SBAC Grade 8 Concepts and Procedures Practice

SBAC Grade 8 Concepts and Procedures. Practice it free.

Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. Content is drawn from the Grade 8 clusters listed as targets below, with a much greater proportion from clusters the blueprint designates as priority (major) clusters. This Grade 8 reporting domain maps to 26 practice skills and 8 representative questions from the playable bank.

Grade 8Claim 126 mapped skills

Concepts and Procedures skills

Target A: Know that there are numbers that are not rational, and approximate them by rational numbers

Target B: Work with radicals and integer exponents

Target C: Understand the connections between proportional relationships, lines, and linear equations

Target D: Analyze and solve linear equations and pairs of simultaneous linear equations

Target E: Define, evaluate, and compare functions

Target F: Use functions to model relationships between quantities

Target G: Understand congruence and similarity using physical models, transparencies, or geometry software

Target H: Understand and apply the Pythagorean theorem

Target I: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

Target J: Investigate patterns of association in bivariate data

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — national

How the SBAC reports it

Smarter Balanced math is organized into four claims with published assessment targets (Mathematics Content Specifications). Claim 1 (Concepts and Procedures) publishes per-grade assessment targets for grades 3-8 and high school, each a verbatim CCSS-M cluster heading (e.g. grade 3 Target A is cluster 3.OA.A); Claims 2-4 are cross-cutting process claims whose targets are constant across grades and draw on the same grade-level content. On score reports, Claims 2 and 4 are combined into a single reporting category, so three claim scores accompany the overall math score.

Blueprint & weighting

Content Specifications (Reporting Categories section): the total mathematics score is a weighted composite of the four claims — Claim 1 (Concepts and Procedures) contributes roughly 50%, Claim 3 (Communicating Reasoning) roughly 25%, and combined Claims 2 and 4 (Problem Solving / Modeling and Data Analysis) about 25%. The summative blueprint (as of 2018-19) publishes item counts per test event rather than percentages: Claim 1 is 17-20 items in grades 3-5, 16-20 in grades 6-8, and 19-22 in grade 11; the Claim 2/4 and Claim 3 reporting categories are 8-10 items each, totaling 18-20 across the two.

Official sources

Smarter Balanced Mathematics Content Specifications (July 2015)
Smarter Balanced Mathematics Summative Assessment Blueprint (as of 2018-19)
Smarter Content Explorer (per-target pages, e.g. Grade 3 Claim 1 Target A)

8 free questions · 0/0 correct

Practice playeasy

A cylinder has radius $1$ and height $5$ . Using $\pi = 3$ , what is its volume?

$V = \pi r^2 h = 3 \times 1 \times 5 = 15$ .

Practice playeasy

What is the $y$ -intercept of the graph of $y = 5x + 27$ in the coordinate plane?

In $y = mx + b$ , the $y$ -intercept is the point $(0, b)$ . Here $b = 27$ , so the $y$ -intercept is $(0, 27)\textsf{.}$

Practice playeasy

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

$\sqrt{2} \approx 1.414$ .

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 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

What is the slope of the line $y = \dfrac{3}{2}x + 2$ ?

In $y = mx + b$ , the slope is $m = \dfrac{3}{2}$ .

Practice playeasy

Which of the following systems of linear equations has no solution?

Both equations have slope $2$ but different $y$ -intercepts ( $3$ and $-1$ ), so the lines are parallel and the system has no solution.

Practice playeasy

In $\triangle PQR$ , $\angle P$ and $\angle Q$ are congruent. The measure of $\angle R$ is $118.6^{\circ}$ . What is the measure of $\angle Q$ ?

Let each congruent angle measure $x^{\circ}$ . Then $2x + 118.6 = 180$ , so $x = \dfrac{180 - 118.6}{2} = 30.7^{\circ}$ .

SBAC Grade 8 Concepts and Procedures. Practice it free.

Concepts and Procedures skills

Target A: Know that there are numbers that are not rational, and approximate them by rational numbers

Target B: Work with radicals and integer exponents

Target C: Understand the connections between proportional relationships, lines, and linear equations

Target D: Analyze and solve linear equations and pairs of simultaneous linear equations

Target E: Define, evaluate, and compare functions

Target F: Use functions to model relationships between quantities

Target G: Understand congruence and similarity using physical models, transparencies, or geometry software

Target H: Understand and apply the Pythagorean theorem

Target I: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

Target J: Investigate patterns of association in bivariate data

Topics mapped to this domain

Volume of prisms and cylinders

Y-intercept as a point

Irrational number approximations

Exponent rules

Evaluating exponential functions

Graphing linear equations

Inconsistent linear systems (ACT/SAT/PSAT 8/9/10)

Isosceles triangle angles

Linear Algebra Basics: Systems

Linear functions with an unknown constant

Modeling linear situations (ACT/SAT/PSAT 8/9/10)

Multi-step linear equations

8 free questions · 0/0 correct

Turn concepts and procedures into game time.