Pennsylvania · Grades 3 to 8 · From PDE’s test design

PSSA math practice for grades 3 to 8

The PSSA math test starts in an unusual way. In grades 4 to 8, the first four questions must be answered without a calculator, and once a student confirms they are done, the test will not let them back. After that, any calculator that meets the state policy is allowed, graphing calculators included. Three open-ended questions, each scored out of 4, carry almost a quarter of the points. Below is the Pennsylvania Department of Education’s own account of the 2026 to 2027 test, followed by what separates a 4 from a 2 on an open-ended answer, using a problem we wrote.

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In short

The PSSA (Pennsylvania System of School Assessment) math test is the state’s annual test for every student in grades 3 to 8. Each grade has 52 core points: 40 multiple-choice and technology-enhanced items plus three 4-point open-ended questions, over two sections. Grade 3 allows no calculator; grades 4 to 8 open with four calculator-free questions. Math is tested May 3 to 7, 2027. Our live online PSSA lessons at Modern Age Coders run as a group batch or 1-on-1, beginning with the Elementary Maths course for younger children.

Courses for Pennsylvania students

Three courses mapped to the PSSA reporting categories

Each teaches the Pennsylvania Core Standards in the order schools use, with open-ended writing every week.

Elementary Maths for Grades 1-5 course thumbnail

PSPR / 01

PSSA years 3 to 5

Base ten, fractions and the grade 3 no-calculator test.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

PSPR / 02

PSSA years 6 to 8

Ratios, expressions and the grade 8 functions category.

Open the syllabus →
Algebra Foundations course thumbnail

PSPR / 03

On to Algebra I

For eighth graders who will meet the Keystone next.

Open the syllabus →

Test design

How is the PSSA math test built, and what is it worth?

Every grade from 3 to 8 has the same shape: 40 core multiple-choice and technology-enhanced items worth 40 points, plus 3 core open-ended items worth 4 points each, for 52 core points. Field-test items sit alongside them.

PSSA Mathematics operational plan per form, grades 3 to 8 (PDE PSSA Mathematics Test Design, 2025, read 31 October 2026)
Item typeCorePsychometric useEmbedded field testCore points
Multiple choice and technology enhanced402640
Open-ended (4 points each)30112
Total core, as PDE prints it40 MC/TE and 3 OE52

Two sections

PDE’s layout plan has two sections, each with 24 multiple-choice or technology-enhanced items and 2 open-ended items, and an estimated testing time of 78 minutes per section.

Those section counts include the non-scored items, so a child answers more questions than the core set that counts, and cannot tell which ones are field tests.

Standards-based, not ranked

PDE describes the PSSA as “a standards-based, criterion-referenced assessment”. Children are measured against the Pennsylvania Core Standards, not against each other.

PDE also notes that “Individual student scores, provided only to their respective schools” are used to help teachers spot students who need more support. Ask the school for your child’s report.

Sources: PSSA Mathematics Test Design (2025) and the PSSA page, Pennsylvania Department of Education, read 31 October 2026. We are not connected with PDE, its test contractor or any Pennsylvania district.

The calculator gate

Can you use a calculator on the PSSA math test?

Not in grade 3 at all. In grades 4 to 8, questions 1 to 4 of section 1 are calculator-free, and after that a calculator is allowed, including scientific and graphing models that meet the state policy.

PSSA mathematics calculator rules (PSSA Mathematics Test Design 2025; 2026 Grades 3 to 8 Mathematics Directions for Online Administration; Pennsylvania Calculator Policy, revised October 2023)
Grade or partRule
Grade 3Calculators are not allowed on the test
Grades 4 to 8, section 1, questions 1 to 4No calculator; once the student confirms these are done, they cannot return to them
Grades 4 to 8, the rest of the testCalculators allowed, including scientific and graphing, if they meet the policy; an online calculator is provided
Not permittedPhones and other devices, wireless calculators unless disabled, computer algebra systems, calculators that print or talk, sharing
MemoryCleared before and after each session by the test administrator, not the student

The four-question gate

The spring 2026 directions say students “will be asked to confirm that they have finished answering questions 1 through 4. After confirming, students will not be allowed to return to questions 1 through 4.”

So those four answers must be checked before pressing on. We teach a ten-second habit: reread the question, re-estimate the answer, then confirm.

Bring a familiar calculator, or none

The directions add that calculators are not mandatory. A child can use the online calculator, their own, or one from the school, provided it follows the Pennsylvania Calculator Policy.

If your child brings their own, make sure it is one they use every day. A new graphing calculator on test day costs more time than it saves.

