From mult/div to frac/dec, to reasoning and justification?!

It all turns on the word “unit”

Three fourths is three units of one fourth, and the day students can say that, draw it, and defend it, fractions stop being a rule pile. Multiplication is the same idea at whole-number scale: 6 × 24 is six units of 24, drawn with an area model they can take apart.

That's why our lessons put the model first and the procedure second, and why students stop rebuilding fractions every September. Watch the free Grade 4 lesson →

The area model and the bar model are the spatial engine.

Spatial reasoning predicts later math achievement more than verbal ability does, and the upper grades are where it either gets trained or gets skipped.

The area model is that training in disguise: students who can draw 6 × 24 as six units of 24 carry the picture into multi-digit work, fractions, and beyond. Students who never drew models are the ones rebuilding fractions every September.

Measurement works the same way: units iterated and compared by hand before a ruler ever abbreviates them.

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

“It taught me math personally in a way that I had never learned before. My students started growing within just a couple of months. They were already hitting end-of-year benchmarks.”

“In 14 years, I've never seen a company come in and support the children directly. DMTI works with the teachers and the students side by side.” Principal Chinita Irby

The evidence: 16% to 55% in four years.

Fifth-grade SBAC math proficiency at Iowa Elementary (Nampa, Idaho), one of the state's highest-poverty schools, went from 16% to 55% across four years of DMTI partnership: a +39-point gain. And it wasn't the already-successful students who moved most: in the peer-reviewed cluster-randomized study (25 schools, 4,618 students), the students who started furthest behind made the largest gains. Independent evaluation (RMC Research): 79.2% of students in DMT classrooms proficient or advanced vs 65.7% in comparison classrooms, with DMT schools serving more students in poverty and more English learners.

The models do not change. That is the point.

Upper-elementary math does more than hit benchmarks: it decides how algebra feels. The language (unit, compose, decompose, iterate) and the models (area model, bar model, number line) students learn in Grades 3-6 are the same ones that carry them through ratios, algebra, and college. Nothing to unlearn. Everything builds.

in Grades 3-6

Fractions named by their unit, products drawn as area models

in middle school

Ratios, rates, proportionality: same words, new numbers

in high school & beyond

Algebra that scales: models still work, language still precise

Dr. Jonathan Brendefur laughing with math manipulatives — Dr. Jonathan Brendefur, founder

40+ years of research.
And he still answers the weekly call himself.

“Multiplication and fractions are the grades' hardest work, and it is never the kids' fault. Let me show you the unit-first version where it finally clicks.”

Our service promise to teachers

Real people answer: portal Q&A and live weekly Zooms with Dr. Brendefur & Dr. Ismail
Start yourself today. No contract, no district decision, no purchase order
One click to leave: cancel anytime, no forms

Not a program. Actual math learning experts, on your side.

The people behind 40+ years of classroom research don't hand you a binder and disappear. They're in the portal, on the weekly calls, and, when you need it, building a plan for your students with you.

A DMTI math specialist teaching an open number line lesson: students' hands up, everyone in

Dr. Jackie Ismail and Dr. Jonathan Brendefur (DMTI founder) coaching a teacher over Zoom, the real weekly virtual session

$Dr. Sam Strother teaching fractions at the board$ Fraction questions? He's got them.

We listen first

Your classroom, your students, your constraints. You tell us what Tuesday actually looks like, and we start there, not with a script.

We build the plan together

Diagnostic → instruction → intervention, mapped to your roster. You'll know exactly what to do tomorrow and why it works.

We stay in the room

Weekly live calls with Dr. Brendefur & Dr. Ismail, portal Q&A answered by people who've taught the lesson. When you hit a wall, we're there.

“Effective mathematics instruction isn’t more complicated. When teachers understand the mathematics and what to look for in student thinking, they can focus on what matters most, and the work gets easier, not harder.”

Every teacher is in a different place. Our goal is to meet teachers where they are, help them better understand the mathematics and their students’ thinking, and make good decisions about what to do next.

Tell us about one student who is stuck, or one lesson that keeps falling flat, and we will build the plan with you. That is the partnership: teacher-led, expert-backed. We do not push a system downward; we listen, advise, question, and support.

Dr. Jonathan Brendefur, founder, DMTI

Everything below is included. Here's the value math.

