1: Students will understand numerical concepts and mathematical operations.

1.A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1.A.1: Determine the absolute value of rational numbers.

Comparing and Ordering Integers
Real Number Line - Activity A

1.A.2: Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers.

Comparing and Ordering Integers

1.A.5: Simplify numerical expressions using order of operations.

Order of Operations

1.B: Understand the meaning of operations and how they relate to one another.

1.B.1: Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive rational numbers to whole-number powers.

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

1.B.2: Convert terminating decimals into reduced fractions.

Percents, Fractions and Decimals

1.B.3: Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest).

Percent of Change
Percents and Proportions
Simple and Compound Interest

1.B.4: Add and subtract fractions with unlike denominators.

Fractions with Unlike Denominators

1.B.5: Multiply, divide, and simplify rational numbers by using exponent rules.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.B.6: Understand the meaning of the absolute value of a number:

1.B.6.a: interpret the absolute value as the distance of the number from zero on a number line

Comparing and Ordering Integers
Real Number Line - Activity A

1.B.6.b: determine the absolute value of real numbers

Comparing and Ordering Integers
Real Number Line - Activity A

1.B.9: Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations

1.C: Compute fluently and make reasonable estimates.

1.C.2: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

Percents, Fractions and Decimals

1.C.4: Calculate the percentage of increases and decreases of a quantity.

Percent of Change

1.C.5: Add and subtract fractions with unlike denominators.

Fractions with Unlike Denominators

2: Students will understand algebraic concepts and applications.

2.A: Understand patterns, relations, and functions.

2.A.1: Identify and continue patterns presented in a variety of formats.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.A.2: Represent a variety of relationships using tables, graphs, verbal rules, and possible symbolic notation, and recognize the same general pattern presented in different representations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

2.A.3: Simplify numerical expressions by applying properties of rational numbers, and justify the process used.

Order of Operations

2.A.4: Interpret and evaluate expressions involving integer powers and simple roots.

Simplifying Radicals - Activity A

2.A.5: Graph and interpret linear functions.

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

2.A.6: Solve problems involving rate, average speed, distance, and time.

Distance Formula - Activity A
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

2.B: Represent and analyze mathematical situations and structures using algebraic symbols.

2.B.1: Write verbal expressions and sentences as algebraic expressions and equations:

2.B.1.a: evaluate algebraic expressions

Using Algebraic Equations
Using Algebraic Expressions

2.B.1.b: solve simple linear equations

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

2.B.1.c: graph and interpret results

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

2.B.2: Use variables and appropriate operations to write an expression, an equation, or an inequality that represents a verbal description.

Using Algebraic Equations
Using Algebraic Expressions

2.B.4: Simplify numerical expressions by applying properties of rational numbers.

Order of Operations

2.B.5: Graph linear functions and identify slope as positive or negative.

Linear Functions
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

2.B.6: Use letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes.

Using Algebraic Equations
Using Algebraic Expressions

2.C: Use mathematical models to represent and understand quantitative relationships.

2.C.1: Create scale models and use them for dimensional drawings.

Similar Figures - Activity A

2.C.2: Understand and use the coordinate plane to graph ordered pairs and linear equations.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

2.D: Analyze changes in various contexts.

2.D.1: Use variables and appropriate operations to write an expression, an equation, and/or an inequality that represents a verbal description involving change.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Using Algebraic Equations
Using Algebraic Expressions

2.D.2: Interpret and evaluate expressions involving integer powers and simple roots as they relate to change.

Simplifying Radicals - Activity A

2.D.3: Graph and interpret linear functions as they are used to solve problems.

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

2.D.4: Solve two-step equations and inequalities with one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

3: Students will understand geometric concepts and applications.

3.A: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematics arguments about geometric relationships.

3.A.1: Classify geometric figures as similar or congruent.

