1: Calculations and Estimations

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

1.1.1: Model, and compare rational numbers with an emphasis on integers

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

1.1.3: Use rates, ratios, and percents to solve problems

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

1.1.4: Locate rational numbers (with an emphasis on integers) on a number line

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
Real Number Line - Activity A

1.1.5: Interpret, model, and use percents greater than 100 and less than 1 to solve problems

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.6: Determine the prime factorization of a number less than 1000 and express the prime factorization using exponents when applicable

Finding Factors with Area Models

1.2: Compute fluently and make reasonable estimates

1.2.1: Develop and analyze algorithms and compute with integers

Adding and Subtracting Integers with Chips

1.2.2: Multiply and divide fractions and mixed numbers

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

1.2.3: Compute with squares and cubes, with an emphasis on finding area, surface area, and volume

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

1.2.4: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, and part-whole relationships)

Percent of Change
Percents and Proportions
Simple and Compound Interest

1.2.5: Apply order of operations including exponents, to simplify calculations and evaluate expressions

Exponents and Power Rules
Order of Operations

1.2.6: Develop and use strategies to estimate the results of integer computations and judge the reasonableness of results

Adding and Subtracting Integers with Chips
Estimating Population Size
Estimating Sums and Differences

1.2.7: Use referent numbers in estimating answers to calculations with fractions and percents (e.g., 12 x 3/8 < 6, since 3/8 < 1/2 and 1/2 of 12 is 6)

Estimating Population Size
Estimating Sums and Differences

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

1.3.2: Use inverse operations (addition and subtraction, multiplication and division) to solve problems and check solutions involving calculations with integers

Adding and Subtracting Integers
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Order of Operations
Solving Two-Step Equations

1.3.3: Apply the associative, commutative, and distributive properties to simplify computations with rational numbers (with an emphasis on integers)

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

1.3.5: Apply the property of additive inverses to determine solutions of equations

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

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, including mean and interquartile range for given or derived data

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode

2.2: Understand and apply basic concepts of probability

2.2.1: Compute experimental probabilities from a set of data and theoretical probabilities for single and simple compound events, using various methods (e.g., organized lists, tree diagrams, area models)

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Permutations and Combinations

2.2.2: Determine probabilities of simple independent and dependent events

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

2.2.3: Compare experimental probability of an event with the theoretical probability and explain any difference

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

2.2.4: Determine all possible outcomes of a particular event or all possible arrangements of objects in a given set by applying various methods including tree diagrams and systematic lists

Permutations and Combinations

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

2.3.2: Identify situations in which it makes sense to sample and identify methods for selecting a sample (e.g., convenience sampling, responses to survey, random sampling) that are representative of a population

Polling: Neighborhood

2.3.3: Distinguish between random and biased samples and identify possible sources of bias in sampling

Polling: Neighborhood

2.3.4: Represent and interpret data using frequency distribution tables, box-and whisker-plots, stem-and-leaf plots, and single- and multiple- line graphs

Box-and-Whisker Plots
Describing Data Using Statistics
Populations and Samples
Stem-and-Leaf Plots

2.3.5: Determine the graphical representation of a set of data that best shows key characteristics of the data

Box-and-Whisker Plots
Line Plots
Stem-and-Leaf Plots

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

2.4.1: Analyze data from frequency distribution tables, box-and whisker-plots, stem-and-leaf plots using measures of center and spread and draw conclusions

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode
Populations and Samples
Stem-and-Leaf Plots

2.4.2: Predict and evaluate how adding data to a set of data affect measures of center

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

3: Algebraic Relationships

3.1: Understand patterns, relations, and functions

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

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Using Tables, Rules and Graphs

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

3.2.1: Algebraically represent situations and solve problems involving linear equations and inequalities

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

3.2.3: Interpret algebraic relationships represented by two-column tables, number lines and coordinate graphs (four quadrants)

Linear Functions
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A
Using Tables, Rules and Graphs

3.2.4: Graph linear equations on a coordinate grid by making a table using integer coordinates

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line
Using Tables, Rules and Graphs

3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model situations, make predictions and inferences, and solve problems using linear equations

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

3.3.2: Recognize and represent direct variation using tables, graphs, and equations

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.3.3: Identify and sketch a graph that models a given situation

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

3.4: Analyze change in various contexts

3.4.1: Identify and describe how a change in one variable relates to a change in a second variable

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Using Algebraic Equations

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 surface area and volume

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

4.1.2: Convert from a measurement expressed in one unit within a system to another using a different unit within the same system to measure surface and volume

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

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

4.2.1: Develop and use strategies and formulas for calculating surface area and volume of right prisms, pyramids, and cylinders

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

4.2.2: Develop strategies for determining approximate volumes of irregular shapes

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

4.2.3: Determine surface area and volume of three-dimensional block constructions, given a two-dimensional representation

3D and Orthographic Views - Activity A
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

4.2.4: Compare and contrast the formulas for surface area and volume of prisms and pyramids

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

4.2.5: Create examples of rectangular prisms having the same volume, but different surface areas

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

4.2.6: Describe what happens to the surface area and volume of a solid when its shape is changed

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

4.2.7: Use referents to make estimates of surface area and volume and evaluate the reasonableness of the estimate

Estimating Population Size
Estimating Sums and Differences

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: Determine defining properties that characterize classes of quadrilaterals including side and angle measurements and their component parts (e.g., altitudes, medians, diagonals, bisectors)

Classifying Quadrilaterals - Activity A
Special Quadrilaterals

5.1.2: Identify parallel and intersecting lines and pairs of angles formed (right, vertical, adjacent) by parallel lines cut by a transversal and determine their measure

Investigating Angle Theorems - Activity A

5.1.3: Use proportional reasoning, drawings, models or technology to demonstrate congruence and similarity of polygons with an emphasis on quadrilaterals

Classifying Quadrilaterals - Activity A
Similar Figures - Activity A

5.1.4: Determine the measures of missing sides and angles in congruent quadrilaterals and their component parts

Classifying Quadrilaterals - Activity A

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

5.2.1: Model, sketch, and label prisms, pyramids, cylinders, and quadrilaterals with specified side lengths or angle measures

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

5.2.2: Use two-dimensional representation of three-dimensional objects, including nets, to solve problems involving surface area and volume

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

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

5.3.1: Identify properties of quadrilaterals and their component parts on a coordinate graph

Classifying Quadrilaterals - Activity A

5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Determine the image of a point (with integer coordinates) on a graph under translations and reflections

Reflections
Rotations, Reflections and Translations