Sources: Grades 3 to 8 Mathematics Directions for Online Administration (spring 2026) and the Pennsylvania Calculator Policy.

Reporting categories

What is on the PSSA math test in each grade?

PDE groups the content into four clusters, Numbers and Operations, Algebraic Concepts, Geometry, and Data Analysis and Probability, and gives each grade a percent range by reporting category.

PSSA Mathematics blueprint, percent of the core by reporting category (PDE PSSA Mathematics Test Design, 2025, read 31 October 2026)
GradeNumbers and OperationsAlgebraic ConceptsGeometryData and Probability
3Base ten 14 to 17%; fractions 14 to 17%Operations and algebraic thinking 26 to 32%14 to 17%Measurement and data 26 to 32%
4Base ten 18 to 22%; fractions 20 to 25%Operations and algebraic thinking 24 to 28%14 to 17%Measurement and data 17 to 21%
5Base ten 24 to 28%; fractions 26 to 30%Operations and algebraic thinking 14 to 17%14 to 17%Measurement and data 17 to 21%
6Number system 18 to 22%; ratios 17 to 21%Expressions and equations 26 to 30%14 to 17%Statistics and probability 18 to 22%
7Number system 14 to 17%; ratios 24 to 28%Expressions and equations 24 to 28%18 to 22%Statistics and probability 14 to 17%
8Number system 14 to 17%Expressions and equations 30 to 35%; functions 20 to 25%17 to 21%Statistics and probability 14 to 17%

What jumps out

Grade 5 is a heavy number year: fractions at 26 to 30 percent and base ten at 24 to 28 percent are its two largest shares. Grade 3 puts as much weight on measurement and data as on operations.

Grade 8 is the algebra year. Expressions and equations reach 30 to 35 percent, and functions appear as their own category for the first time at 20 to 25 percent.

In points

PDE also prints each range in points out of 52. Grade 8 expressions and equations, for example, is 16 to 18 points, while grade 3 measurement and data is 14 to 17 points.

We plan a child’s spring around the two largest categories for their grade, and keep the smaller ones ticking over.

Open-ended questions

How are PSSA math open-ended questions scored?

On a 0 to 4 scale. PDE’s general guideline describes a 4 as showing a thorough understanding, with correct answers, clear and complete procedures, and a correct explanation where the task asks for one.

General Description of Scoring Guidelines for Mathematics Open-Ended Questions, in short (PDE grade 6 scoring guidelines and formula sheet, 2025, read 31 October 2026)
ScoreUnderstanding shownWhat PDE says the response looks like
4ThoroughCorrect answers, clear and complete procedures, correct explanation; may contain a minor “blemish” or omission
3GeneralMostly complete and correct; minor errors or omissions
2PartialSomewhat correct; some work incomplete or unclear
1MinimalMarginally correct; work undeveloped and rudimentary
0None shownNo correct answer and insufficient evidence; blank, off-task, other-language and illegible responses are reported separately
  1. Our grade 7 problem (not a PSSA item). At a school fun run, Dev runs 3 laps every 4 minutes at a steady pace. Part A: how long will 9 laps take? Part B: write an equation for the time t in minutes for n laps. Part C: Priya runs 25% faster than Dev. How many laps does she run in 12 minutes? Explain.
  2. Part A. 9 laps is 3 groups of 3 laps, so 3 x 4 = 12 minutes.
  3. Part B. Each lap takes 4/3 minutes, so t = (4/3)n. Check with Part A: (4/3) x 9 = 12.
  4. Part C. Dev runs 9 laps in 12 minutes. 25% faster means 25% more laps in the same time: 9 x 1.25 = 11.25 laps. Priya runs 11 1/4 laps in 12 minutes.
  5. Three responses, judged against PDE’s general guideline as we read it. Response 1 gives 12, t = (4/3)n and 11.25 with every step and the sentence about “more laps in the same time”: thorough, a 4. Response 2 gets Parts A and B right but writes 9.6 laps in Part C by dividing instead of multiplying, with working shown: general understanding, likely a 3. Response 3 writes only 12, 4/3 and 11, with no work: partial at best, likely a 2. Real scoring uses item-specific rubrics; these judgements are our teaching illustration.

The lesson from Response 3 is the one we repeat most: the guideline rewards “clear and complete mathematical procedures shown”, so a bare answer cannot reach the top score even when the number is right.

Spring 2027

When is the PSSA math test in 2027?

Mathematics is scheduled for May 3 to 7, 2027, with an optional second week of May 10 to 14 for math, science and make-ups. ELA comes first, the week before.

