MSP / A / 01
Elementary math
Grade 5 fractions and division.
Open the syllabusUnited States · Grades 5 to 8 · Placement and Algebra 1 readiness
Two decisions shape a child's middle school math: whether they start grade 6 on an accelerated track, and when they take Algebra 1. In many districts both decisions rest partly on a test, and families understandably want to prepare. The honest way to prepare is not to guess the questions. It is to find out exactly what your district measures, check the math that test is built on, and close the gaps properly. This page shows how placement works in published state and district rules, what the tests cover, and gives two original practice sets, one for each move.
Teaching live since 2020 · 10,000+ students · math and coding
In short
Middle school math placement means deciding whether a student starts an accelerated grade 6 course or takes Algebra 1 in grade 7 or 8. Each district or state picks the evidence: last spring's state test, an adaptive screener such as MAP Growth, a district exam or class grades. Modern Age Coders prepares students for it with live online lessons, in batches of 15 to 20 or privately, using our Middle School Mathematics and Algebra Foundations courses. Your first class costs nothing.
Where to start
Choose by the move your child is facing.

MSP / 01
Ratios, rational numbers and equations, the core of most placement measures.
Open the syllabus →
MSP / 02
Pre-algebra into Algebra 1, for the Algebra 1 placement move.
Open the syllabus →
MSP / 03
Grade 5 fractions and division, for the move into grade 6.
Open the syllabus →Two placement moves
There is no single national test. What it covers depends on the move: a placement at the end of grade 5 looks at grade 5 and early grade 6 math, while an Algebra 1 placement looks at the grade 7 and grade 8 standards that Algebra 1 is built on.
| Move | Usual timing | Math it checks | Example standards |
|---|---|---|---|
| Move 1: into an accelerated grade 6 track | Spring of grade 5 | Multi-digit division, fractions, decimals, early ratio and negatives | 5.NBT.B.6 division with two-digit divisors; 5.NF.B.7 dividing unit fractions; 6.NS.C.5 positive and negative numbers |
| Move 2: into Algebra 1 in grade 8 | Spring of grade 7 | Rational numbers, equations, proportional reasoning, first linear functions | 7.EE.B.4 equations of the form px + q = r; 8.F.A.1 what a function is; 8.EE.C.8 pairs of linear equations |
| Move 2, early: into Algebra 1 in grade 7 | Spring of grade 6 | All of the above, often after a compacted course | 6.NS.A.1 dividing fractions by fractions; 8.EE.A.1 integer exponents; 8.G.B.7 Pythagorean Theorem |
Montgomery County Public Schools in Maryland states it directly: "Proficiency with all grade level math standards from Kindergarten through grade 8 ensures success in Algebra I." Whatever a district calls its test, the content it checks is the content Algebra 1 depends on.
That is good news for preparation. The skills are public, listed grade by grade, so a family can find them without ever seeing a test.
A grade 5 placement is often a test of fluency as much as knowledge: can the child divide 4,368 by 24 accurately, add fractions with unlike denominators and reason with a ratio table without slowing down? Children who know the ideas but work slowly can be placed below what they understand.
So for this move, we split preparation between closing content gaps and building calm, accurate speed on the grade 5 essentials.
Sources: the Common Core mathematics standards and MCPS mathematics, read 31 October 2026. States with their own standards use other codes for the same ideas. Modern Age Coders is independent and not connected with any state, district or test publisher.
