NDSA Grade 8 The Number System Practice

What the test measures

The Number System skills

Know that there are numbers that are not rational, and approximate them by rational numbers.
Work with radicals and integer exponents.
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and use scientific notation to compute with such numbers.

Standards basis

North Dakota State Content Standards for Mathematics — North Dakota

How the NDSA reports it

North Dakota administered its own state assessment program (the NDSA, a Cambium computer-adaptive test in grades 3-8 and 10; replaced by ND A+ beginning spring 2025). An official NDSA mathematics public-facing CAT blueprint (Cambium/NDDPI, Oct 2020) does exist and lists per-grade reporting categories with percentage ranges, but its full per-grade table could not be retrieved character-for-character from a citable primary source for transcription here (the Cambium content CDN blocks programmatic access). The NDSA reporting categories are the CCSS-M grade-level domains: the assessment was built on North Dakota's 2017 math standards, which are verbatim CCSS-M organized by grade-level domains. The coverage map below uses North Dakota's 2023-standards-style domain/standard codes (e.g. 3.AR.OA) but the skill content is CCSS-M.

Blueprint & weighting

An official NDSA mathematics CAT blueprint (Cambium/NDDPI public-facing CAT version, Oct 2020) publishes per-grade reporting-category percentage ranges (e.g. grade 3 Operations and Algebraic Thinking ~31-34%, Number and Operations in Base Ten ~22-24%; grade 6 groups Ratios & Proportional Relationships and The Number System ~28-34% and Expressions and Equations ~25-29%). The complete per-grade table could not be retrieved verbatim from a citable primary source (the Cambium content CDN returns HTTP 403 to programmatic fetches), so domain weights in the mapping are left null rather than transcribing partial/uncertain figures or splitting blueprint percentages across the grade-6+ domain groupings.

Official sources

North Dakota DPI – State Assessment page
North Dakota DPI – Home
North Dakota Department of Agriculture – Ag Mag teacher guide with ND math standards references

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Rewrite $a^{-2}$ with a positive exponent.

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$

Practice playeasy

What is $\sqrt{64}$ ?

$8 \times 8 = 64$ , so $\sqrt{64} = 8$ .

Practice playhard

Let $f(t) = e^{3t}$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = e^{15}$ . Since $e^{15} \approx 3{,}269{,}017$ , $f(5) \approx 3 \times 10^{6}$ .

Practice playeasy

Which is closest to $\sqrt{2}$ ?

$\sqrt{2} \approx 1.414$ .

Practice playeasy

Write $4500$ as $a \times 10^n$ where $1 \le a < 10$ . What is $n$ ?

$4500 = 4.5 \times 10^3$ , so $n = 3$ .

Practice playmedium

$(1.5 \times 10^{4})(8 \times 10^{3})$ equals

Multiply coefficients and add exponents: $1.5 \cdot 8 = 12$ and $4+3=7$ , giving $12 \times 10^{7}$ . Rewrite as $1.2 \times 10^{1} \times 10^{7}=1.2 \times 10^{8}\textsf{.}$

Practice playeasy

$(3 \cdot 7)^{4} = 3^{a} \cdot 7^{a}\textsf{.}$ What is $a\textsf{?}$

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$ , so $a = 4\textsf{.}$