Calculation Guidance SCITT 2017 A calculation learning journey

Calculation Guidance SCITT 2017 A calculation learning journey for Primary Schools Intention: To inform your subject knowledge and pedagogy when planning mental/ written calculation lessons

A ‘How to…’ guide for Addition and Subtraction

Published 2010 [Age related examples if needed – 3 slides ‘hidden’]

Aggregation/ augmentation Take away / difference Addition and Subtraction to follow… Key Messages: ØCPA ØCombining images ØHow they connect & when they don’t • Mental strategies • Informal jottings • Expanded • A Standard method Number lines 10 frames Numicon Number rods Bar model ] ] 100 squares Base 10 apparatus Place Value disks Counters Exchange Boards Throughout mental visualisation

OR 3 Count all: “ 1, 2, 3… Aggregation 1, 2, 3, 4… 1, 2, 3, 4, 5, 6, 7” 4+3=7 3+4=7 7=4+3 7=3+4 OR 4 7 -4=3 7 -3=4 3=7 -4 4=7 -4 Unstructured (reliant on counting) Structured (seeing and using pattern, grouping) NOT A GOOD MODEL Count on: “Start at 4, count on 2. ” Mental strategy: Put the largest number first. Why? OR Augmentation 4 **

Making 10 (‘bridging’ through 10) Augmentation Partition 5 into 4 and 1 Aggregation Making ‘blocks’ and ‘rows’ of ten (links to 100 sq) Augmentation: Partition 5 into 4 and 1 Informal Jottings Aggregation Expanded written methods NB: Image ‘quantity value’ Alongside… Mental strategies 36 + 25 = i. 35 + 25 + 1 = ii. 36 + 20 + 5 = iii. 25 + 30 + 6 = iv. 30 + 20 + 6 + 5 = v. 25 + 11 + 25 = vi. 25 + 40 – 4 = vii. … partition - known facts N 10 number line 1010 leads to column methods partitioning ‘flexibly’ (fluency) compensate and adjust Progression of examples in columns: TO + O (no exchange required) TO + O (with exchange) TO + T (no exchange) TO + T (with exchange) TO + TO (any) Making 10

Yr 3 Progression of examples in columns: HTO + O ] HTO + T ] Encourage mental visualisation HTO + H ] HTO + TO ] No exchange THEN with exchange Examples should include 0 as a ‘place holder’ HTO + TO Visualise ‘making 10’ HTO + HTO in each column No exchange THEN with exchange Working mentally on paper then visualise. Number line (N 10) PV grids + apparatus Base 10 PV disks Counters Informal Jottings (1010) (Note change in order of calculating columns from mental to written) ‘Quantity value’ ‘Column value’ (Abstraction) Expanded written