Constructing numbers to 100 An important feature to note… There are no zeros. If there are no X’s in the number it means there aren’t any tens! This number system is Base 5 and Base 10.

Subject Knowledge Overt Subject Knowledge Curriculum Knowledge Pedagogic Subject Knowledge Contingency We will consider different elements of your subject knowledge…

CPA Place Value - Representing Numbers H T U Exchange Boards Ian Thompson (2003) Quantity Value Column Value CPA Exchange Boards H T U Represent 13, 103, 130, 310, 301 What’s the same, what’s different? When representing… Concepts: grouping and exchanging

+/- ‘fundamentals’ in ks1

Range of situations - addition ‘Aggregation’ (join together) or ‘Augmentation’ (change by adding on) Range of situations - addition Mary had 12 sweets in her pocket. She bought another 3. How many sweets did she have altogether? Mrs Jones had 25 children in her classroom. Seven more came in from the library. How many children were in the classroom? Brian has 12 marbles and his brother Michael has 12. How many altogether? John’s family is travelling 35 miles to the seaside each day. How far would they travel over two days?

Range of situations - subtraction ‘take away’ or ‘change’ ‘difference’ or ‘comparison’ Range of situations - subtraction Mary had 12 sweets in her pocket. She took out 3 and ate them. How many sweets did she have left? Mrs Jones had 25 children in her classroom. Seven were taken out to change their books in the library. How many children remained in the classroom? Brian has 12 marbles and his brother Michael has 9. How many more marbles does Brian have than his brother? John’s family is travelling 35 miles to the seaside. They have travelled 19 miles so far. How much further?

Year 1 Mastery Video

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? Does suggested methodology move from: mental with jottings  expanded  written?

Number Track Games 9 8 7 6 5 4 3 2 1 Player A rolls ‘3’ Race to the Moon 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?

Hundred Squares Place a counter over numbers that have significance for you Find the Number (PV) Hide the number 1 number A cross (+ or x) 5 random numbers

Bonds to 10

Fluency in mental calculation Efficiency in calculation requires having a variety of mental strategies. Emphasise the importance of “magic 10” and partitioning numbers to bridge through 10. Ten Frames Use counters to show: Compare your image with others on your table. 9 5 + =

Note the stages that you go through… Represent ‘7 + 6 = ?’ Note the stages that you go through… Numicon Number Rods What's the same? What's different?

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

Use a real-life context, giving the learning a ‘purpose’. How Do I Understand Addition? Let me Count the Ways https://www.ncetm.org.uk/resources/49966 Use a real-life context, giving the learning a ‘purpose’. How would you teach a class to add 5 to 27? Calculate using… Ten Frames Numicon Number rods Anything else…

Exchange Boards Hundreds Tens Units ‘Make 50’

Constructing meaning (Hiebert 1997) Mathematical tools should be seen as supports for learning but using tools does not happen automatically. Learners must construct meaning by using them. This requires more than ‘watching demonstrations’; it requires working with tools over extended periods of time, trying them out, and watching what happens. Meaning [understanding] does not reside in tools; it is constructed by learners as they use the tools. The tools themselves don’t construct meaning – the meaning is constructed by the child using them.

Mental Calculation TU + TU Use a mental method to calculate… 25 + 36 = 35 + 19 = 32 – 14 = 64 – 59 = Now model using: Number line Tens frames 100[] Exchange boards Dienes Record it: Pictorially Abstract informally formally

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?

Addition

White Rose (WRMH) Block 2 Consider the small steps for your year group Explore ideas for fluency, reasoning and problem solving