How districts decide
Usually with more than one measure. Texas sets a statewide rule with automatic enrollment; Seattle Public Schools uses MAP scores; San Francisco Unified uses eligibility criteria with routes for students who miss them. Here is what each publishes.
| Who | Measure | What happens | Family role |
|---|---|---|---|
| Texas (statewide) | STAAR Grade 5 Math, top 40% of scores statewide (60th percentile), or the top 40% on a local measure | Automatic enrollment in a grade 6 advanced math program aimed at Algebra I in grade 8 | Parents can decline the automatic place |
| Seattle Public Schools | "Eligibility is determined by math MAP (RIT) scores." | Three sixth-grade options, including direct enrollment in Compacted Math 7/8 | Families of eligible students choose an option with the district |
| San Francisco Unified | District eligibility criteria for grade 8 Algebra I | At most schools, eligible students automatically enrolled in Math 8 and Algebra I from 2026 to 2027 | Others "can choose to take Algebra I as an elective" |
The TEA FAQ says the cut is statewide, not set by each district: "Students whose scores place them in the top 40% of scores (60th percentile) across the state" must be automatically enrolled. It adds that "TEA will provide the scale score which indicates that a student is in the 60th percentile annually."
Timing matters too: "STAAR results are available in late May and early June each year." For a student with no grade 5 STAAR result, 19 TAC section 74.2101 says "A local measure shall be used to determine enrollment of Grade 6 students for whom there are no results on the state Grade 5 mathematics assessment."
TEA leaves the local measure to districts and lists examples from districts: "a summative assessment, the average of unit assessments over the year, or a performance-based portfolio of student work." So in Texas, steady class work in grade 5 can count as much as one test day.
TEA also says a district cannot make a summer course a condition: every qualifying student must have the opportunity to participate "regardless of whether or not they are available to attend classes in the summer."
San Francisco's 26 March 2026 announcement adds a second path for strong students: families can request Algebra I as the only math class, skipping Math 8, "if they meet additional academic eligibility criteria", and this "requires a meeting with the school counselor and formal written consent from parents or guardians." For its 2026 program, now closed, Seattle said families of eligible students would receive details on Thursday, April 23.
Sources: TEA Middle School Advanced Mathematics Program FAQ and program page; Seattle Public Schools; SFUSD; read 31 October 2026. Rules change; always check your district's current page.
The tests
Three kinds turn up most often: a state test score from the previous spring, a computer-adaptive screener taken during the year, and a test or set of unit exams written by the district. Many districts combine one of these with grades and teacher input.
| Measure | What it is | What preparation makes sense |
|---|---|---|
| State test score | For example, STAAR Grade 5 Math in Texas, taken in spring of the year before | Solid grade-level skills across the whole year; the state publishes its own practice tests |
| Adaptive screener | For example, NWEA MAP Growth: "computer-adaptive MAP Growth assessments" reported on "the grade-level independent RIT scale" | Breadth and accuracy; questions adjust to the student, so cramming one topic helps little |
| District placement exam | A test the district writes, often near the end of the year | Ask the district which standards it covers and whether a calculator is allowed |
| Course grades and unit tests | Class performance over the year, sometimes as a local measure | Consistent work and corrections all year, not a last-minute push |
It depends entirely on the test. Some district exams allow a basic calculator for one part and not another, and an adaptive screener may show an on-screen calculator only on some questions. There is no general rule, so ask the school for the test's own instructions.
We prepare students to work without one either way. Fluent fractions and division are what placement measures are really checking, and a student who relies on a calculator for 4,368 divided by 24 will be slower everywhere else.
It is meant to separate students, so it will feel harder than a normal unit test, and an adaptive test is designed to reach questions the student finds difficult. Getting questions wrong is expected and is not a sign of failure.
What helps most is a calm student who reads carefully and checks answers. We practice that directly: estimate first, solve, then check by a second route.
