For Grades 3-6 Teachers · DMT Insight

Multiplication sticks when it's
models, words, progressions, not memorized tables.

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Multiplication Models, Vocabulary and Progressions

This insight synthesizes the research on how interconnected models, structural vocabulary, and thoughtfully designed learning progressions enhance students' understanding of multiplication. The area model anchors it: 6 × 24 as six units of 24, drawn, and the structural words (unit, compose, decompose, iterate) do the teaching alongside it.

Students building the area model with their teacher
Area-model multiplication, built together
35%+
avg. test score increase
300+
schools transformed
40+ yrs
of classroom research

What this insight covers

The three ideas that do the heavy lifting. The full article goes deeper , free, no gate.

1

The area model is the anchor

6 × 24 as six units of 24, drawn, students take it apart, rearrange it, and the distributive property stops being a rule to memorize.

2

Structural vocabulary does the heavy lifting

Unit, compose, decompose, iterate. When students say "six iterations of 24," the math and the language reinforce each other.

3

Progressions prevent the September reset

Learning designed to build from what came before means students extend their multiplication instead of starting over every year.

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From real classrooms, on tape

Teachers who watched understanding arrive, and said so.

“I saw light bulbs turn on and thinking turn on that I had never seen with math.”

ANGELA WILLIAMS · TEACHER

“This is it. This is how to teach math.”

MOLLY YORK · TEACHER

“These kids aren't just saying math words anymore. They can explain them and show models to back it up.” (Rosie Ashcraft · and Ms. Hochstrasser's 4th graders made dramatic gains, the kind you can point to on the assessments and see in how students talk about the math.

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The full insight

Multiplication Models, Vocabulary and Progressions , the article, with the research and the classroom takeaways.

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Multiplication Models, Vocabulary & Progressions, DMT Insight teaching video still
DMT INSIGHT · Multiplication Models, Vocabulary & Progressions

The teaching video

Watch the lesson taught, models, questions, and the language, on tape.

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Try it with students

The activities and demo lesson that go with this idea, open now.

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