PSSA testing windows, 2026 to 2027 school year (PDE PSSA page, read 31 October 2026)
AssessmentDatesGrades
English Language ArtsApril 26 to 30, 20273 to 8
Mathematics, Science and Make-upsMay 3 to 7, 20273 to 8
Mathematics, Science, and Make-ups (Optional)May 10 to 14, 20273 to 8

The make-up deadline

PDE states that the PSSA administration “needs to be completed by the end of the make-up window, which concludes May 14, 2027.” Schools pick their own days within these weeks.

PDE also notes that Early Reporting is not available in the 2026 to 2027 school year, so results arrive on the normal schedule.

Firefly during the year

The same PDE page lists Firefly windows for ELA, mathematics and science from October 5, 2026 to April 16, 2027. Some schools use it during the year; ask your school whether it does.

For planning, count back from May 3, 2027. Our five-week plan below is built on that date.

Source: Pennsylvania System of School Assessment (PSSA), testing windows section, PDE.

Results

What do PSSA math scores Advanced, Proficient, Basic and Below Basic mean?

They are the four performance levels set by the State Board of Education. Proficient and Advanced mean a student has met or gone beyond the grade’s standards.

PDE’s PSSA page says that, under the Pennsylvania School Code, the State Board of Education approved “specific criteria for advanced, proficient, basic and below basic levels of performance.” Each child’s scaled score falls into one of those four bands for the grade.

Read the category scores

The report breaks results down by reporting category, so you can see whether the gap is in fractions, expressions or data.

Compare to the blueprint

A weak result in a category worth 26 to 32 percent matters more than one in a 14 to 17 percent category.

Talk to the teacher

PDE says scores help teachers identify students who may need extra support. That conversation is the useful next step.

We do not print scaled-score cut points here. The only cut score table we found on PDE’s site is undated and still lists a grade 11 PSSA, which Pennsylvania replaced with the Keystone Exams, so we would rather not quote it.

Practice

Twelve PSSA-style math practice questions, grades 3 to 8

Ours, two per grade, each tagged with the PDE reporting category it practises. The first in each grade suits the calculator-free start.

Original practice (ours, not PDE items), with answers
GradeQuestionCategoryAnswer
3What is 9 x 6?B-O Operations and Algebraic Thinking54
3A movie starts at 2:15 and lasts 1 hour 50 minutes. When does it end?D-M Measurement and Data4:05
4Write 0.7 as a fraction and as a number of hundredths.A-F Fractions7/10; 70 hundredths
4A rectangle has perimeter 30 cm and length 9 cm. Find its width.D-M Measurement and Data6 cm
5Compute 2 1/2 + 1 3/4.A-F Fractions4 1/4
5Divide 1,248 by 6.A-T Base Ten208
6What is the absolute value of -14?A-N Number System14
6Find the mean of 4, 7, 9, 12 and 13.D-S Statistics and Probability9
7Simplify 3(2x - 5) + 4x.B-E Expressions and Equations10x - 15
7A circle has diameter 10 cm. Find its circumference to the nearest tenth.C-G Geometry31.4 cm
8Write 0.000045 in scientific notation.A-N Number System4.5 x 10^-5
8A function rule is y = -3x + 4. Find y when x = -2, and say whether the function is increasing.B-F Functions10; decreasing

PDE publishes Item and Scoring Samplers for each grade, with released questions and scoring notes, on its PSSA page, along with the grade-level formula sheets. We use the samplers for rehearsal and teach first with problems like these.

A plan

A five-week PSSA math plan to May 3, 2027

Our plan for the run-in to the math window, after the year’s teaching is mostly done.

  1. Week 1: one sampler, scored by category. We use a recent PDE Item and Scoring Sampler for the grade and sort errors by reporting category.
  2. Week 2: the two heaviest categories. From the blueprint table: base ten and fractions in grade 5, expressions and equations plus functions in grade 8, and so on.
  3. Week 3: open-ended answers. Two four-point problems a lesson, written in parts with labelled working, judged against PDE’s general guideline.
  4. Week 4: the calculator gate. Four calculator-free questions to start every session, checked and confirmed, then the rest with the child’s own calculator and the grade’s formula sheet.
  5. Week 5: one full section, then rest. A 78-minute rehearsal of a section, then a lighter final few days before May 3.

Grade by grade

Where PSSA points are won in each grade

Our reading of PDE’s blueprint percentages.

