1 Addition. 57 Models for addition Combining two sets of objects (aggregation) 2.

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Presentation transcript:

1 Addition

57 Models for addition Combining two sets of objects (aggregation) 2

57 Models for addition Combining two sets of objects (aggregation) 3

57 Models for addition Combining two sets of objects (aggregation) 4

57 Models for addition Combining two sets of objects (aggregation) 5

57 Models for addition Adding on to a set (augmentation) Counting on with a bead bar/number line Combining two sets of objects (aggregation) 12 Issue: Tend to count one set, count the other and then count all Issue: Requires fluency with counting from any number Issues: Bead bar is a useful bridge from cardinal to ordinal. Number line helps to stop counting all Also: Bead bar and number line (showing 10s) encourages use of number bonds and place value for added efficiency

More than single digits? 7

8

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12

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14

10 TensOnes

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25 Subtraction

12 Models for subtraction Removing items from a set (reduction or take-away) = 7 Issue: Relies on ‘counting all’, again. Comparing two sets (comparison or difference) Issue: Useful when two numbers are ‘close together’, where ‘take-away’ image can be cumbersome Seeing one set as partitioned Seeing 12 as made up of 5 and 7 Issue: Helps to see the related calculations; 5+7=12, 7+5=12, 12-7 = 5 and 12-5=7 as all in the same diagram N.B. When this is done on a bead bar, there are links with both counting back and difference on a number line 26

Models for subtraction Counting back on a number line Finding the difference on a number line Issue: Number line helps to stop ‘counting all’. Also: Knowledge of place value and number bonds can support more efficient calculating Issue: Useful when two numbers are ‘close together’, use of number bonds and place value can help

More than single digits? 28

This is now “Sixty- twelve”

= 25 33

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Addition and Subtraction: Both Ways

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