BOE / APP / 01
Middle school math
Pre-algebra and geometry, deeply.
Open the syllabusBoston · Grades 6 and 8 · Entry in September 2027
Entry to Boston’s three exam schools does not hang on one test. Boston Public Schools combines a student’s grade point average, weighted at 70 percent, with a MAP Growth test score, weighted at 30 percent, and then invites students within four socioeconomic tiers. That means the math that matters most is the math on report cards this fall and winter, with the January 2027 test as the smaller part. This guide explains the process from the BPS exam school pages as they stood on 31 October 2026, works the composite through with our own numbers, and closes with math practice for students in grades 6 and 8.
Teaching math and coding live since 2020 · 10,000+ students · grades K to 12
In short
Boston Public Schools has three exam schools: Boston Latin Academy, Boston Latin School and the John D. O’Bryant School of Mathematics and Science. Boston residents need a B or higher GPA and a MAP Growth score; the composite is 70 percent GPA and 30 percent MAP Growth. Modern Age Coders teaches the math live online, in a batch or 1-on-1, through our Middle School Mathematics course.
Learn with a teacher
School math for the GPA first, then our entrance-test course for timed problem solving, then algebra for the grade 8 applicant.

BOE / 01
Grades 6 to 8. The math marks that make up most of the GPA.
Open the syllabus →
BOE / 02
Our SHSAT Math Prep course, used here for timed reasoning before the January test.
Open the syllabus →
BOE / 03
For grade 8 applicants heading for grade 9 entry.
Open the syllabus →Eligibility
Boston residents entering grade 6, 8 or 9 in September 2026 can apply for September 2027. To be considered, a student needs a GPA of B or higher, must rank at least one exam school, and must have a valid MAP Growth score.
| Requirement | What BPS publishes |
|---|---|
| The schools | Boston Latin Academy, Boston Latin School, and the John D. O’Bryant School of Mathematics and Science |
| Entry grades | All three admit new students in grades 7 and 9; the O’Bryant also takes a small number in grade 10 |
| Residency | Both the parent and the student must live in the City of Boston |
| GPA | B or higher, from unweighted report card marks |
| Test | MAP Growth, Reading and Math; both sections must be completed |
| Choice | At least one exam school ranked on the school choice form |
| Composite | 70 percent GPA and 30 percent MAP Growth, plus 10 points for some students |
| Not eligible | Students on a modified curriculum, in MCAS Alternate Assessments, or enrolled in SLIFE |
BPS says that after a five-year review of its exam school policy, the School Committee accepted revisions in fall 2025, effective from the 2026 to 2027 admissions cycle. School-based points were eliminated.
The 10 extra points now go only to students experiencing homelessness, living in Boston Housing Authority public housing, or in the care of the Department of Children and Families, and they apply within the tier-based share of invitations.
A student receives an invitation to only one exam school, set by the composite score, the tier, the ranked choices and the seats. Once invited, the student is assigned to that school; BPS says families cannot make a final decision afterwards.
BPS states that "exam school decisions are final, and we do not accept appeals." Sibling priority does not apply.
Sources: Boston Public Schools Exam Schools, How to Apply and Admissions FAQs, read 31 October 2026. Modern Age Coders is not connected with Boston Public Schools or any exam school.
The composite score
In BPS’s words, "Students will receive a composite score that is based 30% on MAP Growth and 70% GPA." The GPA is worked out on an 11-point scale and then scaled to 100 by dividing by 11 and multiplying by 100.
| Applying for | Marks used |
|---|---|
| Grade 7 | Grade 6 ELA, Math, Science and Social Studies from Quarter 1 and 2, or Trimester 1 or Semester 1; grade 5 ELA and Math from the last marking period |
| Grade 9 | Grade 8 ELA, Math, Science and Social Studies from Quarter 1 and 2, or Trimester 1 or Semester 1; grade 7 ELA and Math from the last marking period |
| Grade 10 | Grade 9 ELA, Math, Science and Social Studies from Quarter 1 and 2, or Trimester 1 or Semester 1; grade 8 ELA and Math from the last marking period |
Worked example (ours): scaling a GPA. Suppose, after BPS converts a grade 6 student’s letter marks, the average on the 11-point scale comes out at 9.9. BPS scales it to 100 by dividing by 11 and multiplying by 100: 9.9 / 11 = 0.9, and 0.9 x 100 = 90. The letter-to-point table itself is on the BPS composite score fact sheet, so check your own child’s marks there; the 9.9 here is an invented figure.
