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