DMT Insight 15 Fractions & Decimals Grades 3-6

Fraction Understanding

Many fraction errors follow from a missing idea about what a fraction is. You will learn the key ideas behind fraction understanding, the misconceptions that follow when one is missing, and the instruction that builds them. The shift is from parts-of-a-whole language to reading the numerator as a count of equal units.

Reading as

Questions for your classroom

  1. A student adds ½ + ⅓ and gets ⅖. What might they be treating as the unit?
  2. How could a model help the student see why both quantities must be expressed in the same unit?
  3. A student can find common denominators but cannot say why they are needed. What would you ask next?

Next in this study path

Fractions and decimals 17 Five Interpretations of a Fraction
17 Fractions & Decimals · Grades 3-8

Five Interpretations of a Fraction

A student shades 3 of 4 equal parts but cannot locate ¾ on a number line. What does each task require them to understand?

Insight · Video · Newsletter
58 Fractions & Decimals · Grades 3-6

Fractions

A student names a fraction correctly but struggles to represent its size. Which underlying understanding should we examine?

Insight · Newsletter · Companion Math Learning Profile

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Core materials

  • Grade 3 · Unit 3 · Fraction Understanding: Part 1
  • Grade 4 · Unit 3 · Equivalence and Unit Fractions
  • Grade 5 · Unit 1 · Number: Fraction Sense
  • Grade 6 · Unit 2 · Fraction Division

Intervention materials

  • Fractions & Decimals, grades 3-5

PD video

  • Fraction Definitions
  • Fraction Warm Up: Counting 0 to 4 by 2/3's
  • Fraction Multiplication: Fractions as Scalar Operators

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Jonathan Brendefur

Who writes DMT Insights

Jonathan Brendefur, PhD

Jonathan founded the Developing Mathematical Thinking Institute. He spent 20 years as a Professor of Mathematics Education at Boise State University, working with teachers in their classrooms every week.

Each Insight is about 3 pages and lists the research it draws on, so you can read the studies yourself.

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