IXL - DoDEA algebra standards

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2009 DoDEA Content Standards 2009 DoDEA Content Standards

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A1.1 Number Sense and Operations

A1.1.1 Identify and use the properties of operations on real numbers, including commutative, associative, distributive, and identity and inverse elements for addition and multiplication;
A1.1.2 Use the binomial theorem to expand binomial expressions;
A1.1.3 Explain the relationship between real numbers and the number line (including the density property) and compare and order real numbers with and without the number line;
A1.1.4 Solve simple equations in one variable using inverse relationships between operations such as addition and subtraction (taking the opposite), multiplication and division (multiplying by the reciprocal), raising to a power and taking a root;
A1.1.5 Explain and use the laws of exponents, including fractional and integral exponents;
A1.1.6 Simplify numerical expressions, including those involving radicals and absolute value.

A1.2 Polynomials

A1.2.1 Add, subtract, multiply, and divide monomials and polynomials and solve multistep problems by using these techniques;
A1.2.2 Apply basic factoring techniques to second-degree polynomials;
A1.2.3 Solve multistep problems that involve adding, subtracting, multiplying, and dividing rational expressions and reduce solutions to lowest terms by factoring the numerator and denominator;
A1.2.4 Solve problems involving equations with algebraic fractions including direct, inverse, and joint variation.

A1.3 Linear Equations and Inequalities

A1.3.1 Write an equation of a line when given the graph of the line, a data set, two points on the line, or the slope and a point of the line;
A1.3.2 Describe and calculate the slope of a line given a data set or graph of a line, recognizing that the slope is the rate of change;
A1.3.3 For bivariate data that appear to form a linear pattern, find the line of best fit by estimating visually and/or using appropriate technology to determine the least squares regression equation. Interpret the slope of the equation for a regression line within the context of the data and use the equation to make predictions;
- Charts and graphs: Scatter plots: line of best fit (Algebra - N.7)
A1.3.4 Identify rates of change (slope) and distinguishing properties of data from tables, graphs, and equations to predict what happens to one variable as another variable changes;
A1.3.5 Describe and analyze lines that have positive, negative, zero and undefined slopes;
- Linear functions: Graph a horizontal or vertical line (Algebra - S.13)
A1.3.6 Represent linear relationships graphically, algebraically (including the slope-intercept form) and verbally and relate a change in the slope or the y-intercept to its effect on the various representations;
A1.3.7 Graph inequalities and shade the regions that they define;
A1.3.8 Verify if a point lies on the graph of a line from tables, graphs and equations;
A1.3.9 Understand and identify characteristics (parallel, perpendicular, horizontal, vertical) of linear functions and be able to determine linear equations to match given characteristics;
- Linear functions: Equations of horizontal and vertical lines (Algebra - S.12)
- Linear functions: Slopes of parallel and perpendicular lines (Algebra - S.17)
A1.3.10 Solve multistep problems involving linear equations and/or inequalities (including those with absolute value) in one variable and provide justification for each step;
A1.3.11 Apply and use linear equations and/or inequalities as mathematical representations of proportional relationships to solve problem; including rate problems, work problems, and percent mixture problems;
A1.3.12 Represent and solve problems that can be modeled using a system of linear equations and/or inequalities in two variables, sketch the solution sets, and interpret the results within the context of the problem.

A1.4 Quadratic Functions and Equations

A1.4.1 Recognize the characteristic shape of the graph of a quadratic function and describe its line of symmetry, vertex, and intercepts;
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
A1.4.2 Determine solutions to quadratic equations (with real roots) by graphing, factoring, completing the square, or using the quadratic formula;
A1.4.3 Graph a quadratic polynomial and explain the relationship among the solutions, the zeros, the x-intercepts, and the factors;
A1.4.4 Translate between the standard form of a quadratic equation, the vertex form, and the factored form. Graph and interpret the relationships between the equation and the graph for each form.

A1.5 Data Analysis

A1.5.1 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, histogram, circle graph, etc) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data;
A1.5.2 Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
- Charts and graphs: Scatter plots: line of best fit (Algebra - N.7)