Strategies:

Doubles (By association)

Add 0 (Think “no-change” strategy)

Add 1 (Think “next number: strategy)

1-Aparts (Think “double plus/minus 1” strategy)

Add 2 (Think “next even or odd number” strategy)

Add 9 (Think “make-10” strategy)

Add 8 (Think “make-10” strategy)

Last 12: 5 + 3, 6 + 3, 6 + 4, 7 + 3, 7 + 4, 7 + 5 and their commutative pairs (A variety of strategies, although 2-Aparts using “double the number between” strategy will apply to 6 of the 12 facts.)

Addition Fact Learning

Have students fill in their blank addition charts with the answers for the facts associated with the strategy being discussed, modeled, and reinforced. They could use a different coloured pencil for the answers for the facts associated with each strategy.

A possible sequence of strategies is:

a)Doubles Facts using the association strategy. (9 facts)

b)Add Zero Facts emphasizing there is “no change” resulting from this addition. While it would appear that these facts are easy, many students expect the act of addition to make a change and that this change will be a greater number. (19 facts)

c)Add 1 Facts using the association to “next number” relationship (16 facts)

d)One-Apart Facts (Near Doubles) using a “doubles plus one” strategy. (Some students might prefer a “doubles less 1” where they double the larger of the two numbers and take one away.) (14 facts)

e)Add 2 Facts using the association to “next even or next odd number” relationship. (See grade 1 handout.) This would be applied initially to 4 + 2, 5 + 2, 6 + 2, 7 + 2, 8 + 2, and 9 + 2; then to their commutative pairs. (12 facts)

f)The Make-Ten Facts uses a strategy of building on 8 or 9 to make 10 using part of the second addend and then adding on the rest. (10 facts involving 9 and 8 facts involving 8 for a total of 18 fact

g)The Last 12 Facts: (5 + 3, 6 + 3, 6 + 4, 7 + 3, 7 + 4, 7 + 5, and their commutative pairs). Ask students for suggestions of strategies for these. Some students might suggest a make-10 strategy for the “7 + “ facts; others might visualize the ten-frames for all of these; others might suggest two skips of 2 for 6 + 4 and 7 + 4; others might suggest adding 2 and then 1 for the addition of 3; others might suggest that 7 + 5 is (5 + 5) + 2.

Not included in the list above, but an interesting strategy, is one for addends that are 2-apart: 3 + 5, 4 + 6, and 5 + 7 (also 1 + 3, 2 + 4, 6 + 8, and 7 + 9). Representing these two addends with unifix cube towers and sharing one cube from the larger with the smaller reveals that you get the double of the number between the two. That is, 3 + 5 = 4 + 4; 4 + 6 = 5 + 5, etc. Many students might find this strategy difficult because they are doubling a number that they don’t see. However, for the same 2-aparts, some children might suggest doubling the smaller and adding 2. That is, for 3 + 5 = (3 + 3) + 2.

Some Summary Statements About the Learning of Addition Facts

  1. Students have to developmentally ready if strategies are to be meaningful and integrated into students’ thought processes.
  2. Try to have the strategies come from students in your class who have invented them on their own.
  3. Make sure that strategies are explicitly discussed and understood well before they are drilled.
  4. Practice of the facts should be varied using visuals and oral language, using games, and using calculators, in whole class, partner, and individual situations.
  5. The oral language used in practices can be varied. For example, for 7 + 2, on some occasions you might say, “Seven plus two.” On other occasions, you might say, “The sum of seven and two.” Or “Two more than seven.” Or “Seven add two.” Etc. Initially you should use one phrase throughout a practice session, and build upon the various phrases until you use a variety of phrases in a single practice session.
  6. Facts for each strategy should be practiced on their own until they are efficiently recalled, and then integrated with facts using other strategies.
  7. Practice of facts should include discussion of the strategy(ies) used. After the introduction of three or more strategies, students should also practice strategy selection.
  8. Time for a response might initially be 8-10 seconds and with continued practice be narrowed until the 3-second goal is achieved. (The timing is to promote the use of efficient mental strategies and to discourage finger counting and other external inefficient methods.)
  9. When a strategy is introduced, students should examine new facts for this strategy as well as re-examine facts for which they already may have an alternative strategy. For example, there are 5 new facts and their commutative pairs for 9s in the make-ten strategy; however, students should look again at 9 + 1, 9 + 2, 9 + 8, and 9 + 9 to see that make-ten could also be used for these facts as well.
  10. In the end, the goal is to have students be able to give quick responses (3 seconds) to the addition facts. They may be using any of a number of techniques including the mental strategies you have discussed and practiced or they have invented, visualization strategies such as images of ten-frames or number lines, and simply memory from repetitive exposure. Any one student may be employing a variety of these techniques depending upon the particular facts they are responding to.