1: The student understands and applies the concepts and procedures of mathematics.

1.1: Understand and apply concepts and procedures from number sense.

1.1.1: Understand the concept and symbolic representation of fractions, decimals, and integers.

1.1.1.b: Convert between equivalent forms of fractions, decimals, or percents.

Percents, Fractions and Decimals

1.1.1.d: Explain or demonstrate that decimals may have multiple equivalent representations.

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

1.1.2: Understand the relative values of decimals, fractions, or integers.

1.1.2.a: Order decimals, fractions, and/or percents and explains why one number is greater than, less than, or equal to another number.

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
Percents and Proportions

1.1.2.b: Order decimals, fractions and/or integers based on a picture of a real world model, locations on a number line, or symbolic representation.

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

1.1.2.c: Explain why one integer, fraction, decimal, or percent is greater than, less than, or equal to another given number.

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
Percents and Proportions

1.1.3: Understand and use the inverse property of addition on integers (W) and the inverse property of multiplication on non-negative decimals or fractions.

1.1.3.a: Use the inverse relationship between multiplication and division to simplify computations.

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

1.1.4: Understand the concept of direct proportion.

1.1.4.a: Explain or illustrate the meaning of a ratio, percent or proportion.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood
Proportions and Common Multipliers

1.1.4.b: Express proportional relationships using objects, pictures, and symbols.

Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A

1.1.4.c: Complete or write a proportion for a given situation.

Estimating Population Size

1.1.4.d: Predict a future situation using direct proportion

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

1.1.4.e: Represent equivalent ratios and/or percents using pictures, diagrams, or symbols.

Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

1.1.4.f: Determine or use a ratio, percent, or proportion in a given situation.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood
Proportions and Common Multipliers

1.1.5: Understand the meaning of addition and subtraction of integers.

1.1.5.a: Explain or show the meaning of addition and subtraction of integers using words, pictures, or real-world models.

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

1.1.5.b: Translate a symbolic addition or subtraction of integers into a real-life situation.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations

1.1.5.c: Show addition and subtraction of integers using technology.

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

1.1.5.d: Translate a given picture or illustration representing addition or subtraction of integers into an equivalent symbolic representation.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations

1.1.5.e: Explain why multiplication of fractions involves multiplying denominators while addition of fractions requires finding common denominators.

Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.1.5.f: Select and/or use an appropriate operation to show understanding of addition and subtraction of integers.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips

1.1.6: Apply strategies or uses computational procedures using order of operations to add, subtract, multiply, and divide non-negative decimals and fractions.

1.1.6.a: Find the product or quotient using non-negative decimals and fractions.

Dividing Fractions
Multiplying Fractions
Multiplying with Decimals

1.1.6.b: Use multiplication and division in real world situations involving non-negative rational numbers.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.1.6.c: Multiply non-negative decimals and fractions.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.1.6.e: Compute with non-negative rational numbers using order of operations.

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

1.1.6.g: Complete multi-step calculations requiring two or more operations with non-negative decimals and fractions.

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

1.1.7: Apply strategies and uses tools to complete tasks involving addition and subtraction of integers and the four basic operations on non-negative decimals and fractions.

1.1.7.c: Describe strategies for mentally adding and/or subtracting integers and multiplying and/or dividing non-negative decimals and fractions.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Dividing Fractions
Multiplying Fractions
Multiplying with Decimals
Order of Operations

1.1.8: Apply estimation strategies involving addition and subtraction of integers and the four basic operations on non-negative decimals and fractions to predict results or determine reasonableness of answers.

1.1.8.a: Determine and explain when an approximation, estimation, or exact computation is appropriate and selects or illustrates a real-life situation where estimation is sufficient.

Estimating Sums and Differences

1.1.8.b: Use estimation strategies to predict an answer prior to operations on non-negative rational numbers.

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

1.1.8.d: Compute to check the reasonableness of estimated answers for a given situation.

Adding Real Numbers

1.1.8.e: Explain an appropriate adjustment when an estimate and a computation do not agree.

Estimating Sums and Differences

1.1.8.f: Explain or describe a strategy for estimation involving computation with non-negative decimals and fractions.

Estimating Population Size
Estimating Sums and Differences

1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Understand how changes in one linear dimension affect other linear measurements and area of rectangles, triangles, and circles.

1.2.1.a: Determine and/or describe the impact on the perimeter, circumference, and/or area of a rectangle, triangle, and/or circle caused by a change in one dimension.

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

1.2.1.b: Determine and/or describe the impact on one dimension caused by a change in perimeter, circumference and/or area of a rectangle, triangle, and/or circle.

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

1.2.3: Understand how the unit of measure affects the precision of measurement.

1.2.3.a: Identify, describe, or explain how the unit selected for a situation can affect the precision of the measurement.

Triple Beam Balance

1.2.3.b: Explain why measurement systems have different size units and how that allows for different levels of precision.

Triple Beam Balance

1.2.4: Understand and use a systematic procedure to measure and describe angles.

1.2.4.a: Suggested Procedure:

1.2.4.a.3: Select a tool that matches the unit chosen.

Triple Beam Balance

1.2.4.a.4: Use the selected tool to determine the number of units.

Triple Beam Balance

1.2.5: Use formulas to determine measurements related to circles, triangles, and rectangular prisms.

1.2.5.a: Use formulas to determine and label missing measurements for circles, including radius, diameter, circumference, and area, in given situations.

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

1.2.5.b: Use formulas to determine and label missing measurements for rectangular prisms, including length, width, height, volume, and surface area, in given situations.

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

1.2.5.c: Use formulas to determine and label missing measurements for triangles, including base, height, perimeter, and area, in given situations.

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

1.2.5.d: Demonstrate or explain how to use a formula for finding the area and circumference of a circle.