Classifying Quadrilaterals - Activity A
Constructing Congruent Segments and Angles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Special Quadrilaterals

3.A.2: Understand the concept of a constant (e.g., pi) and use the formulas for the circumference and area of a circle.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

3.A.3: Explain and use the Pythagorean theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

3.A.4: Determine the radius, diameter, and circumference of a circle and explain their relationship.

Circle: Circumference and Area

3.A.5: Use properties to classify solids including pyramids, cones, prisms, and cylinders.

Classifying Quadrilaterals - Activity A
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

3.B: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.B.1: Construct and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine the image under translations and reflections.

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Points in the Coordinate Plane - Activity A
Rectangle: Perimeter and Area
Reflections
Rotations, Reflections and Translations

3.D: Use visualization, spatial reasoning, and geometric modeling to solve problems.

3.D.1: Compute the perimeter and area of common geometric shapes and use the results to find measures of less common objects.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

3.D.2: Identify and describe the properties of two-dimensional figures:

3.D.2.a: identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms

Investigating Angle Theorems - Activity A

3.D.2.b: use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

4: Students will understand measurement systems and applications.

4.A: Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.A.1: Choose appropriate units of measure and ratios to recognize new equivalences (e.g., 1 square yard equals 9 square feet) to solve problems.

Estimating Population Size
Proportions and Common Multipliers

4.B: Apply appropriate techniques, tools, and formulas to determine measurements.

4.B.2: Select and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

4.B.3: Solve problems involving scale factors, ratios, and proportions.

Dilations
Estimating Population Size
Proportions and Common Multipliers
Similar Figures - Activity A

5: Students will understand how to formulate questions, analyze data, and determine probabilities.

5.A: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

5.A.1: Describe how data representations influences interpretation.

Correlation
Solving Using Trend Lines

5.A.2: Select and use appropriate representation for presenting collected data and justify the selection.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.3: Use measures of central tendency and spread to describe a set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.A.4: Choose between median and mode to describe a set of data and justify the choice for a particular situation.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.A.5: Determine the quartiles of a data set.

Box-and-Whisker Plots

5.A.6: Identify ordered pairs of data from a graph and interpret the data in terms of the situation depicted by the graph.

Points in the Coordinate Plane - Activity A

5.A.7: Use various scales and formats to display the same data set.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.9: Collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.10: Compute the minimum, lower quartile, median, upper quartile, and maximum of a data set.

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode

5.A.12: Use and explain sampling techniques (e.g., observations, surveys, and random sampling) for gathering data.

Polling: Neighborhood

5.A.13: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, and selecting, collecting, and displaying appropriate data to address the problem.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.B: Select and use appropriate statistical methods to analyze data.

5.B.1: Choose and justify appropriate measures of central tendencies (e.g., mean, median, mode, range) to describe given or derived data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.B.2: Know various ways to display data sets (e.g., stem and leaf plot, box and whisker plot, scatter plots) and use these forms to display a single set of data or to compare two sets of data.

Box-and-Whisker Plots
Line Plots
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.B.4: Use appropriate technology to gather and display data sets and identify the relationships that exist among variables within the data set.

Solving Using Trend Lines

5.B.6: Identify data that represent sampling errors and explain why the sample and the display might be biased.

Polling: Neighborhood

5.C: Develop and evaluate inferences and predictions that are based on data.

5.C.3: Approximate a line of best fit for a data set in a scatter plot form and make predictions using the simple equation of that line.

Correlation
Solving Using Trend Lines

5.D: Understand and apply basic concepts of probability.

5.D.1: Determine the probability of a compound event composed of two independent events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

5.D.2: Identify examples of events having the probability of one or zero.

Geometric Probability - Activity A

5.D.3: Describe the probability of events using fractions, decimals, and percents.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.D.4: Express probability as a fraction, zero, or one.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.D.5: Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.

Geometric Probability - Activity A

5.D.6: Make predictions based on theoretical probabilities of compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.D.7: Determine the probability of a simple event or a compound event composed of a simple, independent events.

Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Independent and Dependent Events