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Algebra Readiness Path
Find the foundations each student is missing for Algebra 1, from fractions to proportional reasoning, and give every student a path to rebuild them.
The problem
Where the foundations for Algebra 1 break down
Algebra 1 is where gaps from earlier grades catch up with students. A student who struggles with linear equations is often missing something older: fractions, negative numbers or proportional reasoning.
- A course grade says a student is behind, not which idea is missing.
- Gaps from earlier grades rarely show up on grade-level tests.
- Reteaching a whole unit spends time on skills the student already has.
Inside the Path
What the Algebra Readiness Path covers
The Algebra Readiness Path covers the Common Core standards that lead into Algebra 1: operations and algebraic thinking, fractions, ratios and proportional relationships, the number system, expressions and equations, and the early functions work of middle school. Each standard sits in a map of the standards it depends on, so a gap in eighth-grade equations can be traced back to the fraction or integer skills underneath it.
Where students get stuck
Many of the misconceptions it looks for are familiar to math teachers: treating a fraction as two separate whole numbers, believing multiplication always makes a number bigger, adding the same amount to both parts of a ratio instead of scaling them, and reading the equals sign as “write the answer next” rather than a statement that two sides are equal. Wrong answer choices are written to reveal misconceptions like these, so a missed question points to a specific idea rather than a general weakness.
What it does for you
Built for everyone working on the gap
For teachers
Each wrong answer is tagged to the misconception behind it, and students practice from the skill where their gap begins.
More for teachersFor school leaders
Every student gets a diagnostic that traces gaps to their source and a skill path that starts there, so support time goes to the skill that’s missing.
More for school leadersFor districts
One diagnostic, built on Common Core, for every school that feeds into Algebra 1.
More for districtsHow it works
How the Path works
Diagnose
An adaptive 15-question screener across the math domains, then up to 25 targeted follow-up questions only where it finds possible gaps.
Trace
Answers are traced back through a prerequisite map of the Common Core standards to the skill where understanding breaks down, with the misconception behind each wrong answer.
Rebuild
Each student gets a Frontier skill tree, with lessons and skill checks that rebuild from the gap forward.
Standards
Built on published standards
Common Core State Standards, grades 3–8
Every question is written to a Common Core standard, and every standard sits in a prerequisite map, so every question connects directly to the standards your teachers already teach.
The science
The method behind every Path
Item Response Theory
Each student’s ability is estimated from their answers, and each next question is the one expected to tell the most.
Prerequisite maps
Standards are mapped as a graph of which skills build on which, so a gap can be traced to where it starts.
Misconception tagging
Wrong answer choices are written to reveal specific misconceptions, from a controlled catalog.
Research
The research behind this Path
These published studies are about how students learn, not about SubjectPath itself.
Siegler and colleagues found that elementary students’ knowledge of fractions and division predicted their algebra knowledge and overall math achievement in high school, even after accounting for other math knowledge, general ability and family background.
Siegler et al. (2012)Booth and Newton found evidence that middle school students’ understanding of fraction size was related to their readiness for algebra, more so than their understanding of whole-number size.
Booth & Newton (2012)Knuth and colleagues found that many middle school students did not fully understand the equal sign, and that students with a stronger understanding of it solved equations more successfully, even accounting for overall math ability.
Knuth et al. (2006)
The Algebra Readiness Path at a glance
- Students served
- grades 3–9
- Standards assessed
- 177
- Catalogued misconceptions
- 402
- Questions per session
- ≤ 40
- A 15-question screener, then up to 25 targeted follow-ups, never more than 40 questions.
- 177 standards assessed, within a prerequisite graph of 197 standards.
- Lessons for 197 standards, and 10-question skill checks passed at 8 out of 10.
Question types: Multiple choice, Numeric entry, Multi-select, Graphing.
Frequently asked questions
- Who is the Algebra Readiness Path for?
- For students in grades 3–9, including ninth graders still building toward Algebra 1.
- How many questions are in a session?
- A 15-question screener, then up to 25 targeted follow-ups, never more than 40 questions. A session stops sooner when another question would add little precision.
- What do students do after the diagnostic?
- They work through a skill tree of lessons and skill checks, starting from the gap the diagnostic found.
- Can we pilot it first?
- Yes. Ask us about piloting SubjectPath with your students.
See the Algebra Readiness Path in action
Schedule a demo, or ask us about piloting SubjectPath with your students.