Practice
Two original practice sets written by our teachers, one for each move. They are not copied from or modeled on any real district or publisher test; they check the standards those tests are built on. Answers are in brackets.
| # | Problem | Skill | Answer |
|---|---|---|---|
| 1 | 4,368 ÷ 24 | Division with a two-digit divisor | (182) |
| 2 | 3/4 + 5/6 | Unlike denominators | (19/12, or 1 7/12) |
| 3 | 1/3 ÷ 4 | Unit fraction divided by a whole number | (1/12) |
| 4 | 2.5 × 0.4 | Decimal multiplication | (1) |
| 5 | A drink uses 4 cups of juice for 6 cups of water. Water for 10 cups of juice? | Ratio reasoning | (15 cups) |
| 6 | What is 20% of 45? | Percent as a rate per 100 | (9) |
| 7 | −8 + 13 | Positive and negative numbers | (5) |
| 8 | Volume of a box 3 by 4 by 5 units | Volume | (60 cubic units) |
| # | Problem | Skill | Answer |
|---|---|---|---|
| 1 | 2/3 ÷ 5/6 | Dividing fractions | (4/5) |
| 2 | −2.5 × 4 | Rational number operations | (−10) |
| 3 | 3(x + 4) = 27 | Two-step equation | (x = 5) |
| 4 | 4x − 7 < 9 | Inequality | (x < 4) |
| 5 | A class of 40 students grows by 15%. New size? | Percent increase | (46) |
| 6 | Slope through (−1, 4) and (3, −4) | Linear functions | (−2) |
| 7 | 32 × 3−4 | Integer exponents | (1/9) |
| 8 | x + y = 12 and x − y = 4 | System of equations | (x = 8, y = 4) |
| 9 | Right triangle with legs 5 and 12: hypotenuse? | Pythagorean Theorem | (13) |
Estimate first: 24 is close to 25, and 4,368 divided by 25 is a little under 175, so the answer is around 180. Then divide: 24 goes into 43 once, remainder 19; bring down 6 to make 196, and 24 goes in 8 times (192), remainder 4; bring down 8 to make 48, and 24 goes in exactly 2 times. The answer is 182.
Check: 24 × 182 = 24 × 180 + 24 × 2 = 4,320 + 48 = 4,368. The estimate, the working and the check all agree.
Add 7 to both sides: 4x < 16. Divide both sides by 4, a positive number, so the sign stays the same: x < 4. The solution is every number less than 4, drawn as an open circle at 4 with the arrow pointing left.
Check with a number on each side. If x = 3, then 12 − 7 = 5, which is less than 9. If x = 5, then 20 − 7 = 13, which is not. Students who check like this rarely lose marks on inequalities.
How to use the sets: give the matching set without a calculator and without a time limit first, then look at which skills went wrong rather than the total. A wrong answer on problem 2 of set 2 and on problem 7 of set 1 points to the same thing, signs with negative numbers, and that is the domain to fix first. For official practice, use the free practice tests your state or the test publisher provides.
How to prepare
Start early, prepare for the math rather than the test, and keep it low pressure. This is the plan our teachers follow.
| When | Focus |
|---|---|
| Fall | Read the district rule; first diagnostic; start on the weakest domain |
| Winter | Close gaps one domain at a time; keep up with class work, which may count |
| Early spring | Mixed practice across the whole year's content |
| Final weeks | Short mixed sets, checking habits, rest |
We do not obtain, copy or imitate real placement tests, and we do not teach test-taking tricks in place of math. Placement is meant to find the right course for a child, and a placement won by drilling can leave a student in a course they are not ready for.
We also never promise a placement. That decision belongs to the school, using its own measures.
It is rarely the end of the road. SFUSD lets students who miss automatic enrollment take Algebra I as an elective, and TEA notes that the Texas rule "is focused on students entering sixth grade" while districts can set policy for advancement in later grades.
A year of strong work at grade level, with gaps closed, often puts a student in a better position for the next decision point than a rushed placement would have.
Where your child is
How we describe a student after the first diagnostic class.
| Level | On our practice set | What we suggest |
|---|---|---|
| 1. Not yet | Under half right; several domains weak | Grade-level work first; plan for the next decision point |
| 2. Close | Half to three quarters right; one or two weak domains | Focused work on those domains for a term |
| 3. Ready | Most right, with clear explanations | Mixed practice and checking habits |
| 4. Well ahead | All right, quickly, with reasons | Depth: competition-style problems, not more speed |
Placement measures differ, so treat our levels as a guide to what to work on, not a prediction of a result.