Worked example (ours): combining the two parts. Keep the GPA at 90 and suppose the MAP Growth part works out at 80 on a 100-point scale. Then the composite is 0.7 x 90 + 0.3 x 80 = 63 + 24 = 87. Now see what each part is worth. Raising the GPA from 90 to 95 adds 0.7 x 5 = 3.5 points. Raising the test part from 80 to 85 adds only 0.3 x 5 = 1.5 points. How BPS turns a MAP Growth percentile into its 30 percent share is set out in its fact sheet, which we have not reproduced, so the 80 is an assumption for the arithmetic.
Because the GPA is weighted more than twice as heavily as the test, a steady report card in grade 6 or grade 8 does more for the composite than a strong January morning. And unlike the test, the marks build over months, so effort shows.
BPS gives no extra points for advanced classes and uses unweighted marks. An A+ counts the same as an A, so the target is a consistent A or B+ across all four subjects, not a single star subject.
The FAQs say BPS cannot calculate GPA until early March, after the second quarter marking period closes on January 29, 2027. For a grade 6 or grade 8 student, that means the Quarter 1 and 2 marks being earned right now are the ones that count.
The grade 5 or grade 7 marks used are only ELA and Math from the last marking period, already fixed. So this autumn’s math class is where help can still change the picture.
Source: Boston Public Schools Admissions FAQs (11-point scale, scaling, 70/30 split, unweighted marks) and How to Apply page, read 31 October 2026. Both worked examples use invented figures and are ours.
The calendar
BPS students in grades 6 and 8 at non-exam schools take MAP Growth in school between January 11 and 15, 2027. Everyone else who needs the weekend test sits it on January 9 to 10, 2027, after registering by December 4, 2026.
| Date | Step | Who |
|---|---|---|
| Tuesday, October 13 to Friday, December 4, 2026 | Weekend MAP registration; residency verification and ranked choices | Students not in BPS, and BPS grade 9 students for the test |
| Tuesday, December 1, 2026, 6 p.m. | BPS online information session | Any family |
| Saturday and Sunday, January 9 to 10, 2027 | Weekend MAP Growth test | Non-BPS students, BPS grade 9 students, current exam school students changing school |
| Saturday and Sunday, January 16 to 17, 2027 | Reserved in case of severe weather | Weekend test takers |
| Monday, January 11 to Friday, January 15, 2027 | In-school MAP Growth test, no registration needed | BPS grade 6 and 8 students at non-exam schools |
| Tuesday, January 5 to Friday, February 5, 2027 | School choice form | BPS students in grades 6 and 8; grade 9 and exam school students via a Welcome Center |
| Friday, January 29, 2027 | Second quarter marking period closes; GPA calculated in early March | All applicants |
| Late April 2027 | Decision letters through the Avela portal | All applicants |
BPS says students have two opportunities to take MAP Growth, in the spring and winter, and that if a student tests twice, BPS uses the higher achievement percentile in each subject, Reading and Math, separately.
For a grade 6 student, that means a spring MAP taken at school and the January administration can both count. Ask your school which administrations apply to your child.
Private, parochial, Commonwealth charter, METCO and homeschooled students must verify City of Boston residency between October 13 and December 4, 2026, through apply.avela.org/boston, and submit ranked choices at the same time.
BPS stresses this applies even if the family has other children in BPS, receives BPS special education services, or works for the city.
