1: Number Sense and Operations

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

1.1.PO5: Recognize the absolute value of a number used in contextual situations.

Comparing and Ordering Integers
Real Number Line - Activity A

1.1.PO 6: Locate integers on a number line.

Comparing and Ordering Integers
Real Number Line - Activity A

1.1.PO 7: Order integers.

Comparing and Ordering Integers

1.1.PO 8: Classify rational numbers as natural, whole, or integers.

Comparing and Ordering Integers

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

1.2.PO 1: Add integers.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips

1.2.PO 2: Subtract integers.

Adding and Subtracting Integers

1.2.PO 7: Apply grade level appropriate properties to assist in computation.

Adding Real Numbers

1.2.PO 8: Apply the symbols + and - to represent positive and negative, and | | to represent absolute value.

Comparing and Ordering Integers
Real Number Line - Activity A

1.2.PO 10: Calculate the percent of a given number.

Percent of Change
Percents and Proportions
Polling: Neighborhood

1.2.PO 12: Simplify numerical expressions using the order of operations with grade appropriate operations on number sets.

Order of Operations

1.3: Use estimation strategies reasonably and fluently.

1.3.PO 5: Determine whether an estimation of the circumference of a circle is approximately equal to the actual measure.

Circle: Circumference and Area

2: Data Analysis, Probability, and Discrete Mathematics

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

2.1.PO 3: Determine when it is appropriate to use histograms, line graphs, double bar graphs and stem-and-leaf plots.

Histograms
Populations and Samples
Stem-and-Leaf Plots

2.1.PO 4: Interpret data displays including histograms, stem-and -leaf plots, circle graphs and double line graphs.

Histograms
Stem-and-Leaf Plots

2.1.PO 5: Answer questions based on data displays including histograms, stem-and -leaf plots, circle graphs and double line graphs.

Histograms
Stem-and-Leaf Plots

2.1.PO 6: Find the mean, median, mode and range of a given numerical data set.

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

2.1.PO 7: Interpret trends from displayed data.

Correlation
Solving Using Trend Lines

2.1.PO 8: Compare trends in data related to the same investigation.

Populations and Samples
Solving Using Trend Lines

2.1.PO 9: Solve contextual problems using histograms, line graphs of continuous data, double bar graphs, and stem-and-leaf plots.

Histograms
Populations and Samples
Stem-and-Leaf Plots

2.2: Understand and apply the basic concepts of probability.

2.2.PO 1: Determine the probability that a specific event will occur in a single stage probability experiment. (e.g., Find the probability of drawing a red marble from a bag with 3 red, 5 blue, and 9 black marbles)

Geometric Probability - Activity A

2.2.PO 4: Record the data from performing a grade level appropriate probability experiment.

Geometric Probability - Activity A
Probability Simulations

2.2.PO 5: Compare the outcome of an experiment to predictions made prior to performing the experiment.

Populations and Samples

2.2.PO 6: Make predictions from the results of student-generated experiments using objects (e.g., coins, spinners, number cubes, and cards).

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

2.2.PO 7: Compare the results of two repetitions of the same grade level appropriate probability experiment.

Populations and Samples

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

2.3.PO 1: Determine all possible outcomes involving the combination of up to three sets of objects. (e.g. How many outfits can be made with 3 pants, 2 tee-shirts and 2 pairs of shoes?)

Permutations and Combinations

2.3.PO 2: Determine all possible arrangements of a given set, using a systematic list, table, tree diagram or other representation.

Permutations and Combinations

3: Patterns, Algebra, and Functions

3.1: Identify patterns and apply pattern recognition to reason mathematically.

3.1.PO 1: Communicate a grade level appropriate recursive pattern, using symbols or numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

3.1.PO 2: Extend a grade level appropriate recursive pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

3.1.PO 3: Solve grade level appropriate recursive pattern problems.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

3.2: Describe and model functions and their relationships.

3.2.PO 1: Describe the rule used in a simple grade level appropriate function. (e.g., T-chart, input/output model)

Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

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

3.3.PO 2: Use variables in contextual situations.

Using Algebraic Equations

3.3.PO 3: Translate a written sentence into a one-step, one-variable algebraic equation.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 4: Translate a sentence written in context into an algebraic equation involving one operation.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 5: Solve one-step equations using inverse operations with positive rational numbers. (e.g., (2/3)n =6.)

Modeling One-Step Equations - Activity A

3.4: Analyze change in a variable over time and in various contexts.

3.4.PO 1: Analyze change in various linear contextual situations.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

4: Geometry and Measurement

4.1: Analyze the attributes and properties of two and three dimensional shapes and develop mathematical arguments about their relationships.

4.1.PO 2: Classify three-dimensional solids by their configuration and properties. (e.g., parallelism, perpendicularity and congruency)

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

4.1.PO 3: Identify the net (two-dimensional representation) that corresponds to a rectangular prism, cone, or cylinder.

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

4.1.PO 4: Distinguish between length, area, and volume, using two- and three-dimensional geometric figures.

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

4.1.PO 6: Identify the angles created by two lines and a transversal.

Investigating Angle Theorems - Activity A

4.1.PO 7: Recognize the relationship between central angles and intercepted arcs.

Chords and Arcs

4.1.PO 8: Identify arcs and chords of a circle.

Chords and Arcs

4.1.PO 9: Model the triangle inequality theorem using manipulatives.

Triangle Inequalities

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

4.2.PO 1: Identify rotations about a point, using pictorial models.

Rotations, Reflections and Translations

4.2.PO 2: Recognize simple single rotations, translations or reflections on a coordinate grid.

Reflections
Rotations, Reflections and Translations

4.3: Specify and describe spatial relationships using coordinate geometry and other representational systems.

4.3.PO 1: Graph data points in (x, y) form in any quadrant of a coordinate grid.

Introduction to Functions
Points in the Coordinate Plane - Activity A

4.3.PO 2: State the missing coordinate of a given figure in any quadrant of a coordinate grid using geometric properties. (e.g. find the coordinates of the missing vertex of a rectangle when two adjacent sides are drawn)

Classifying Triangles
Points in the Coordinate Plane - Activity A
Special Quadrilaterals

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

4.4.PO 1: Identify the appropriate unit of measure for the volume of an object. (e.g., cubic inches or cubic cm)

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

4.4.PO 4: Solve problems involving the circumference of a circle.

Circle: Circumference and Area

4.4.PO 5: Solve problems involving the area of a circle.

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

4.4.PO 6: Solve problems for the areas of parallelograms, triangles, and circles.

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

4.4.PO 7: Identify polygons having the same perimeter or area.

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

5: Structure and Logic

5.1: Use reasoning to solve mathematical problems in contextual situations.

5.1.PO 2: Analyze algorithms for computing with fractions.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

5.2: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications.

5.2.PO 1: Solve a logic problem using multiple variables.

Biconditional Statement
Conditional Statement