MCAP Grade 8 The Number System. Practice it free.

Measures irrational numbers and their rational approximations. This Grade 8 reporting domain maps to 1 practice skill and 8 representative questions from the playable bank.

Grade 8Content Subclaim1 mapped skills
What the test measures

The Number System skills

  1. 8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers.

Standards basis

Maryland College and Career Ready Standards for Mathematics (MCCRSM) — Maryland

How the MCAP reports it

MCAP is Maryland's statewide successor to PARCC, built on the Maryland College and Career Ready Standards for Mathematics (which mirror CCSS-M) — it is not a Smarter Balanced administration despite the claims-style family resemblance. Each grade/course High Level Blueprint (September 2022) organizes the assessment into three subclaims: Content (23-24 one-point machine-scored items, listed per domain/conceptual category as MCCRSM cluster headings), Reasoning (6 items), and Modeling (6 items), the latter two defined by per-grade evidence statements and including constructed-response items. Cluster headings are transcribed verbatim from the blueprints, including their minor typographical deviations from the parallel CCSS-M headings; two evident misprints are normalized (a duplicated sentence fragment on 4.OA.C, and the domain codes printed as G.P.E / T.TF for G.GPE / F.TF). Since March 2025, grade 6-7 students enrolled in a high-school mathematics course may take the corresponding MCAP course assessment instead of the grade-level test.

Blueprint & weighting

Each High Level Blueprint (September 2022) publishes per-domain operational item counts. Content Subclaim (1-point machine-scored items): Grade 3 — OA 7, NBT 2, NF 7, Measurement 5, Geometry 2 (23 items); Grade 4 — OA 4, NBT 5, NF 10, Measurement 3, Geometry 1 (23); Grade 5 — OA 2, NBT 6, NF 9, Measurement 4, Geometry 2 (23); Grade 6 — RP 3, NS 8, EE 8, Geometry 2, SP 2 (23); Grade 7 — RP 8, NS 4, EE 5, Geometry 3, SP 3 (23); Grade 8 — NS 2, EE 10, Functions 5, Geometry 4, SP 2 (23); Algebra I — Number and Quantity 1, Algebra 12, Functions 9, Statistics 2 (24); Geometry — G.CO 7, G.SRT 8, G.C 3, G.GPE 3, G.GMD 1, G.MG 1 (23); Algebra II — Number and Quantity 3, Algebra 8, Functions 11, Statistics 1 (23). Every assessment adds 6 Reasoning Subclaim and 6 Modeling Subclaim operational items — four 1-point machine-scored each, plus two constructed-response items (two 3-point in grades 3-4; one 3-point and one 4-point in grades 5-8; two 4-point in Algebra I, Geometry, and Algebra II) — so a form carries 35 operational items (36 for Algebra I).

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Which is closest to π\pi?

π3.14159\pi \approx 3.14159.

Practice playeasy

Which is closest to 2\sqrt{2}?

21.414\sqrt{2} \approx 1.414.

Practice playeasy

Which is closest to 3\sqrt{3}?

31.732\sqrt{3} \approx 1.732.

Practice playeasy

Which is closest to 5\sqrt{5}?

52.236\sqrt{5} \approx 2.236.

Practice playeasy

40\sqrt{40} is between two consecutive integers. Enter the smaller one.

62=36<40<49=726^2 = 36 < 40 < 49 = 7^2, so 40\sqrt{40} is between 66 and 77; the smaller is 66.

Practice playeasy

27\sqrt{27} lies between two consecutive integers. Enter the larger one.

52=25<27<36=625^2 = 25 < 27 < 36 = 6^2, so 27\sqrt{27} is between 55 and 66; the larger is 66.

Practice playeasy

What integer is closest to 120\sqrt{120}?

112=12111^2 = 121 sits right above 120120 and 12010.95\sqrt{120} \approx 10.95, so the closest integer is 1111.

Practice playeasy

What is the integer part of 10+2\sqrt{10} + 2?

103.16\sqrt{10} \approx 3.16, so 10+25.16\sqrt{10} + 2 \approx 5.16; the integer part is 55.

Keep practicing

Turn the number system into game time.

The MCAP placement starts with this test's real coverage map and finds the right difficulty.