Gizmos for North Dakota - Mathematics: Algebra (Content Standards adopted 2017)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

HS.A-SSE: : Seeing Structure in Expressions

1.1: : Interpret the structure of expressions

HS.A-SSE.1: : Interpret expressions that represent a quantity in terms of its context.

HS.A-SSE.1.a: : Interpret parts of an expression, such as terms, factors, and coefficients.

HS.A-SSE.1.b: : Interpret complicated expressions by examining one or more of their parts as a single entity.

HS.A-SSE.2: : Use the structure of an expression to identify ways to rewrite it.

1.2: : Write expressions in equivalent forms to solve problems

HA.A.SSE.3: : Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

HA.A.SSE.3.a: : Factor a quadratic expression to reveal the zeros of the function it defines.

HA.A.SSE.3.b: : Complete the square in a quadratic expression to produce an equivalent expression.

HA.A.SSE.3.c: : Use the properties of exponents to transform exponential expressions.

HS.A-APR: : Arithmetic with Polynomials and Rational Expressions

2.1: : Perform arithmetic operations on polynomials

HS.A-APR.1.i: : Add, subtract, and multiply polynomials.

HS.A-APR.1.ii: : Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.

2.2: : Understand the relationship between zeros and factors of polynomials

HS.A-APR.2: : Apply the Remainder Theorem.

2.2.1.1: : Remainder Theorem: For a polynomial ??(??) and a number ??, the remainder on division by ?? – ?? is ??(??), so ??(??) = 0 if and only if (?? – ??) is a factor of ??(??).

HS.A-APR.3.i: : Identify zeros of polynomials when suitable factorizations are available.

HS.A-APR.3.ii: : Use the zeros to construct a rough graph of the function defined by the polynomial.

2.3: : Use polynomial identities to solve problems

HS.A-APR.5: : Apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n.

2.3.2.1: : Coefficients in the expansion of (?? + ??)? can be determined using Pascal’s Triangle or combinations.

HS.A-CED: : Creating Equations and Inequalities

3.1: : Create equations that describe numbers or relationships

HS.A-CED.1: : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HS.A-CED.2.i: : Create equations in two or more variables to represent relationships between quantities.

HS.A-CED.2.ii: : Graph equations on coordinate axes with appropriate labels and scales.

HS.A-CED.3: : Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

HS.A-CED.4: : Rearrange formulas to isolate a quantity of interest, using the same reasoning as in solving equations.

HS.A-REI: : Reasoning with Equations and Inequalities

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

HS.A-REI.1: : Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

HS.A-REI.2: : Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

4.2: : Solve equations and inequalities in one variable

HS.A-REI.3: : Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HS.A-REI.4: : Solve quadratic equations in one variable.

HS.A-REI.4.a.i: : Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions.

HS.A-REI.4.a.ii: : Derive the quadratic formula from this form.

HS.A-REI.4.b.i: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

HS.A-REI.4.b.ii: : Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

4.3: : Solve systems of equations

HS.A-REI.6: : Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables.

HS.A-REI.8: : Represent a system of linear equations as a single matrix equation.

HS.A-REI.9: : Find the inverse of a matrix, if it exists, and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

4.4: : Represent and solve equations and inequalities graphically

HS.A-REI.10: : Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

HS.A-REI.11: : Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) are the x-value(s) that result in the y-values of f(x) and g(x) being the same.

HS.A-REI.12.i: : Graph the solutions to a linear inequality in two variables as a half-plane.

HS.A-REI.12.ii: : Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Correlation last revised: 9/22/2020

North Dakota - Mathematics: Algebra

Content Standards | Adopted: 2017

HS.A-SSE: : Seeing Structure in Expressions

HS.A-APR: : Arithmetic with Polynomials and Rational Expressions

HS.A-CED: : Creating Equations and Inequalities

HS.A-REI: : Reasoning with Equations and Inequalities