• Summary
• Contents

Any way you slice it, fractions are foundational

Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler provides research-based tools that are aligned with NCTM and Common Core State Standards. He describes powerful diagnostic methods for error analysis that pinpoint specific student misconceptions and supplies specific intervention strategies and activities for each error pattern. Also included are tools for analyzing student work and providing timely, specific, and meaningful interventions within an RTI framework. The targeted interventions for each error pattern promote teaching for conceptual understanding and are supported by documented academic research. Practical materials include: Reproducibles for diagnostic tests; Practice pages for exercises keyed to the diagnostic tests and error patterns; Pages for practicing alternative algorithms and estimation; Teacher resources for hands-on activities, game sheets and pieces, and more; Worksheets, answer keys, and online resources

Each main unit, along with the sections on academic research and “Big Ideas,” concludes with a set of teacher reflection questions for use in a professional development setting. Get ready, get set, and help your students tackle fractions with confidence!

### A Look at the Academic Research: Intervention in the Mathematics Classroom

##### Answers for Unit 1: Fraction Concepts

The answers for the Diagnostic Test on Fraction Concepts are included in the Item Analysis Table on page 41.

Practice Exercises: Fraction Concepts (pages 86–87)

• or 0
• or
• See below.
• See below.
• 1, 2, 3, 4, 6, 8, 12, 24
• Any five of these: 0, 18, 36, 54, 72, etc.
• 10
• 42
• 11, 13, 17, 19, 21, 23
• 2 × 2 × 5 × 5
• 8 of the 12 parts should be shaded.
• Sample:
• Any two: , etc.
• <
• 7 ÷ 12
• 0.65
• 0.625

For 7 and 8, students should mark the approximate locations of and , respectively.

Number Lines (marked 0–1) (page 160)

Number Lines (marked beyond ...

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