Pre-Algebra

Pattern & Algebraic Thinking

Numeracy & Numerical Reasoning

Geometry & Spatial Reasoning

Measurement & Statistical Reasoning

Functions & Graphs

Use variables to represent two quantities in a proportional relationship in a real-world problem; write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.

Apply the properties of operations (e.g., identity, inverse, commutative, associative, and distributive properties) to create equivalent linear expressions, including situations that involve factoring (e.g., given 2x - 10, create an equivalent expression 2(x - 5)).

Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.

Accurately use square root and cube root symbols.

Solve systems of two linear equations algebraically and graphically using elimination and substitution methods.

Solve linear equations in one variable with one solution, infinitely many solutions or no solutions.

Solve linear equations with rational numbers

Use variables to represent quantities in a real-world problem to construct simple equations and inequalities.

Solve equations of the form x + p = q, x - p = q, px = q, and x/p = q fluently for cases in which p, q and x are all nonnegative rational numbers. Represent real world problems using equations of these forms and solve such problems.

Represent real-world problems using linear equations and inequalities in one variable, including those with rational number coefficients and variables on both sides of the equal sign.

Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.

Interpret and convert between scientific and standard notations.

Identify, compare, and order rational and common irrational numbers (√2, √3, √5, ∏) and plot them on number line.

Interpret sums of rational numbers by describing real-world contexts.

Illustrate that the absolute value of a number is the distance from zero on a number line in real-world contexts.

Develop the multiplication counting principle and apply it to situations with many numbers of outcomes.

Define, evaluate, and compare functions including rational numbers.

Use variables to represent two quantities in a proportional relationship in a real-world problem.

Evaluate square roots. 

Use proportional relationships to solve ratio and percent problems with multiple operations (e.g. simple interest, tax, markups, markdowns, gratuities, conversions within and across measurement systems, percent increase and decrease, and percent error).

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane.

Draw triangles (freehand, with ruler and protractor, and using technology) with given conditions from three measures of angles or sides, and notice when the conditions determine a unique triangle, more than one triangle, or no triangle.

Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional reasoning.

Explain that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. Describe a sequence that exhibits the congruence between two given congruent figures.

Describe the effect of dilations, translations, rotations, and reflections on two dimensional figures using coordinates.

Interpret the formulas for area and circumference of a circle and use them to solve real-world problems.

Verify experimentally the properties of rotations, reflections, and translations, including: lines mapped to lines, line segments to line segments of the same length, angles mapped to angles of the same measure, and parallel lines mapped to parallel lines.

Make observations about the degree of visual overlap of two numerical data distributions represented in line plots or box plots.

Find, use, and interpret measures of center (mean and median) and measures of spread (range, interquartile range, and mean absolute deviation) for numerical data from random samples to draw comparative inferences about two populations.

Explain how statistics is a process for making inferences about a population based on a random sample from that population.

Explain that statistics and data are non-neutral and designed to serve a particular interest. Analyze the possibilities for whose interest might be served and how the representations might be misleading.

Summarize bivariate categorical data in two-way frequency tables.

Use data from a random sample to draw inferences about a population.

Explain the probability of an event occurring as a number between 0 and 1 where 0 indicates an unlikely event and 1 indicates an event certain to occur.

Explain that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Represent sample spaces and find probabilities of compound events (independent and dependent) using methods, such as organized lists, tables, and tree diagrams.

Develop and compare probability models.

Interpret relative frequencies in the contexts of the data (including joint, marginal, and conditional relative frequencies), and recognize possible associations and trends in data.

Solve inequalities of the form px +q (> or ≥) r or px + q (< or ≤) r, where p, q, and r are specific rational numbers.

Represent and graph the solution set of the inequality and interpreted in the context of a real-world problem.

Identify and describe situations with constant or varying rates of change in a linear function.

Use mathematical exponents to illustrate correlations and causation.

Make observations about the visual overlap of two numerical distributions represented in line or box plots.

Describe how data particularly outliers added to a data set may affect the mean and/or median.

Find, use, and interpret measures of center (mean and median) and measures of spread (range, interquartile range, and mean absolute deviation) for numerical data from random samples to draw comparative inferences about two populations.