1: Number and Operations

1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.1.1: Recognize and convert between expressions for positive and negative rational numbers, including fractions, decimals, percents, and ratios.

Percents, Fractions, and Decimals

1.1.2: Find or use factors, multiples, or prime factorization within a set of numbers.

Chocomatic (Multiplication, Arrays, and Area)
Finding Factors with Area Models
Operations with Radical Expressions

1.1.3: Compare and order rational numbers using various models and representations.

Comparing and Ordering Decimals

1.1.4: Model and solve simple problems involving absolute value.

Absolute Value with Linear Functions

1.2: Understand and apply numerical operations and their relationship to one another.

1.2.1: Add, subtract, multiply, and divide integers.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

1.2.2: Solve problems with rational numbers and appropriate operations using exact answers or estimates.

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

1.2.3: Solve problems involving percentages, ratio and proportion, including tax, discount, tips, and part/whole relationships.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Road Trip (Problem Solving)

1.2.5: Simplify numerical expressions using the order of operations and appropriate mathematical properties.

Order of Operations
Solving Algebraic Equations II

1.3: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

1.3.1: Estimate and apply benchmarks for rational numbers and common irrational numbers.

Estimating Sums and Differences

1.3.3: Estimate square roots of numbers less than 1000 by locating them between two consecutive whole numbers.

Square Roots

2: Data Analysis, Probability, and Discrete Mathematics

2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.1: Solve problems by selecting, constructing, and interpreting displays of data including multi-line graphs and scatterplots.

Box-and-Whisker Plots
Correlation
Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Prairie Ecosystem
Reaction Time 2 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

2.1.2: Interpret trends in a data set, estimate values for missing data, and predict values for points beyond the range of the data set.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

2.1.3: Identify outliers and determine their effect on mean, median, mode, and range.

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

2.1.4: Distinguish between a simple random and non-random sample.

Polling: City
Polling: Neighborhood
Populations and Samples

2.2: Understand and apply the basic concepts of probability.

2.2.1: Determine conditional probabilities (experimental) in compound probability experiments.

Independent and Dependent Events

2.2.2: Experiment with two different events to determine whether the two events are dependent or independent of each other.

Independent and Dependent Events
Theoretical and Experimental Probability

2.2.3: Compare the results of multiple repetitions of the same probability experiment to the theoretical probability.

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

2.2.4: Compare probabilities to determine fairness in experimental situations.

Probability Simulations
Theoretical and Experimental Probability

2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.1: Analyze relationships among the tree diagrams where items repeat and do not repeat; make numerical connections to the multiplication principle of counting.

Independent and Dependent Events
Permutations and Combinations

3: Patterns, Algebra, and Functions

3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Recognize, describe, create, and analyze numerical and geometric sequences using tables or graphs; make conjectures about these sequences.

Arithmetic Sequences
Geometric Sequences

3.2: Describe and model functions and their relationships.

3.2.1: Use a table of values to graph an equation or proportional relationship; describe the graph's characteristics.

Direct and Inverse Variation
Points, Lines, and Equations

3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.1: Write a single variable algebraic expression or one-step equation given a contextual situation.

Using Algebraic Expressions

3.3.3: Solve multi-step equations using inverse properties with rational numbers.

Solving Algebraic Equations II

3.3.4: Translate between graphs and tables that represent a linear equation.

Points, Lines, and Equations

3.3.6: Create and solve one-step inequalities with whole numbers.

Compound Inequalities
Solving Linear Inequalities in One Variable

3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.1: Use graphs and tables to model and analyze change.

Graphing Skills

4: Geometry and Measurement

4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Recognize the relationship between central angles and intercepted arcs; identify arcs and chords of a circle.

Chords and Arcs

4.1.2: Analyze and determine relationships between angles created by parallel lines cut by a transversal.

Constructing Congruent Segments and Angles
Triangle Angle Sum

4.1.4: Describe the relationship between the number of sides in a regular polygon and the sum of its interior angles.

Polygon Angle Sum

4.1.5: Identify corresponding parts of congruent figures.

Constructing Congruent Segments and Angles

4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Model the result of a double transformation (translations or reflections) of a 2-dimensional figure on a coordinate plane using all four quadrants.

Circles
Dilations
Rotations, Reflections, and Translations

4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.2: Identify polygons having the same perimeter or area.

Area of Parallelograms
Unit Conversions

4.4.3: Calculate the area and perimeter of composite 2-dimensional figures.

Area of Triangles
Fido's Flower Bed (Perimeter and Area)

4.4.5: Create a net to calculate the surface area of a given solid.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

4.4.4: Determine actual lengths based on scale drawings or maps.

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

4.4.6: Identify the appropriate unit of measure to compute the volume of an object and justify reasoning.

Pyramids and Cones