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.PO 1: Express fractions as ratios, comparing two whole numbers. (e.g., ¾ is equivalent to 3:4 and 3 to 4)

Beam to Moon (Ratios and Proportions)
Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Probability Simulations
Proportions and Common Multipliers
Theoretical and Experimental Probability

1.1.PO 2: Compare two proper fractions, improper fractions or mixed numbers.

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

1.1.PO 3: Order three or more proper fractions, improper fractions or mixed numbers.

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

1.1.PO 4: Determine the equivalency between and among fractions, decimals, and percents in contextual situations.

Percents, Fractions and Decimals

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

1.2.PO 3: Apply grade level appropriate properties to assist in computation.

Adding Real Numbers

1.2.PO 7: Add or subtract proper fractions and mixed numbers with unlike denominators with regrouping.

Fractions with Unlike Denominators

1.2.PO 8: Demonstrate the process of multiplication of proper fractions using models.

Multiplying Fractions
Multiplying Mixed Numbers

1.2.PO 9: Multiply proper fractions.

Multiplying Fractions
Multiplying Mixed Numbers

1.2.PO 10: Multiply mixed numbers.

Multiplying Mixed Numbers

1.2.PO 11: Demonstrate that division is the inverse of multiplication of proper fractions.

Dividing Fractions
Dividing Mixed Numbers
Modeling and Solving Two-Step Equations
Multiplying Fractions
Multiplying Mixed Numbers
Solving Two-Step Equations

1.2.PO 12: Divide proper fractions.

Dividing Fractions
Dividing Mixed Numbers

1.2.PO 13: Divide mixed numbers.

Dividing Mixed Numbers

1.2.PO 15: Simplify numerical expressions using the order of operations with grade appropriate operations on number sets.

Operations with Radical Expressions
Order of Operations

1.3: Use estimation strategies reasonably and fluently.

1.3.PO 4: Estimate and measure for the area and perimeter of polygons using a grid.

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter 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 2: Construct a histogram, line graph, scatter plot, or stem-and-leaf plot with appropriate labels and title from organized data.

Histograms
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

2.1.PO 5: Find the mean, median (odd number of data points), mode, range, and extreme values of a given numerical data set.

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

2.1.PO 7: Compare trends in data related to the same investigation.

Populations and Samples

2.2: Understand and apply the basic concepts of probability.

2.2.PO2: Express probabilities of a single event as a decimal.

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.

Geometric Probability - Activity A
Populations and Samples
Probability Simulations

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

2.3.PO 1: Determine all possible outcomes involving a combination of 3 sets of 3 items, using a systematic approach. (e.g., 3 different shirts, 3 different pairs of pants, and 3 different belts)

Permutations and Combinations

2.3.PO 2: Determine all possible arrangements given a set with four or fewer objects using a systematic list, table or tree diagram when order is not important.

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 iterative pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

3.1.PO 3: Solve grade level appropriate iterative 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
Using Tables, Rules and Graphs

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

3.3.PO 1: Evaluate expressions involving the four basic operations by substituting given fractions for the variable. (e.g., n+3, when n= ½ )

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

3.3.PO 2: Use variables in contextual situations.

Using Algebraic Equations

3.3.PO 3: Translate a written phrase to an algebraic expression. (e.g., The quotient of m and 5 is m/5 or m ÷ 5.)

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 4: Translate a phrase written in context into an algebraic expression. (e.g., Write an expression to describe the situation: John has x pieces of candy and buys three more. x + 3)

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 5: Solve one-step equations with one variable represented by a letter or symbol, using inverse operations with whole numbers.

Modeling One-Step Equations - Activity A

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

3.4.PO 1: Identify values on a given line graph or scatter plot. (e.g., Given a line showing wages earned per hour, what is the wage at five hours?)

Scatter Plots - Activity A

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 1: Classify polygons by their attributes. (e.g., number of sides, length of sides, angles, parallelism, perpendicularity)

Classifying Quadrilaterals - Activity A
Classifying Triangles

4.1.PO 3: Classify prisms, pyramids, cones, and cylinders by base shape and lateral surface shape.

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 4: Classify three-dimensional figures by their attributes.

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 5: Compare attributes of two- dimensional figures with three-dimensional figures.

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

4.1.PO 6: Draw triangles with appropriate labels.

Classifying Triangles

4.1.PO 7: Identify supplementary or complementary angles.

Investigating Angle Theorems - Activity A

4.1.PO 8: Identify the diameter, radius and circumference of a circle or sphere.

Circle: Circumference and Area

4.1.PO 9: Draw a two-dimensional shape with a given number of lines of symmetry.

Holiday Snowflake Designer

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

4.2.PO 1: Identify reflections, and translations using pictures.

Rotations, Reflections and Translations

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

4.3.PO 1: Graph a polygon in the first quadrant using ordered pairs.

Introduction to Functions
Points in the Coordinate Plane - Activity A

4.3.PO 2: State the missing coordinate of a given figure in the first 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

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

4.4.PO 2: Determine the appropriate tool needed to measure to the needed accuracy.

Triple Beam Balance

4.4.PO 6: Solve problems involving the perimeter of polygons.

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

4.4.PO 7: Determine the area of triangles.

Area of Parallelograms - Activity A

4.4.PO 8: Distinguish between the perimeter and area in contextual situation.

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

4.4.PO 9: Solve problems for the areas of parallelograms (includes rectangles).

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

4.4.PO 10: Identify parallelograms having the same perimeter or area.

Area of Parallelograms - Activity A
Minimize Perimeter
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 decimals.

Multiplying with Decimals
Sums and Differences with Decimals

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 simple logic problem from given information. (Which of three different people live in which of three different colored houses?)

Biconditional Statement
Conditional Statement