1: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

1.1: Demonstrate meanings for integers, rational numbers, percents, exponents, square roots and pi using physical materials and technology in problem-solving situations.

1.1.a: Recognize and use equivalent representations of positive rational numbers and common irrational numbers (for example, locate rational numbers on a number line and demonstrate the meaning of square roots and perfect squares).

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

1.2: Read, write and order integers, rational numbers and common irrational numbers such as square root of 2, and square root of and x.

1.2.a: Compare and order sets of integers and rational numbers* that are expressed in a variety of ways.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.3: Apply number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways.

1.3.a: Apply number theory concepts (for example, primes, factors, multiples, exponents) in problem-solving situations.

Adding Real Numbers

1.4: Use the relationships among fractions, decimals, and percents, including the concepts of ratio and proportion, in problem-solving situations.

1.4.a: Use the relationships among fractions, decimals and percents including the concepts of ratio and proportion in problem-solving situations (similarity, scale factor, unit rate).

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

2: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.

2.1: Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation.

2.1.a: Represent, describe, and analyze patterns (for example, geometric and numeric) and relationships using tables, graphs, verbal rules, and standard algebraic notation.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.b: Convert from one functional representation (table, graph, verbal rule, standard algebraic notation) to another.

Exponential Functions - Activity A
Introduction to Functions
Linear Functions
Polynomials and Linear Factors
Using Algebraic Equations

2.2: Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.

2.2.a: Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Using Algebraic Equations
Using Algebraic Expressions

2.3: Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how the area of a circle changes as the radius increases, or how a person's height changes over time).

2.3.a: Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how a person’s height changes over time).

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A

2.4: Distinguish between linear and nonlinear functions through informal investigations.

2.4.a: Distinguish between linear and nonlinear functions through informal investigations.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

2.5: Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphical) and a variety of tools (physical materials, calculators, and computers).

2.5.a: Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphic).

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

3: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.

3.1: Read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots, box plots, stem-and-leaf plots) and appropriate technology.

3.1.a: Read and construct displays of data using appropriate techniques (for example, circle graphs, scatter plots, box and whisker plots, stem-and-leaf plots).

Box-and-Whisker Plots
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

3.2: Display and use measures of central tendency, such as mean, median and mode and measures of variability, such as range and quartiles.

3.2.a: Display and use measures of central tendency, (such as mean, median, and mode) and measures of variability, (such as range and quartiles) in problem-solving situations.

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

3.6: Make predictions and compare results using both experimental and theoretical probability drawn from realworld problems.

3.6.a: Use a model (list, tree diagram, area model) to determine theoretical probabilities* to solve problems involving uncertainty.

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

3.6.b: Make predictions using theoretical probability in real-world problems.

Probability Simulations
Theoretical and Experimental Probability

4: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

4.2: Describe, analyze and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures.

4.2.a: Describe, analyze and reason informally about properties (for example, parallelism, perpendicularity, congruence*, and similarity*) of two- and three-dimensional figures.

Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Similar Polygons

4.3: Apply the concept of ratio, proportion and similarity in problem-solving situations.

4.3.a: Apply the concept of ratio, proportion, and similarity in problem-solving situations.

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

4.4: Solve problems using coordinate geometry.

4.4.a: Solve problems in real-world situations using coordinate geometry (for example, maps, distance on a number line).

Real Number Line - Activity A

4.5: Solving problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.

4.5.a: Solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions (include right prisms and cylinders).

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders

4.5.b: Apply the Pythagorean Theorem to solve real-world problems.

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

4.6: Transform geometric figures using reflections, translations, and rotations to explore congruence.

4.6.a: Transform geometric figures using reflections, translations, and rotations to determine congruence.

Constructing Congruent Segments and Angles
Reflections
Rotations, Reflections and Translations
Translations

5: Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.

5.1: Estimate, use and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison.

5.1.a: Estimate and use measures of area, volume, capacity, weight, and angle comparisons to solve problems.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

5.2: Estimate, make, and use direct and indirect measurements to describe and make comparisons.

5.2.a: Estimate, make and use direct and indirect measurements to describe and make comparisons (for example, use a proportion to find the height of a flag pole).

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Proportions and Common Multipliers

5.3: Read and interpret various scales including those based on number lines, graphs, and maps.

5.3.a: Read and interpret scales on number lines, graphs and maps (for example, given a map and a scale, determine the distance between two points on the map).

Real Number Line - Activity A

5.4: Develop and use formulas and procedures to solve problems involving measurement.

5.4.a: Develop and use procedures or formulas to solve problems involving measurement (for example, distance, area, surface area, and volume of right prisms and cylinders).

Distance Formula - Activity A
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

5.5: Describe how a change in an object's linear dimensions affects its perimeter, area, and volume.

5.5.a: Describe how a change in an object’s linear dimensions affects its perimeter, area and volume (for example, how the area of a circle changes as the radius increases).

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area

6: Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.

6.1: Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.

6.1.a: Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons

6.2: Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers.

6.2.a: Apply order of operations to evaluate simple expressions with integers.

Order of Operations

6.4: Select and use appropriate methods for computing with commonly used fractions and decimals, percents, and integers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determining whether the results are reasonable.

6.4.a: Apply computational methods (including ratio and proportion) to solve problems involving commonly used fractions, decimals, percents, and integers (for example, discount, tax, sale price, unit price) and determine whether the results are reasonable.

Estimating Population Size
Geometric Probability - Activity A
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons