#### IM1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

IM1.1.1: Compare real number expressions.

IM1.1.2: Simplify square roots using factors.

IM1.1.3: Understand and use the distributive, associative, and commutative properties.

IM1.1.5: Use dimensional (unit) analysis to organize conversions and computations.

#### IM1.2: Students solve linear equations and inequalities in one variable. They write equations of lines and find and use the slope and y-intercept of lines. Students solve pairs of linear equations using graphs and algebra. Students add, subtract, multiply, and divide polynomials and solve word problems using exponential functions.

IM1.2.1: Solve linear equations.

IM1.2.2: Solve equations and formulas for a specific variable.

IM1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

IM1.2.4: Solve linear inequalities using properties of order.

IM1.2.5: Solve word problems that involve linear equations, formulas, and inequalities.

IM1.2.6: Sketch a reasonable graph for a given relationship.

IM1.2.8: Understand the concept of a function, decide if a given relation is a function and link equations to functions.

IM1.2.9: Find the domain and range of a relation.

IM1.2.10: Graph a linear equation.

IM1.2.11: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

IM1.2.12: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept are related to the equation.

IM1.2.13: Write the equation of a line given appropriate information.

IM1.2.16: Understand and use the substitution method to solve a pair of linear equations in two variables.

IM1.2.17: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

IM1.2.18: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

IM1.2.19: Use pairs of linear equations to solve word problems.

IM1.2.21: Multiple and divide monomials.

IM1.2.23: Multiply polynomials.

IM1.2.24: Divide polynomials by monomials.

IM1.2.30: Graph exponential functions.

#### IM1.3: Students identify and describe polygons, including finding measures of sides, perimeters, and areas. They use congruence, similarity, symmetry, tessellations, and transformations. Students understand the Pythagorean Theorem and use it to solve problems. They describe relationships and symmetries in geometric solids.

IM1.3.1: Identify and describe convex, concave, and regular polygons.

IM1.3.3: Find and use measures of sides, perimeter, and areas of polygons, and relate these measures to each other using formulas.

IM1.3.4: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

IM1.3.5: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

IM1.3.6: Prove and use the Pythagorean Theorem.

#### IM1.4: Students find measures of the center and variability of a set of data, as well as construct and analyze data displays and plot least square regression lines.

IM1.4.1: Construct a line plot.

IM1.4.2: Find measures of central tendency for a set of data.

IM1.4.3: Find skewness and symmetry from a graph of data.

IM1.4.5: Identify clusters, gaps, and outliers for a set of data.

IM1.4.6: Find a linear transformation.

IM1.4.8: Find the mean absolute deviation for a set of data.

IM1.4.9: Find the standard deviation and describe its properties.

IM1.4.10: Construct a frequency table for a set of data.

IM1.4.11: Summarize and interpret sets of data using center and variability.

IM1.4.12: Construct a scatterplot from a set of data.

IM1.4.13: Calculate the sum of squared differences for a set of data.

IM1.4.14: Plot the least square regression line from a set of data.

IM1.4.15: Compare sets of data using scatterplots and the line y = x, and interpret these comparisons for real-world data.

IM1.4.16: Recognize patterns in tables and graphs that are modeled by linear equations.

#### IM1.5: Students use simulations, find probabilities, and use the Law of Large Numbers.

IM1.5.2: Use empirical (experimental) and theoretical probabilities.

IM1.5.3: Understand independent events.

IM1.5.4: Use the Law of Large Numbers to understand situations involving chance.

IM1.5.5: Understand the concept of a probability distribution. Understand how an approximate probability can be constructed using simulation involving chance.

#### IM1.6: Students construct graphs, explore algorithms, and use recursion equations and matrices.

IM1.6.6: Use a variety of recursion equations to describe a function.

#### IM1.7: Students use a variety of strategies to solve problems and develop and evaluate mathematical arguments and proofs.

IM1.7.1: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

IM1.7.3: Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

IM1.7.4: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

Correlation last revised: 1/20/2017

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