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

I.1: Represent rational numbers in a variety of ways.

I.1.a: Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and real-life examples.

Dividing Mixed Numbers
Fraction Garden (Comparing Fractions)
Improper Fractions and Mixed Numbers
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Toy Factory (Set Models of Fractions)

I.1.b: Simplify numerical expressions with whole number exponents using order of operations, and recognize that any positive number to the 0 power is 1.

Order of Operations

I.1.c: Represent numbers greater than one using scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

I.1.d: Select the most appropriate form of a rational number for a given context.

Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

I.2: Compare and order rational numbers, including positive and negative fractions, positive and negative mixed numbers, and positive and negative decimals.

I.2.a: Identify, read, and locate rational numbers on a number line.

Fraction Garden (Comparing Fractions)
Rational Numbers, Opposites, and Absolute Values

I.2.b: Compare pairs of rational numbers in different forms.

Rational Numbers, Opposites, and Absolute Values

I.2.c: Order rational numbers with and without a number line.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

I.3: Explain relationships and equivalences among rational numbers.

I.3.a: Find equivalent forms for common fractions, decimals, percents, and ratios, including repeating or terminating decimals.

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

I.3.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.4: Model meanings of ratios and operations with rational numbers.

I.4.a: Demonstrate that the fraction a/b represents a divided by b.

Dividing Fractions
Dividing Mixed Numbers
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Solving Algebraic Equations II

I.4.b: Recognize percents as ratios based on 100 and decimals as ratios based on powers of 10.

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

I.5: Solve problems involving rational numbers.

I.5.a: Compute fluently using all four operations with integers and positive fractions and decimals.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

I.5.b: Solve problems using factors, multiples, prime factorization, relatively prime numbers, and common divisibility rules.

Finding Factors with Area Models

I.5.c: Solve application problems involving rational numbers.

Estimating Population Size

I.5.d: Determine if an answer is reasonable using estimation.

Estimating Sums and Differences

II: Students will use proportional reasoning to solve problems.

II.1: Solve problems involving ratios, rates, proportions and percentages.

II.1.b: Solve percent problems using ratio and proportion, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.

Compound Interest
Percent of Change

II.1.c: Solve problems involving proportions, rates, and measures.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

II.2: Apply the properties of proportionality to different units of measurement.

II.2.a: Convert from one unit of measurement to an equivalent unit of measurement in the same system using a given conversion factor.

Unit Conversions

II.2.b: Understand that in a proportional relationship, all dimensions change by the same scale factor.

Beam to Moon (Ratios and Proportions)
Dilations

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

III.1: Evaluate, simplify, and solve algebraic expressions and equations.

III.1.b: Translate verbal expressions into algebraic expressions.

Improper Fractions and Mixed Numbers
Multiplying with Decimals
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

III.1.c: Simplify and evaluate algebraic expressions.

Compound Interest
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Operations with Radical Expressions
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

III.1.d: Show that performing the same operation on both sides of an equation will produce an equivalent equation.

Absolute Value Equations and Inequalities
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Linear Functions
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Using Algebraic Equations

III.1.e: Solve single-variable linear equations and inequalities of the formax + b = c, ax + b < c, or ax + b > c.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable

III.2: Represent relationships using graphs, tables, and other models.

III.2.a: Identify integer coordinates when given the graph of a point on a rectangular coordinate system.

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

III.2.b: Graph ordered pairs of integers on a rectangular coordinate system.

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

III.2.c: Model real-world problems using graphs, tables, equations, manipulatives, and pictures.

Solving Equations on the Number Line

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

IV.1: Draw, label, and describe attributes of geometric figures to determine geometric relationships.

IV.1.c: Draw, label, and describe attributes of angles, triangles, and quadrilaterals.

Classifying Quadrilaterals
Classifying Triangles
Special Parallelograms

IV.2: Determine measurements in metric and customary units using appropriate tools and formulas.

IV.2.b: Measure length, area, volume, and angles to appropriate levels of precision.

Measuring Trees

IV.2.c: Calculate the measurement of everyday objects using formulas for perimeters and areas of triangles and quadrilaterals, and circumferences and areas of circles.

Area of Parallelograms
Perimeter and Area of Rectangles

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

V.1: Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments.

V.1.a: Write the results of a probability experiment as a fraction, ratio, or decimal, between zero and one, or as a percent between zero and one hundred, inclusive.

Geometric Probability
Spin the Big Wheel! (Probability)

V.1.b: Compare experimental results with theoretical probability.

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

V.1.c: Compare individual, small group, and large group results of a probability experiment.

Polling: City

V.2: Display and compare data to make predictions and formulate conclusions.

V.2.a: Display data using tables, scatter plots, and circle graphs.

Correlation
Graphing Skills
Reaction Time 2 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

V.2.b: Compare two similar sets of data on the same graph.

Graphing Skills
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

V.2.c: Compare two different kinds of graphs representing the same set of data.

Graphing Skills
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

V.2.d: Propose and justify inferences and predictions based on data.

Polling: City
Real-Time Histogram