Addition within 20

Method

1. Start concrete with two separate, physically distinct groups of objects (two colours of counters, or objects in two hoops), and count all objects together from 1 to find the total - this is the method every child starts with and it is always correct, just slow.
2. Introduce counting-on as an efficient shortcut once counting-all is secure: instead of counting both groups from 1, start at the larger number and count on the smaller amount, e.g. for 12 + 3, say '12' then count on '13, 14, 15' rather than recounting the 12.
3. Use a number line or bead string as the pictorial bridge for counting-on: draw jumps above the line, one jump per unit being added, landing on the answer - this makes the start-big-count-on-small strategy visible and checkable.
4. Teach bridging through 10 explicitly for any addition where the smaller number needs to be split to get over a tens boundary, e.g. 8 + 5: first add enough to reach 10 (8 + 2 = 10), then add what is left of the 5 (2 has been used, 3 remains, so 10 + 3 = 13). This depends entirely on instant bonds-to-10 recall, so revisit that topic if bridging is shaky.
5. Show the bridging method on a number line with two jumps rather than five or six small ones: one jump to the next multiple of 10, then a second jump for the remainder, so the strategy stays visual as well as numerical.
6. Move to the abstract stage - a number sentence with the answer, or with a missing number in any position (7 + ? = 15, ? + 6 = 20) - once counting-on and bridging are both secure without the number line.
7. Watch for children who count on by including the starting number as the first count (e.g. counting '12' as their first counted-on step for 12 + 3, landing on 14 instead of 15): this off-by-one error is extremely common and is best caught by checking the answer against a number line jump by jump.

Practice questions

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