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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
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A ‘How to…’ guide for Addition and Subtraction
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Published 2010 [Age related examples if needed – 3 slides ‘hidden’]
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Addition and Subtraction to follow…
Aggregation/ augmentation Take away / difference Addition and Subtraction to follow… Mental strategies ] Informal jottings ] Expanded ] A Standard method ] Throughout - mental visualisation Key Messages: CPA Combining images How they connect & when they don’t Number lines 10 frames Numicon Number rods Bar model 100 squares Base 10 apparatus Place Value disks Counters Exchange Boards
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Put the largest number first. Why?
OR 3 4 Count all: “1, 2, 3… 1, 2, 3, 4… 1, 2, 3, 4, 5, 6, 7” 4+3=7 7-4=3 3+4=7 7-3=4 7=4+3 3=7-4 7=3+4 4=7-4 Aggregation Unstructured (reliant on counting) Structured (seeing and using pattern, grouping) OR NOT A GOOD MODEL OR Count on: “Start at 4, count on 2.” 4 ** Augmentation Mental strategy: Put the largest number first. Why?
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Making 10 (‘bridging’ through 10) Augmentation Making ‘blocks’ and ‘rows’ of ten (links to 100 sq) Partition 5 into 4 and 1 Aggregation Partition 5 into 4 and 1 Augmentation: Aggregation Informal Jottings NB: Image ‘quantity value’ Making 10 Expanded written methods Mental strategies = = partition - known facts = N10 number line = N10 number line = 1010 leads to column methods = partitioning ‘flexibly’ (fluency) – 4 = 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) Alongside…
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Examples should include 0 as a ‘place holder’
Number line (N10) Yr 3 Progression of examples in columns: HTO + O ] HTO + T ] HTO + H ] HTO + TO ] No exchange THEN with exchange Encourage mental visualisation Working mentally on paper then visualise. Informal Jottings (1010) Examples should include 0 as a ‘place holder’ (Note change in order of calculating columns from mental to written) HTO + TO HTO + HT HTO + HTO No exchange THEN with exchange PV grids + apparatus Base 10 PV disks Counters Visualise ‘making 10’ in each column ‘Quantity value’ ‘Column value’ (Abstraction) Expanded written
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