I’m reading Developing Number Knowledge: Assessment, Teaching, and Intervention with 7-11-Year -Olds by Robert J. Wright, David Ellemor-Collins, and Pamela Tabor. The authors stress the importance of moving students away from counting by one’s to solve problems. On page 52 they state, “the most commonly observed characteristic of low attaining mathematics students is a persistent dependence on counting by ones.” As teachers, we need to provide visual models that will give students opportunities to move away from over-reliance on counting by ones. At the same time we need to make sure we do not promote strategies that will make students dependent on counting by ones to solve all problems. Students should not be given problems that require counting on by more than 5. We can move students away from counting by ones by teaching; doubles, doubles+1, combinations to 5, 5+, combinations to 10, 10+, and combinations to 20. All of these combinations are taught through the use of visual models and active learning. Here is a link to a “Ways to Make 5” BINGO Game.