I: Students will expand number sense to understand, perform operations, and solve problems with rational numbers.

I.1: Compute fluently with understanding and make reasonable estimates with rational numbers.

I.1.c: Check the reasonableness of results using estimation.

 Estimating Sums and Differences

I.2: Analyze relationships among rational numbers, including negative rational numbers, and operations involving these numbers.

I.2.a: Order rational numbers in various forms, including scientific notation (positive and negative exponents), and place numbers on a number line.

 Comparing and Ordering Decimals
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values
 Unit Conversions

I.2.c: Recognize and use the identity properties of addition and multiplication, the multiplicative property of zero, the commutative and associative properties of addition and multiplication, and the distributive property of multiplication over addition.

 Adding and Subtracting Integers
 Adding on the Number Line
 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Square Roots

I.2.d: Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.

 Dividing Polynomials Using Synthetic Division
 Function Machines 3 (Functions and Problem Solving)
 Modeling One-Step Equations
 Simplifying Algebraic Expressions I
 Solving Two-Step Equations
 Square Roots

I.3: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

I.3.a: Recognize the absolute value of a rational number as its distance from zero.

 Absolute Value Equations and Inequalities
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values

I.3.b: Simplify numerical expressions, including those with whole number exponents and absolute values, using the order of operations.

 Order of Operations

I.3.c: Solve problems involving rational numbers, percents, and proportions.

 Beam to Moon (Ratios and Proportions)
 Direct and Inverse Variation
 Estimating Population Size
 Geometric Probability
 Part-to-part and Part-to-whole Ratios
 Percent of Change
 Percents, Fractions, and Decimals
 Proportions and Common Multipliers
 Rational Numbers, Opposites, and Absolute Values
 Real-Time Histogram
 Time Estimation

II: Students will use proportion and similarity to solve problems.

II.1: Model and illustrate meanings of ratios, percents, and decimals.

II.1.a: Compare ratios to determine if they are equivalent.

 Part-to-part and Part-to-whole Ratios
 Percents, Fractions, and Decimals

II.1.c: Represent percents as ratios based on 100 and decimals as ratios based on powers of ten.

 Beam to Moon (Ratios and Proportions)
 Part-to-part and Part-to-whole Ratios
 Percents and Proportions
 Percents, Fractions, and Decimals

II.2: Solve a wide variety of problems using ratios and proportional reasoning.

II.2.b: Solve percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.

 Compound Interest
 Percent of Change
 Percents, Fractions, and Decimals
 Real-Time Histogram
 Time Estimation

II.2.c: Solve ratio and rate problems using informal methods.

 Estimating Population Size

II.3: Recognize similar polygons and use properties of similar triangles to solve problems and define the slope of a line.

II.3.a: Define similar polygons as polygons with corresponding angles congruent and corresponding sides that are proportional.

 Perimeters and Areas of Similar Figures
 Similar Figures

II.3.b: Identify pairs of similar triangles using two pairs of congruent angles, or two pairs of proportional sides with congruent included angles.

 Similar Figures

III: Students will develop fluency with the language and operations of algebra to analyze and represent relationships.

III.1: Generalize and express patterns using algebraic expressions.

III.1.a: Compare representations of a relation using tables, graphs, algebraic symbols, and mathematical rules.

 Function Machines 1 (Functions and Tables)
 Introduction to Functions
 Linear Functions

III.1.b: Describe simple patterns using a mathematical rule or algebraic expression.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences
 Pattern Finder

III.1.c: Create and extend simple numerical and visual patterns.

 Finding Patterns
 Function Machines 1 (Functions and Tables)
 Pattern Finder

III.2: Evaluate, simplify, and solve algebraic expressions, equations, and inequalities.

III.2.b: Simplify algebraic expressions using the order of operations, algebraic properties, and exponent rules.

 Dividing Exponential Expressions
 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Exponents and Power Rules
 Multiplying Exponential Expressions
 Operations with Radical Expressions
 Order of Operations
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Solving Algebraic Equations I
 Solving Algebraic Equations II

III.2.c: Solve single-variable linear equations and inequalities, including those that must be simplified on one side or those with variables on both sides of an equation.

 Solving Algebraic Equations II

III.3: Represent relationships using graphs, tables, and other models.

III.3.b: Graph ordered pairs of rational numbers on a rectangular coordinate system.

 City Tour (Coordinates)
 Elevator Operator (Line Graphs)
 Points in the Coordinate Plane
 Points, Lines, and Equations

III.3.c: Graph linear equations using ordered pairs or tables.

 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Solving Equations by Graphing Each Side

IV: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

IV.1: Apply the properties of proportionality of different units of measure.

IV.1.a: Convert units of measure within the same system.

 Unit Conversions

IV.1.c: Solve problems using scale factors.

 Dilations
 Similar Figures

IV.2: Derive formulas for surface areas and volume of three-dimensional figures.

IV.2.a: Derive formulas for and calculate surface area and volume of right prisms and cylinders using appropriate units.

 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders

IV.2.b: Explain that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related and the cube of the scale factor describes how corresponding volumes are related.

 Dilations

IV.2.c: Find lengths, areas, and volumes of similar figures, using the scale factor.

 Dilations
 Perimeters and Areas of Similar Figures
 Similar Figures

V: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

V.1: Calculate probabilities of events and compare theoretical and experimental probability.

V.1.b: Calculate the probability of an event or sequence of events with and without replacement using models.

 Independent and Dependent Events
 Spin the Big Wheel! (Probability)
 Theoretical and Experimental Probability

V.1.d: Make approximate predictions using theoretical probability and proportions.

 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

V.1.e: Collect and interpret data to show that as the number of trials increases, experimental probability approaches the theoretical probability.

 Geometric Probability

V.2: Formulate questions and answer the questions by organizing and analyzing data.

V.2.a: Formulate questions that can be answered through data collection and analysis.

 Correlation
 Describing Data Using Statistics
 Movie Reviewer (Mean and Median)
 Reaction Time 2 (Graphs and Statistics)
 Real-Time Histogram
 Time Estimation

V.2.d: Compute the mean and median of a numerical characteristic and relate these values to the histogram of the data.

 Populations and Samples
 Real-Time Histogram
 Sight vs. Sound Reactions
 Stem-and-Leaf Plots

V.2.e: Use graphical representations and numerical summaries to answer questions and interpret data.

 Graphing Skills
 Reaction Time 2 (Graphs and Statistics)
 Stem-and-Leaf Plots

Correlation last revised: 5/24/2018

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