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4. Arithmetic Foundations

Focus interventions on whole and rational numbers, word problems, and fact fluency.

In grades K through 5, math interventions should focus intensely on in-depth treatment of whole numbers and operations, while grades 4 through 8 should address rational numbers as well as advanced topics in whole-number arithmetic, such as long division.

Interventions on solving word problems should include instruction that helps students identify common underlying structures of various problem types. Students can learn to use these structures to categorize problems and determine appropriate solutions for each problem type. Intervention teachers at all grade levels should devote about ten minutes of each session to building fluent retrieval of basic arithmetic facts. Primary-grade students can learn efficient counting-on strategies to improve math fact retrieval, and intermediate and middle-grade students should learn to use their knowledge of properties (e.g., the commutative, associative, and distributive laws) to derive facts in their heads.