Source: Boston Public Schools How to Apply and Admissions FAQs, read 31 October 2026. BPS links a MAP Growth demo by NWEA for students to try the testing platform.
Tiers and invitations
Every Boston address falls in one of four socioeconomic tiers. BPS gives 20 percent of each school’s invitations to the highest-ranking students citywide and 80 percent to the highest-ranking students within each tier.
| Point | What BPS says |
|---|---|
| Citywide share | 20 percent of invitations at each school, to the highest-ranking students citywide |
| Tier share | 80 percent, to the highest-ranking students in each of the 4 socioeconomic tiers |
| Tier assignment | By home address; students compete only with others in their tier for the tier share |
| Seats per tier | Approximately the same number in each tier |
| Order of rounds | Invitations go out in several cycles, with the lowest socioeconomic tier first in each round |
| Tier updates | Every winter, pending data |
| Waitlists | Grades 7, 9 and 10 only, one per school and grade, capped at 100 students, until November 30 |
| Waitlist order | Composite score and a random number within the tier |
BPS encourages students to apply to all three exam schools for grades 7 and 9, and to rank them, along with any other BPS schools, in true order of preference. A student who is not invited keeps their current BPS seat where that grade is offered.
Because an invitation is automatic and final, rank only schools you would really accept, in the order you would choose them.
A family cannot change its tier, the seat count or the ranking of other students. The only parts in a student’s hands are the report card marks and the MAP Growth result.
We teach the math behind both and tell families plainly what we see; we make no forecast of invitations.
Source: Boston Public Schools Exam Schools page and Admissions FAQs, read 31 October 2026. BPS publishes a tier map and previous year data summaries on the same pages.
The math
Two things at once: the grade-level math that earns the Quarter 1 and 2 report card marks, and confident reasoning for the MAP Growth Math section in January. Our focus list below is our own reading of the two grade levels.
| Applicant | For the GPA this fall | For MAP Growth in January |
|---|---|---|
| Grade 6, for grade 7 entry | Ratios and rates, dividing fractions, negative numbers, expressions, area and volume | Fluent fraction and percent work; multi-step word problems; reading graphs |
| Grade 8, for grade 9 entry | Linear equations, functions and slope, systems, exponents, the Pythagorean theorem | Solving and checking equations; interpreting functions; geometry with right triangles |
| Grade 9, for grade 10 at the O’Bryant | Algebra 1 or the school’s grade 9 course | Algebra reasoning, quadratics where taught |
For most students, the quickest gain is in class: homework handed in, quizzes corrected, a weak unit revisited before the quarter test. A one-letter rise in math moves the GPA, and the GPA carries 70 percent.
We work on whatever unit the school is teaching that week, so our classes pull in the same direction as the report card.
BPS points students to the free MAP Growth demo by NWEA so they can get used to the testing platform before January. Use it once or twice to remove surprises on the day.
We do not reproduce MAP items. We build reasoning with our own problems and leave platform practice to the official demo.
Worked examples
Problems we wrote ourselves, two at grade 6 and one at grade 8. They are not MAP Growth items and are not drawn from any BPS or NWEA material.
Example 1 (grade 6): a weighted average. A student’s quarter math grade is 60 percent tests and 40 percent homework. Test average 82, homework average 95. What is the quarter grade? Reasoning: 0.6 x 82 = 49.2 and 0.4 x 95 = 38, so the grade is 87.2. The same idea runs the exam school composite, which is why we teach it early: a heavier weight moves the total more.
Example 2 (grade 6): dividing fractions in context. A recipe needs 3/4 cup of oats per batch. How many full batches can be made from 5 cups? 5 divided by 3/4 is 5 x 4/3 = 20/3, which is 6 and 2/3. So 6 full batches, with 2/3 of a batch of oats left, which is 2/3 x 3/4 = 1/2 cup. The trap is answering 6 and 2/3 when the question asks for full batches.
