WA SBAC High School Concepts and Procedures Practice

WA SBAC High School 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 high school clusters listed as targets below (in Washington the high school test is administered in grade 10), with a much greater proportion from clusters the blueprint designates as priority (major) clusters. This High School reporting domain maps to 70 practice skills and 8 representative questions from the playable bank.

High SchoolClaim 170 mapped skills

Concepts and Procedures skills

Target A: Extend the properties of exponents to rational exponents

Target B: Use properties of rational and irrational numbers

Target C: Reason quantitatively and use units to solve problems

Target D: Interpret the structure of expressions

Target E: Write expressions in equivalent forms to solve problems

Target F: Perform arithmetic operations on polynomials

Target G: Create equations that describe numbers or relationships

Target H: Understand solving equations as a process of reasoning and explain the reasoning

Target I: Solve equations and inequalities in one variable

Target J: Represent and solve equations and inequalities graphically

Target K: Understand the concept of a function and use function notation

Target L: Interpret functions that arise in applications in terms of a context

Target M: Analyze functions using different representations

Target N: Build a function that models a relationship between two quantities

Target O: Define trigonometric ratios and solve problems involving right triangles

Target P: Summarize, represent, and interpret data on a single count or measurement variable

Standards basis

Common Core State Standards for Mathematics (CCSS-M; adopted as the Washington State K-12 Learning Standards) — Washington

How the WA SBAC reports it

Washington is a member of the Smarter Balanced Assessment Consortium and administers the consortium's summative mathematics assessment (OSPI calls it the SBA) as its accountability test. Math is organized into the four Smarter Balanced 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. Unlike most consortium states, Washington administers the high school test in grade 10 (moved from grade 11 by ESHB 2224, with grade 10 cut scores adopted in January 2018).

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 on the high school test; the Claim 2/4 and Claim 3 reporting categories are 8-10 items each, totaling 18-20 across the two. Smarter Balanced reports Claims 2 and 4 together as a single subscore because they are described as intertwined in the technical report.

Official sources

Washington OSPI – Smarter Balanced Assessment
Washington OSPI – State Testing (SBA ELA and math in grades 3-8 and 10)
Washington OSPI – Mathematics Assessment (claims documents and per-grade claim distributions)

8 free questions · 0/0 correct

Practice playeasy

Which expression is equivalent to $x^2 + 2x - 15$ ?

Find two numbers with product $-15$ and sum $2$ : $5$ and $-3$ . So $x^2 + 2x - 15 = (x+5)(x-3)$ .

Practice playhard

If $\dfrac{2x + 5y}{3x - y} = \dfrac{4}{3}$ , then $\dfrac{x}{y}=$

Cross-multiply to clear the fraction: $3(2x + 5y) = 4(3x - y)$ , so $6x + 15y = 12x - 4y$ . Collect like terms to get $6x = 19y$ . Divide both sides by $y$ , then by $6$ , to obtain $\dfrac{x}{y} = \dfrac{19}{6}\textsf{.}$

Practice playmedium

If $\dfrac{x^{2} - 25}{x + 5} = 2$ and $x \neq -5\textsf{,}$ what is the value of $x\textsf{?}$

Factor the numerator: $x^{2} - 25 = (x-5)(x+5)$ . For $x \neq -5$ , the factor $x+5$ cancels, giving $x-5 = 2$ , so $x = 7\textsf{.}$

Practice playeasy

The graph of $y = -2(x + 15)(x - 8)(x + 3)$ intercepts the $x$ -axis at which value of $x$ ?

Set $y = 0$ : $-2(x + 15)(x - 8)(x + 3) = 0$ . The constant $-2 \neq 0$ , so the zeros are $x = -15$ , $x = 8$ , and $x = -3$ . Among the choices, only $8$ is an x-coordinate of an x-intercept.

Practice playmedium

$\begin{cases} 2x - y \ge 4 \\ x + y \le 7 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 2$ , which of the following could be a value of $x$ ?

Substitute $y = 2$ . From $2x - y \ge 4$ , $2x - 2 \ge 4$ , so $x \ge 3$ . From $x + y \le 7$ , $x \le 5$ . The value $x = 4$ satisfies $3 \le 4 \le 5$ .

Practice playeasy

$f(x) = (x - 8)^2 + 1$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

The equation is in vertex form $f(x) = a(x - h)^2 + k$ with $a = 1 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 8$ , so the vertex is at $x = 8$ . Therefore, $f(x)$ reaches its minimum when $x = 8$ .

Practice playmedium

For the relation $y = 3x^2 - 30x + 70$ , find the value of $x$ at which $y$ is smallest.

The parabola opens upward, so the smallest $y$ is at the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 3$ and $b = -30$ , so $x = -\dfrac{-30}{2(3)} = \dfrac{30}{6} = 5$ . Therefore, $y$ is smallest when $x = 5$ .

Practice playeasy

A chess club ordered custom shirts and name tags. Every member received the same number of shirts and the same number of tags. The shipment contained $45$ shirts and $75$ name tags in all. Which could be the number of members in the chess club?

The number of members must divide both totals evenly. The common factors of $45$ and $75$ greater than $1$ are $3$ , $5$ , and $15$ . Only $15$ is listed: $45 \div 15 = 3$ shirts and $75 \div 15 = 5$ tags per member.

WA SBAC High School Concepts and Procedures. Practice it free.

Concepts and Procedures skills

Target A: Extend the properties of exponents to rational exponents

Target B: Use properties of rational and irrational numbers

Target C: Reason quantitatively and use units to solve problems

Target D: Interpret the structure of expressions

Target E: Write expressions in equivalent forms to solve problems

Target F: Perform arithmetic operations on polynomials

Target G: Create equations that describe numbers or relationships

Target H: Understand solving equations as a process of reasoning and explain the reasoning

Target I: Solve equations and inequalities in one variable

Target J: Represent and solve equations and inequalities graphically

Target K: Understand the concept of a function and use function notation

Target L: Interpret functions that arise in applications in terms of a context

Target M: Analyze functions using different representations

Target N: Build a function that models a relationship between two quantities

Target O: Define trigonometric ratios and solve problems involving right triangles

Target P: Summarize, represent, and interpret data on a single count or measurement variable

Topics mapped to this domain

Factoring quadratic expressions (ACT)

Rational equations — find a ratio (ACT)

Rational equation solving (SAT)

Factored polynomial x-intercepts (SAT)

Linear inequality system solutions

Quadratic minimum from vertex form

Quadratic minimum x-value

Common factor group size (ACT)

Fraction bounds extreme value (ACT)

LCM word problems (ACT)

Monomial expression multiplication (SAT)

Polynomial combining like terms (ACT/SAT)

8 free questions · 0/0 correct

Turn concepts and procedures into game time.