BOX 5-10

Steps in Addition/Subtraction Operations and Relations

Step 1 (ages 2 and 3)

  • Use subitized and counted cardinality to solve situation and oral number word problems with totals ≤ 5.

  • Act out numerical situations with objects and say them in words; see answer at the end.

  • Determine that something is bigger or has more using perceptual, length, and density strategies.

Examples of problems they can solve:

  • Change plus: Two blocks and two blocks make four blocks.

  • Change minus: Four apples take away one apple is three apples.

  • Put together/take apart: I see three apples. I see two and one make three.

Step 2 (age 4/prekindergarten)

  • Use conceptual subitizing and cardinal counting to solve situation, word, and oral number word problems with totals ≤ 8.

  • Solve numerical situations and word problems by modeling actions with objects, fingers, or mentally (or just know the answer); or see or count the answer.

  • Solve number word problems by modeling actions with objects, fingers, or mentally (or just know the answer); or see or count the answer.

  • Learn the partners for 3, 4, 5 (e.g., 5 = 4 + 1, 5 = 3 + 2).

  • For relations, understand and say this is/has less/fewer than that.

  • For more than/less than relations with totals 5, act out or show situation, and count or match to solve.

Examples of problems they can solve:

  • Change plus: Two and two make ?

Levels in Children’s Numerical Solution Methods

There is a large research base from around the world describing three levels through which children’s numerical solution methods for addition and subtraction situations move (e.g., see the research summarized in Baroody, 1987, 2004; Baroody, Lai, and Mix, 2006; Clements and Sarama, 2007, 2008; Fuson, 1988, 1992a, 1992b; Ginsburg, 1983; Saxe, 1982; Sophian, 1984). These levels are summarized in Box 5-11. At all levels, the solution methods require mathematizing the real-world situation (or later the word problem or the problem represented with numbers) to focus on only the



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