#### 7.1: Number & Operation

7.1.1: Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.

7.1.1.1: Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.

7.1.1.3: Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

7.1.1.5: Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.

7.1.2: Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

7.1.2.1: Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.

7.1.2.2: Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense.

7.1.2.4: Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.

7.1.2.5: Use proportional reasoning to solve problems involving ratios in various contexts.

#### 7.2: Algebra

7.2.1: Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

7.2.1.2: Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.

7.2.2: Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

7.2.2.1: Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

7.2.2.2: Solve multi-step problems involving proportional relationships in numerous contexts.

7.2.2.4: Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.

7.2.3: Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.

7.2.3.1: Generate equivalent numerical and algebraic expressions containing rational numbers and whole number exponents. Properties of algebra include associative, commutative and distributive laws.

7.2.3.3: Apply understanding of order of operations and grouping symbols when using calculators and other technologies.

#### 7.3: Geometry & Measurement

7.3.1: Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.

7.3.1.1: Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.

7.3.1.2: Calculate the volume and surface area of cylinders and justify the formulas used.

7.3.2: Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.

7.3.2.1: Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors.

7.3.2.2: Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.

7.3.2.3: Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.

7.3.2.4: Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation.

#### 7.4: Data Analysis & Probability

7.4.1: Use mean, median and range to draw conclusions about data and make predictions.

7.4.1.1: Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions.

7.4.1.2: Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact.

7.4.2: Display and interpret data in a variety of ways, including circle graphs and histograms.

7.4.2.1: Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

Correlation last revised: 9/16/2020

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