Pretty sweet deal, if you ask us =)

Complete K-6 curriculum & unit resourceslesson plans, printables, varied practice: print them and keep them FOREVER$250+

Foundations Masterclassthe full research foundation, taught by Dr. Brendefur$895

MLP Assessments with targeted intervention strategiesfind the gap, teach the gap$1,495

Games & Reportsmathematical play that reinforces the ideas$195

Coaching, live & on demandreal math experts on the weekly calls (coaching runs $100/hr elsewhere)$100/hr

The Coaching Natalie series8 full coaching sessions, from flat scores to breakthrough$395

All of it, valued atover $3,000

Yours included: $21/mo or $210/yr

Plus at least an hour of expert time free, and as many questions as you can ask, answered. Join today, and everything you download is yours to print and keep. FOREVER.

It's the level of a Masters program in the grades where math gets real, for less than a teacher lunch budget a month.

Fractions get to click. You don't need one more thing on your plate. You need the model that makes them click. One routine this week; the rest builds from there.

Join Office Hours

Live every Monday, 3:30pm Mountain.
Bring your questions.

Free weekly Q&A with Dr. Jackie Ismail and Dr. Jonathan Brendefur, the researchers behind the program. Grades 3-6 questions welcome: the fraction unit that won't land, a multiplication model to sharpen, a student who puzzles you. Send your questions ahead of time or drop them in the YouTube chat during the call.

Join Office HoursFree · every Monday · no signup needed to watch ▶ Subscribe on YouTube for the reminder

“Bring one stuck lesson,
leave with a plan.”

Questions teachers ask before they join

Straight answers, the same ones we'd give you on a call.

Does this replace my district's required curriculum?

No, it supplements it. The models, routines, and assessments deepen how your students think about the math you're already required to teach, alongside your adopted curriculum.

Is it aligned to my standards?

The lessons target the concepts your grade-level standards expect (number sense, place value, the operations, fractions), and we'll help you map them onto your district's pacing.

How much prep does this take each week?

Less than you'd think. Lessons come with plans, printables, and practice built in. Most teachers start with one routine a week and grow from there.

Do I need special tech or a printer?

Printables print on any printer; the demo lessons and interactive games run in your browser. Nothing to install.

What if I can't make the live calls?

Coaching is live and on demand. Sessions live in the portal, so you can catch up whenever it works.

How does billing and canceling work?

$21/month or $210/year, month to month. Cancel anytime in one click, and everything you've downloaded is yours to keep. If it doesn't make your teaching clearer within 30 days of your first charge, we refund you. No forms.

Are you ready for Math Success?

Teachers don't need another commitment. Start free, watch a student defend a fraction with a model, feel more confident walking into class tomorrow.

Get Instant Access$21/month. 30-day money-back guarantee. Cancel anytime.

30-day money-back guarantee: full refund, keep everything you've downloaded

Month to month · no contract · cancel anytime.

Plus the 30-day money-back guarantee: if it doesn't make your teaching clearer within 30 days of your first charge, email us and we refund you. No forms, no explanation required, and you keep the materials you already downloaded.

P.S. for the skippers

Here's what you get instantly when you join Math Success by DMTI ($21/month):

The Grades 3-6 Pack, free on this page: the Grade 4 demo lesson, Unit Fraction Match, fraction misconceptions, and Five Interpretations of a Fraction, yours either way.

Deeper dive whenever you want it: Five Interpretations of a Fraction: Dr. Brendefur on the five meanings that make every fraction topic click.

Full K-6 curriculum map + lesson example videos from real classrooms: exactly how to teach each lesson, not just what to say.

Weekly Office Hours + diagnostics & intervention activities: fix the misconception, not reteach the whole unit.

Get Instant Access$21/month. 30-day money-back guarantee. Cancel anytime.

30-day money-back guarantee: full refund, keep everything you've downloaded

Start free, keep it either way

The Grades 3-6 Pack is open right now. Yours to keep whether or not you ever enroll.

Grade 4 Demo Lesson

Equivalence & unit fractions: a full lesson taught, with the interactive practice that goes with it.

Watch it free →

Free Fluency Game

Students play 2-minute probes; you get a report showing exactly where your class stands on their facts.

Play it free →

Fraction Misconceptions

What goes wrong and when, first learning then operations, with the fixes that work.

Read it free →

Plus: Five Interpretations of a Fraction, Dr. Brendefur's teaching video, and the area-model multiplication pack (in production).

Sound familiar?