1: Calculations and Estimations

1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.1: Order, model, and compare positive rational numbers (fractions, decimals, and percentages)

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

1.1.3: Understand rates and ratios as comparisons of two quantities by division

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.1.4: Differentiate between rates and ratios and express both as fractions

Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.1.5: Solve problems by calculating rates and ratios

Estimating Population Size
Geometric Probability - Activity A
Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.1.6: Locate positive rational numbers (fractions, decimals, and percentages) on a number line

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers

1.1.7: Apply equivalent forms of fractions and decimals to solve problems

Percents, Fractions and Decimals

1.1.8: Determine equivalent forms of fractions, mixed numbers and improper fractions

Improper Fractions and Mixed Numbers

1.1.10: Identify prime and composite numbers less than 100

Finding Factors with Area Models

1.2: Compute fluently and make reasonable estimates

1.2.1: Develop and analyze algorithms for computing with fractions and mixed numbers

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

1.2.2: Add and subtract fractions with like and unlike denominators

Fractions with Unlike Denominators

1.2.3: Understand linear, area, and discrete models to multiply and divide fractions

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

1.2.4: Solve problems involving common percentages

Percents and Proportions
Polling: Neighborhood

1.2.5: Convert mentally among common decimals, fractions and percentages

Percents, Fractions and Decimals

1.2.6: Apply grouping symbols to simplify calculations and evaluate expressions

Order of Operations

1.2.7: Develop and use strategies to estimate the results of positive rational number computations and judge the reasonableness of results

Estimating Population Size
Estimating Sums and Differences

1.2.8: Use referent numbers in estimating answers to adding and subtracting fractions and mixed numbers (e.g., 2 1/4 + 3/8 < 3, since both 1/4 and 3/8 are less than 1/2)

Estimating Population Size
Estimating Sums and Differences
Fractions with Unlike Denominators

1.3: Understand meanings of operations and how they relate to one another

1.3.1: Use the inverse operations of addition and subtraction to solve problems and check solutions involving adding and subtracting fractions and mixed numbers

Fractions with Unlike Denominators
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

1.3.2: Apply the associative, commutative, and distributive properties to simplify computations with positive rational numbers

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

2: Statistics and Probability

2.1: Select and use appropriate statistical methods to analyze data

2.1.1: Find, use, and interpret measures of center and spread

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

2.2: Understand and apply basic concepts of probability

2.2.1: Determine experimental probability of an event from a set of data

Geometric Probability - Activity A

2.2.2: Express probability using fractions, ratios, 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

2.2.4: Determine the number of possible combinations of two or more classes of objects (e.g., shirts, pants and shoes)

Permutations and Combinations

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

2.3.1: Design experiments and simulations to determine experimental probability of different outcomes

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

2.3.2: Understand that experimental probability approaches theoretical probability as the number of trials increases

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

2.3.3: Recognize and understand the connections among concepts of independent outcomes, picking at random, and fairness

Polling: Neighborhood

2.3.4: Represent and interpret the outcome of a probability experiment using a frequency distribution, including determining experimental probabilities

Describing Data Using Statistics
Line Plots
Populations and Samples

2.4: Develop and evaluate inferences and predictions that are based on data

2.4.2: Predict the outcome of a probability experiment by computing and using theoretical probability

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

3: Algebraic Relationships

3.1: Understand patterns, relations, and functions

3.1.1: Represent, analyze and determine rules for finding patterns involving positive rational numbers with tables, graphs, words, and when possible, symbolic rules

Using Tables, Rules and Graphs

3.2: Represent and analyze mathematical situations and structures using algebraic symbols

3.2.1: Develop an understanding of different uses of variables (e.g., as a placeholder for a specific unknown, as representative of a range of values)

Using Algebraic Equations

3.2.3: Describe and interpret relationships using information from tables and graphs including coordinate graphs (first quadrant)

Points in the Coordinate Plane - Activity A
Using Tables, Rules and Graphs

3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model and solve contextualized problems using various representations such as graphs, tables, and equations

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations

3.3.2: Recognize and represent direct variation using tables and graphs

Determining a Spring Constant

3.4: Analyze change in various contexts

3.4.1: Investigate how a change in one variable relates to a change in a second variable

Distance-Time Graphs

4: Measurement

4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.1: Select the most appropriate unit to measure area and perimeter

Perimeter, Circumference, and Area - Activity B

4.2: Apply appropriate techniques, tools, and formulas to determine measurements

4.2.1: Determine measurements of length and perimeter to the nearest eighth inch (for length less than one foot) and nearest inch (for lengths greater than one foot)

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

4.2.3: Develop and use formulas for finding perimeter and area of polygons

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

4.2.4: Calculate the area and circumference of a circle using pi as well as common approximations of pi (e.g., 3.14, 22/7)

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

4.2.7: Recognize that two-dimensional shapes having the same perimeter may have different areas and that shapes having the same area may have different perimeters

Perimeter, Circumference, and Area - Activity B

4.2.8: Analyze how changes in area of a figure affect the dimensions of the figure

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

4.2.9: Use referents to make estimates of area and evaluate the reasonableness of the estimate (e.g., estimate area of classroom by measuring area of one floor tile)

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

4.2.10: Calculate rates (e.g., miles per hour, simple interest, people per square mile) to solve problems.

Simple and Compound Interest

5: Geometry

5.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

5.1.1: Identify, describe, compare and classify polygons by their sides and angles

Classifying Quadrilaterals - Activity A
Classifying Triangles
Isosceles and Equilateral Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

5.1.2: Identify and represent the radius, center, diameter, chord and circumference of a circle

Circle: Circumference and Area

5.1.3: Identify combinations of angles that are complementary or supplementary and determine their measures

Investigating Angle Theorems - Activity A

5.1.4: Use properties of polygons to determine the lengths of sides and perimeters

Classifying Triangles
Perimeter, Circumference, and Area - Activity B

5.1.5: Develop, understand, and apply the property of the sum of the measures of the interior angles in a polygon as well as the sum of the exterior angles

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

5.2: Use visualization, spatial reasoning, and geometric modeling to solve problems

5.2.1: Model, sketch, draw and label polygons, circles (including the center, radius, and diameter), complementary angles, supplementary angles, vertical angles, and adjacent angles

Investigating Angle Theorems - Activity A

5.2.2: Identify and describe the intersection of two or more geometric figures in the plane (e.g., the intersection of a circle and a line)

Classifying Triangles

5.3: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

5.3.1: Plot polygons on coordinate graphs (first quadrant)

Points in the Coordinate Plane - Activity A

5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Build or sketch a shape that has a given number of lines of symmetry, or rotational symmetries (e.g., sketch a simple polygon with a given number of lines of symmetry)

Holiday Snowflake Designer