Example 3 (grade 8): a line from two points. A taxi charges a fixed amount plus a rate per mile. A 4-mile ride costs 14 dollars and a 10-mile ride costs 29 dollars. What does a 7-mile ride cost? The slope is (29 minus 14) / (10 minus 4) = 15 / 6 = 2.5 dollars per mile. The fixed part is 14 minus 4 x 2.5 = 4. A 7-mile ride costs 4 + 7 x 2.5 = 21.50 dollars. Check: the answer sits halfway between 14 and 29 because 7 sits halfway between 4 and 10.
Weighted averages, fraction division and linear rates are three ideas that appear constantly in grade 6 and grade 8 classwork, so they serve the GPA and the test together.
Each has a check that needs no calculator: a total between the two parts, a leftover that makes sense, a midpoint that matches.
The student predicts the answer roughly before working it out. For example 1, "between 82 and 95, nearer 82": a prediction catches a swapped weight at once.
We then ask the student to invent a similar problem for a classmate. Writing a problem is a stronger test of understanding than solving one.
Practice set
Problems 1 to 6 suit a grade 6 applicant; 7 to 10 suit grade 8. Written by our teachers; work them without a calculator, then check against the table.
| No. | Answer | Method |
|---|---|---|
| 1 | 216 miles | 135 / 2.5 = 54 miles an hour, times 4 |
| 2 | 3 | 5/2 x 6/5 = 30/10 |
| 3 | Negative 1 degree | Negative 6 + 14 = 8; 8 minus 9 |
| 4 | 60 cubes; 94 square cm | 5 x 4 x 3; 2(20 + 15 + 12) |
| 5 | 2n minus 3; 13 | 2 x 8 minus 3 |
| 6 | 10 | 40 percent of 25 |
| 7 | x = 6 | 3x = 18 |
| 8 | 2 | (11 minus 3) / (6 minus 2) = 8 / 4 |
| 9 | 15 | 81 + 144 = 225, and the square root of 225 |
| 10 | 4 | 2 to the 8th over 2 to the 6th is 2 squared |
Problem 4 asks for two things; students often give the volume and stop. Problem 6 asks who does not walk, so 15 is the answer to the wrong question.
In problem 10, adding exponents to get 8 and then subtracting 6 is right; multiplying them is the usual error.
Take the problems from the unit your child is studying now and bring the ones they missed to class. Fixing a school unit is worth more than any extra test drill.
Before January, add one MAP Growth demo session for the platform itself.
From now to April
Our plan for a grade 6 or grade 8 applicant starting now, built around the published BPS dates.
| When | Math focus | Admin step |
|---|---|---|
| November 2026 | The current school math unit; homework and quiz corrections each week | Non-BPS families: register for the weekend MAP and verify residency by December 4 |
| December 2026 | Revisit the weakest Quarter 1 unit; mixed word problems | Optional BPS info session on December 1 |
| Early January 2027 | One MAP Growth demo session; light mixed review | Weekend test January 9 to 10, or school test January 11 to 15 |
| Mid to late January 2027 | Finish Quarter 2 strongly; it closes January 29 | BPS students submit school choices January 5 to February 5 |
| Late April 2027 | Keep going in class, whatever happens | Decision letter via the Avela portal |
Seventy percent of the composite, earned week by week.
Thirty percent; the higher of two scores per subject.
Residency, registration and choices on time.
Readiness
Our own description of growth in grade 6 or grade 8 math. It is not a BPS measure.
| Stage | How it shows |
|---|---|
| 1. Organized | Homework done and corrections made every week |
| 2. Secure | Each unit test at B+ or above |
| 3. Fluent | Mixed problems solved without being told the topic |
| 4. Calm | Comfortable on the testing platform and under time |
Stage 1 is the cheapest win and the one most often missed. Ask to see quiz corrections, not just grades.
Look at the BPS data summaries and tier map for context, but focus your energy on the marks your child can still earn.