The largest categories by grade (weights from PDE; priorities ours)
GradeBiggest categoriesOur first focus
3Operations and algebraic thinking; measurement and dataMultiplication facts and telling time
4Operations and algebraic thinking; fractionsEquivalent fractions and multi-step word problems
5Fractions; base tenAdding fractions and decimal place value
6Expressions and equationsWriting and solving one-variable equations
7Ratios; expressions and equationsProportional relationships and percent
8Expressions and equations; functionsLinear equations, systems and function rules

For parents

Ask for one open-ended answer your child wrote in class. If it is a bare number, that is the quickest place to gain points before May.

Grade 3 has no calculator at all, so daily fact practice pays off directly.

For students

On questions 1 to 4, check each one before you confirm. You cannot go back.

On open-ended questions, label Part A, Part B and Part C, and show every step even when it feels obvious.

The catalogue

Math courses for Pennsylvania students

From the first PSSA in grade 3 to the Algebra I year.

I

Elementary

Grades 3 to 5

PSPR / E / 01

Elementary math

Every grade 3 to 5 reporting category.

Open the syllabus

PSPR / E / 02

Mental math

For grade 3 and the four-question start.

Open the syllabus
II

Middle school

Grades 6 to 8

PSPR / M / 02

Math competitions

For students who want harder problems.

Open the syllabus

PSPR / M / 03

Math through coding

Patterns and functions in Python.

Open the syllabus
III

After the PSSA

Algebra I and beyond

How lessons run

Lessons that fit a Pennsylvania school week

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

After school ET

Weekday lessons in step with the class.

Weekends

Section rehearsals in April.

1-on-1

Open-ended answers rewritten to a 4.

Category-mapped

Lessons follow PDE’s reporting categories.

Four-question start

Calculator-free warm-ups every session.

Open-ended weekly

Written in parts, judged to the guideline.

Formula sheets

The grade’s own sheet in class.

Samplers late

PDE’s released items for rehearsal.

Two formats

Fifteen to twenty, or one to one.

Student work

From our students

Older students sometimes build their math into code. Look at student labs.

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Pennsylvania families ask

PSSA math: common questions

When is the PSSA math test in 2027?

PDE schedules mathematics for May 3 to 7, 2027, with an optional week of May 10 to 14 for math, science and make-ups. ELA is tested first, April 26 to 30, 2027.

How many questions are on the PSSA math test?

Each grade has 52 core points: 40 multiple-choice or technology-enhanced items worth a point each, and 3 open-ended items worth 4 points each. Field-test items are added, so students answer more than that.

Can you use a calculator on the PSSA math test?

Not in grade 3. In grades 4 to 8 the first four questions of section 1 are calculator-free, and after that calculators are allowed, including scientific and graphing ones that meet the Pennsylvania Calculator Policy.

How long is the PSSA math test?

PDE's test design estimates 78 minutes for each of the two sections. Schools set the exact schedule within the May window.

How are PSSA open-ended math questions scored?

On a 0 to 4 scale. PDE's general guideline gives a 4 for thorough understanding with correct answers, complete procedures shown and a correct explanation, down to 1 for minimal understanding.

What does Proficient mean on the PSSA?

Proficient is one of four performance levels approved by the State Board of Education: Advanced, Proficient, Basic and Below Basic. Proficient and Advanced mean the student met or exceeded the grade's standards.

What is on the grade 8 PSSA math test?

Expressions and equations is the largest category at 30 to 35 percent, then functions at 20 to 25 percent, geometry at 17 to 21 percent, and the number system and statistics at 14 to 17 percent each.

Where can I find PSSA math practice?

PDE posts Item and Scoring Samplers for each grade and the grade-level formula sheets on its PSSA page. The questions on this page are our own extra practice, tagged by reporting category.

Is the PSSA taken on the computer?

PDE publishes Directions for Online Administration for the grades 3 to 8 math test, and an online calculator is provided during testing. Ask your school whether any students test on paper.

When are your classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. All lessons run on Eastern Time.

Are you connected with PDE?

No. Modern Age Coders is an independent online school with no connection to the Pennsylvania Department of Education, its test contractor or any district. We quote PDE's public documents and link to them.

Elsewhere on this site

Related pages

Grade pages and Pennsylvania pages.

Third grade math tutoring

The calculator-free PSSA year.

Fifth grade math tutoring

Fractions and base ten.

Eighth grade math tutoring

Equations and functions.

Middle school math placement

For the move into Algebra I.

Coding and AI in Pennsylvania

Our Pennsylvania page.

Philadelphia classes

For families in Philadelphia.

Related pages in this guide

Part of the guide: US state math tests by state

State tests, grades 3 to 8

High school end-of-course and graduation tests

Standards behind the tests

More guides: US gifted and selective school tests · US math placement and college readiness tests · Homeschool and school math curricula guide · US math and coding competitions guide

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