Ask the school what happens after placement, too. How the course is taught matters as much as which course it is.
Getting hard questions wrong on an adaptive test is normal. It means the test is doing its job.
Estimate before you calculate. It catches more mistakes than anything else.
The catalogue
Live lessons that build the math every placement measure checks.
MSP / A / 01
Grade 5 fractions and division.
Open the syllabusMSP / A / 02
Accurate, calm speed.
Open the syllabusMSP / A / 03
Place value and number sense.
Open the syllabusMSP / B / 01
Ratio, rational numbers and equations.
Open the syllabusMSP / B / 02
Readiness for Algebra 1 and the course itself.
Open the syllabusMSP / B / 03
Functions and patterns in Python.
Open the syllabusMSP / C / 01
For students who are well ahead.
Open the syllabusMSP / C / 02
Geometry and Algebra 2 next.
Open the syllabusMSP / C / 03
Data skills alongside algebra.
Open the syllabusHow lessons run
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.
Fall and winter
Steady weekly work on weak domains.
Spring
Mixed review before the placement window.
1-on-1
Planned around your district's dates.
A free class finds the domain that breaks.
Fix the skill the others depend on.
Correct and calm before fast.
Original problems only, built on the standards.
Placement stays the school's decision.
Join a batch, or book a teacher just for your child.
Student work
Some of our middle schoolers build small math programs as they learn. See a few on student labs.

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Web app
A weather forecasting site with live conditions for any location.
Fees
Placement readiness lessons are paid monthly with no long commitment, so a family can plan a term of focused work before a spring decision and stop afterwards.
Free first class
USD 0
no card required
Group batch
USD 100
a month, billed in US dollars
One to one
USD 150
a month, billed in US dollars
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Questions from families
It depends on the district and the move. A placement at the end of grade 5 usually checks grade 5 division, fractions and decimals plus early ratio work, while an Algebra 1 placement checks grade 7 and 8 skills such as rational numbers, equations and linear functions.
Wherever you live in the US, the teacher comes to you by video. A free diagnostic class comes first, then weekly lessons with one consistent teacher.
Look on the district website for its math pathways or advanced math page, or ask the school counselor. The rule should say which measure is used, in which grade, and whether families can request a review.
It depends on the test, so check its own instructions with the school. We prepare students to work accurately without one, since fluent fractions and division are what most placement measures check.
Some states and publishers post free official practice, and those are the right place for real-format questions. The practice sets on this page are our own, built on the grade 7 and 8 standards, and we do not copy any district test.
By a state rule. A grade 5 student whose STAAR math score falls at or above the statewide 60th percentile, or who ranks high enough on the district's own measure, such as a year-end assessment or a portfolio, goes into the grade 6 advanced program automatically. Families can still decline the place.
Many districts offer later routes. SFUSD, for example, lets students who are not automatically enrolled take Algebra I as an elective, and Texas allows districts to set their own policies for advancement after grade 6.
No. Placement is the school's decision, made with its own measures. We build genuine readiness in the math those measures check, and we tell you honestly where your child stands.
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.
No. We run independently of every state, district, NWEA and other test publisher. Their pages are quoted here with links so you can read the originals.
Elsewhere on this site
More for families facing a placement decision.
How compacted tracks work after placement.
The year before the first placement move.
Ratios, negatives and expressions.
The year before Algebra 1 placement.
Functions, systems and exponents.
Support once Algebra 1 begins.
Grade-level help from kindergarten to grade 8.
For students already well ahead.
Part of the guide: US math placement and college readiness tests
More guides: US state math tests by state · US gifted and selective school tests · Homeschool and school math curricula guide · US math and coding competitions guide
Start here
Tell us the grade, the district and the placement date if you know it. The teacher will run a short diagnostic, show you which domain needs work, and suggest a plan for the time you have.
Learn how we teach math, or see all our courses.
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