Every quiz you correct is a chance to raise the next one. Write down why each wrong answer was wrong.
On test day, estimate before you calculate. It catches the silly mistakes.
The catalogue
Taught live online by a teacher who stays with the student, in a group or privately.
BOE / APP / 01
Pre-algebra and geometry, deeply.
Open the syllabusBOE / APP / 02
Timed reasoning, no shortcuts.
Open the syllabusBOE / APP / 03
For grade 8 applicants.
Open the syllabusBOE / EXT / 01
MATHCOUNTS and AMC 8.
Open the syllabusBOE / EXT / 02
Data and chance.
Open the syllabusBOE / EXT / 03
Mental arithmetic that sticks.
Open the syllabusBOE / NXT / 01
Algebra to calculus.
Open the syllabusBOE / NXT / 02
Numbers meet Python.
Open the syllabusBOE / NXT / 03
For the high school years.
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.
Weekdays
After the school day in Boston.
Weekends
Longer sessions for mixed review.
1-on-1
Following one child’s school units.
We teach what class is teaching now.
Every wrong answer understood.
Problems without a topic label.
A plain note after each month.
Online from any neighborhood.
Groups of 15 to 20, or one student.
Student work
Our students also put math to work in code; the student labs page has examples.

AI and ML
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AI and ML
A chatbot that answers mathematics and programming questions, built and deployed by a student.

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An assistant that helps a young person recognise unsafe situations online.

Web app
A weather forecasting site with live conditions for any location.
Fees
BPS runs exam school admissions and the MAP Growth test; our fee is only for math classes. Monthly billing means you can stop once the decision letter arrives.
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 Boston parents
Boston Public Schools lists Boston Latin Academy, Boston Latin School, and the John D. O'Bryant School of Mathematics and Science. All three admit new students in grades 7 and 9, and the O'Bryant takes a small number in grade 10.
Yes, in the sense that BPS requires the MAP Growth test for all exam school applicants. It counts for 30 percent of the composite score, and the GPA counts for 70 percent.
BPS combines the GPA, weighted 70 percent, with the MAP Growth score, weighted 30 percent. The GPA is worked out on an 11-point scale and scaled to 100 by dividing by 11 and multiplying by 100.
BPS grade 6 and 8 students at non-exam schools test in school between January 11 and 15, 2027. The weekend test is January 9 to 10, 2027, with January 16 to 17 held in case of severe weather.
BPS requires a GPA of B or higher. For grade 7 entry it uses grade 6 marks in ELA, Math, Science and Social Studies from the first two quarters, plus grade 5 ELA and Math from the last marking period.
No. BPS uses unweighted marks and gives no extra points for advanced coursework. Its FAQs say an A+ is treated like an A.
BPS says students have two opportunities, in the spring and winter, and it uses the higher achievement percentile in each subject. Both Reading and Math sections must be completed to get a score.
No. BPS states that exam school decisions are final and that it does not accept appeals. Students not invited to their top choice may be placed on waitlists, which last until November 30.
No. We teach grade-level math and reasoning with our own problems, and point students to the free MAP Growth demo by NWEA that BPS links for platform practice.
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. Modern Age Coders is an independent online school, not connected with Boston Public Schools, any exam school or NWEA. Families apply through BPS and Avela themselves.
Elsewhere on this site
Grade-level math help, other selective entry tests and our Boston coding pages.
The year whose marks count for grade 7 entry.
The year whose marks count for grade 9 entry.
For Boston-area independent schools.
Equations and functions, one to one.
Building alongside math.
Classes for the wider state.
Part of the guide: US gifted and selective school tests
More guides: US state math tests by state · US math placement and college readiness tests · Homeschool and school math curricula guide · US math and coding competitions guide
Start here
Tell us your child’s grade and which math unit they are on. In the first lesson the teacher works on that unit with them and tells you where the next quarter grade can most easily rise.
For a picture of a lesson, see how we teach, or scan the course list.
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