Why our math program looks the way it does
Why the lessons are built the way they are. The other pages tell you how to run each part. This one tells you why, so the parts that feel fixed make sense when you teach them.
Start here
What every lesson is forWe find the one skill that’s blocking a student, unblock it, and keep moving them forward until they reach grade level.
This is an intervention curriculum, not a Tier I program. We don’t need a lesson for every standard, but we do need every skill students are expected to learn and build on. That’s the idea most of this page comes back to.
Why small groups. Tutoring is one of the most reliable interventions there is, and it works best when sessions are frequent, groups are small, and a trained tutor teaches from a structured curriculum. The frequency and the fixed model are what do the work — not improvising. That’s why so much of the lesson is set for you.
Where the five steps come from
Almost line for line out of the research guidanceThe five steps aren’t arbitrary. Each one matches a recommendation from the research on helping students who struggle with math:
This is why the steps matter. They aren’t a house style. Each one does a job the research says has to be done, so dropping a step doesn’t save time — it removes the job.
Two steps worth understanding properly
It isn’t random review. It “activates the collection of recently-learned skills students need for that day’s new material, per scope & sequence.” So how Step 1 goes tells you whether Step 3 will land — before you’ve taught it. More on Student activities.
A student working out 7 × 8 can’t think about what 7 × 8 is for at the same time. Fluency means fast and accurate. Correct but slow is a signal to keep the skill in fluency work, not a pass.
Why objects come first
Concrete → representational → abstractThe order is what does the work. Students who struggle learn more from this sequence than from jumping straight to the numbers, and it also beats staying with the objects the whole time. Starting concrete and moving to abstract is the part that matters.
Objects are a means, not the point. They help when they’re tied closely to the math and set aside on purpose, and they get in the way when handling them becomes the activity. So the abstract stage isn’t the one to run out of time for.
Why domains, not one sequence
And why the diagnostic starts below grade levelReading is one ladder — a student sits at one place on it. Math is eight domains, each its own grade-spanning progression, worked one at a time to grade-level proficiency. A student’s position in one says nothing about their position in another: a 5th grader can be solid in number systems and three years back in fractions.
That structure is what lets placement be precise. “Grade 5” isn’t somewhere you teach to. A numbered lesson inside a named domain is. Full map and grade bands: The domains.
Starting a few grades back gives you something you can teach from. The assessment climbs until it reaches the skill a student hasn’t got yet, and that skill is where you begin — a specific lesson, on a specific day, rather than a score. More on Assessments.
A 5th grader on grade-2 place value means the diagnostic found the real floor. Don’t rush toward grade level — the domain’s post-assessment comes when the skill is actually there, and skipping ahead rebuilds the gap you’re trying to close. And teach a below-grade lesson the same way you’d teach any other. It’s the right lesson for that student today, written for the skill rather than the age.
Math vs. reading
If you teach both, some things transfer and some do notIf you remember one thing
Math intervention isn’t re-teaching a grade. It’s finding the one skill blocking a student and unblocking it. The domains exist so you can be that precise. The five steps keep the student’s attention on the new idea instead of on working out what happens next. And Step 3 starts with objects because that’s the order understanding actually forms in.
Sources
Where every claim in this guide comes fromBraintrust internal
- Math Program, SY 25/26 scope & sequence — all eight domain tabs: lesson numbers, grades, standards
- Production lesson plans — step names, timings, support sections
- Platform question export — confirms graded Activity Steps 1–4
Research base
- Gersten, R. et al. (2009) — Assisting Students Struggling with Mathematics: RtI, IES Practice Guide
- Bruner, J. (1966) — enactive, iconic, symbolic modes
- Witzel, Mercer & Miller (2003) — CRA sequencing in algebra
- Fyfe, McNeil et al. — concreteness fading
- Carbonneau, Marley & Selig (2013) — manipulatives meta-analysis
- Jitendra et al. — schema-based word-problem instruction
- Jordan et al. (2009) — early number competence predicts later achievement
- Geary, D. — fact retrieval and working memory
- Rohrer & Taylor (2007) — distributed and interleaved practice
- Pearson & Gallagher (1983) — gradual release of responsibility
- Rosenshine, B. (2012) — Principles of Instruction
- Black & Wiliam (1998) — formative assessment
- Sweller, J. — cognitive load theory
- Nickow, Oreopoulos & Quan (2020) — tutoring meta-analysis
- NCTM (2014) — Principles to Actions