DMT Insight 59 Models and representations Grades K-8

Math Models that Matter

The model a student reasons on shapes whether number sense is built. You will learn which models grow with the mathematics across grades, and which work for small quantities but stop helping as relationships become more complex. The shift is from choosing a model for today’s problem to choosing one that will still work in later grades.

Reading as

Questions for your classroom

  1. A student finds 8 + 5 on a ten frame. What model can they reason with when the problem is 48 + 25?
  2. Which models do your students still use by grade 5, and which have they set aside?
  3. Which models remain useful as students work with more complex quantities and relationships?
02 Models and representations · Grades K-8

How Math Models Transform Learning

Two students represent 24 ÷ 4 differently. What quantities and relationships does each representation make visible?

Insight · Video · Newsletter · Companion
26 Models and representations · Grades K-5

The Lasting Impact of Math Manipulatives

Students use connecting cubes during a lesson. What mathematical relationship are they expected to represent?

Insight · Newsletter · Companion
49 Models and representations · Grades 1-6

Bar Models and Word Problems

A student computes accurately but struggles to solve a contextual problem. How are they interpreting the quantities?

Insight · Video · Newsletter · Companion

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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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