1: Apply concepts of rational numbers and perform basic operations emphasizing the concepts of ratio, proportion, and percent with and without the use of calculators.

1.a: Use the order of operations to simplify and/or evaluate whole numbers (including exponents and grouping symbols).

Order of Operations

1.b: Solve problems involving addition, subtraction, multiplication, and division of rational numbers. Express answers in simplest form.

Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.c: Convert among decimals, fractions, mixed numbers, and percents.

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

1.d: Evaluate and estimate powers and square roots of real numbers.

Order of Operations
Square Roots

1.f: Multiply and divide numbers written in scientific notation.

Unit Conversions

1.g: Solve real-life problems involving unit price, unit rate, sales price, sales tax, discount, simple interest, commission, and rates of commission.

Compound Interest
Household Energy Usage
Percent of Change
Road Trip (Problem Solving)

1.h: Solve contextual problems requiring the comparison, ordering, and application of integers.

Integers, Opposites, and Absolute Values

2: Develop and apply the basic operations of rational numbers to algebraic and numerical tasks. Create and apply algebraic expressions and equations.

2.a: Recognize, describe, and state the rule of generalized numerical and geometric patterns using tables, graphs, words, and symbols.

Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Square Roots

2.c: Formulate algebraic expressions, equations, and inequalities to reflect a given situation and vice versa.

Absolute Value Equations and Inequalities
Compound Interest
Linear Functions
Linear Inequalities in Two Variables
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Using Algebraic Equations
Using Algebraic Expressions

2.d: Complete a function table based on a given rule and vice versa.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Points, Lines, and Equations

2.e: Identify the following properties using variables and apply them in solving problems:

2.e.3: Commutative and associative properties of addition and multiplication

Addition of Polynomials
Using Algebraic Equations

3: Apply geometric relationships of angles, two- and three-dimensional shapes, and transformations.

3.b: Construct two-dimensional representations of three-dimensional objects.

Surface and Lateral Areas of Prisms and Cylinders

3.d: Perform transformations (rigid and non-rigid motions) on two-dimensional figures using the coordinate plane.

Dilations
Rotations, Reflections, and Translations

3.e: Create an argument using the Pythagorean Theorem principles to show that a triangle is a right triangle.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

3.f: Construct and classify angles.

Segment and Angle Bisectors
Triangle Angle Sum

4: Apply appropriate techniques, tools, and formulas to determine measurements with a focus on real-world problems. Recognize that formulas in mathematics are generalized statements about rules, equations, principles, or other logical mathematical relationships.

4.a: Convert from one unit to another, perform basic operations, and solve real-world problems using standard (English and metric) measurements within the same system.

Unit Conversions

4.b: Use formulas and strategies, such as decomposition, to compute the perimeter and area of triangles, parallelograms, trapezoids, the circumference and area of circles, and find the area of more complex shapes.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

4.c: Develop and justify geometric formulas for volume and surface area of cylinders, pyramids, and prisms.

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

4.d: Solve problems involving scale factors using ratios and proportions.

Beam to Moon (Ratios and Proportions)
Dilations
Similar Figures

5: Organize and interpret data. Analyze data to make predictions.

5.a: Use proportions, estimates, and percentages to construct, interpret, and make predictions about a population based on histograms or circle graph representations of data from a sample.

Polling: City

5.b: Determine how outliers affect mean, median, mode, or range.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

5.c: Construct and interpret line graphs, frequency tables, circle graphs, box-and-whisker plots, and scatter plots to generalize trends from given data.

Correlation
Graphing Skills
Histograms
Solving Using Trend Lines
Trends in Scatter Plots

5.d: Determine probabilities through experimentation, simulation, or calculation. (Note: Make and test conjectures and predictions by calculating the probability of an event.)

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