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

1.2.5.e: Calculate and label dimensions of rectangular prisms with given volumes and/or surface areas.

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

1.2.5.f: Determine the surface area of a rectangular prism.

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

1.2.6: Understand and apply strategies to obtain a reasonable estimate of measurements related to circles, right triangles, and surface area of rectangular prisms.

1.2.6.b: Estimate and label circle, right triangle, and rectangular prism measurements.

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

1.2.6.c: Use common approximations of pi to estimate and label the circumference and the area of circles.

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

1.2.6.e: Explain why estimation or precise measurement is appropriate in a given situation.

Triple Beam Balance

1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Understand the concept of similarity and its relationship to congruence.

1.3.1.a: Identify or describe congruence in figures.

Constructing Congruent Segments and Angles

1.3.1.b: Explain how two figures are similar and/or congruent using definitions or real-world examples.

Constructing Congruent Segments and Angles
Similar Figures - Activity A

1.3.1.c: Produce a sample scale drawing and explains how it is an example of similarity.

Similar Figures - Activity A

1.3.2: Use the attributes of rectangular prisms, polygons, angles, and circles.

1.3.2.a: Sort, classify, and label circles according to their properties.

Circles
Classifying Triangles
Special Quadrilaterals

1.3.2.b: Sort, classify, and describe rectangular prisms according to their properties including vertices, edges, faces, bases, and parallel faces.

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

1.3.2.c: Draw rectangular prisms and circles with specified properties.

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

1.3.2.d: Explain and use the relationship between radius, diameter, and circumference.

Circle: Circumference and Area

1.3.2.e: Find the missing angle given all but one of the angles of a triangle or quadrilateral.

Investigating Angle Theorems - Activity A
Isosceles and Equilateral Triangles
Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

1.3.2.f: Sort, classify, and label figures according to their geometric properties.

Classifying Quadrilaterals - Activity A
Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Triangle Angle Sum - Activity A

1.3.3: Describe the location of points on a coordinate grid in any of the four quadrants.

1.3.3.a: Plot and label ordered pairs in any of the four quadrants.

Introduction to Functions
Points in the Coordinate Plane - Activity A

1.3.3.b: Name the coordinates of a given point in any of the four quadrants.

Points in the Coordinate Plane - Activity A

1.3.3.c: Describe the location of objects on a coordinate grid using coordinates or labels.

Points in the Coordinate Plane - Activity A

1.3.4: Apply a combination of translations and/or reflections to 2-dimensional figures.

1.3.4.a: Explain the result of two or more translations or reflections of a figure with or without a grid.

Reflections
Rotations, Reflections and Translations

1.3.4.b: Plot a combination of two translations and/or reflections of a simple figure with a coordinate grid.

Reflections
Rotations, Reflections and Translations

1.3.4.c: Explain the transformation of one figure to another on a two-dimensional coordinate grid in terms of a combination of two translations or two reflections.

Reflections
Rotations, Reflections and Translations

1.3.4.d: Describe a combination of two translations and/or reflections so that another person could draw them.

Reflections
Rotations, Reflections and Translations

1.3.4.e: Explain a series of transformations in a given diagram or picture.

Dilations
Reflections
Rotations, Reflections and Translations

1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.2: Use procedures to determine the probabilities of complementary and mutually exclusive events.

1.4.2.c: Determine, interpret, or express probabilities in the form of a fraction, decimal, or percent.

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

1.4.2.e: Predict the probability of future events based on empirical data.

Geometric Probability - Activity A

1.4.4: Determine and use range and the measures of central tendency of a set of data.

1.4.4.a: Explain the effects of extreme values on the mean of a set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.b: Describe how additional data added to data sets may affect the measures of central tendency.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.c: Explain the relationship between the range and measures of central tendency.

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

1.4.4.d: Complete a set of data based on a given mean, median, or mode and a partial set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.e: Explain why the mean, median, and mode may not be the same and what each indicates as a measure of central tendency in a given situation.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.f: Determine and/or use the mean, median, mode, and/or range for a set of data.

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

1.4.5: Read and interpret data presented in diagrams, stem-and-leaf plots, scatter plots, and box-and-whisker plots.

1.4.5.a: Describe the accuracy and completeness of the data in a Venn diagram, stem-and-leaf plot, box-and-whisker plot, and/or scatter plot.

Box-and-Whisker Plots
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

1.4.5.b: Read and interpret the data in Venn Diagrams, stem-and-leaf plots, box-and-whisker- plots, and/or scatter plots.

Box-and-Whisker Plots
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

1.4.5.c: Select and explain which graph type is the most appropriate representation for a given set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

1.4.5.d: Interpret and describe trends and patterns represented in data and data displays.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

1.4.5.e: Explain statistical information, including median, range, inter-quartile range, for a given box-and-whisker plot.

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

1.4.5.f: Use data from a sample or data display to make an inference.

Box-and-Whisker Plots

1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Apply knowledge of linear relationships to recognize, extend, and/or create patterns in tables and graphs.

1.5.1.a: Select a linear relationship that has the same pattern as another linear relationship.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions

1.5.1.b: Use technology to generate graphic representations of linear relationships.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

1.5.1.c: Select, extend, or represent patterns and sequences using tables, graphs, or expressions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Finding Patterns
Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

1.5.1.d: Use technology to generate graphic representations of linear and non-linear relationships.

Arithmetic Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Slope-Intercept Form of a Line - Activity A

1.5.1.e: Describe the relationship between a term in a sequence and its position in the sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

1.5.1.f: Identify patterns that are linear relations and provides missing terms in the beginning, middle, and/or end of the pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions

1.5.2: Determine a rule for linear patterns and sequences with combinations of two operations in the rule.

1.5.2.b: Use an equation or graph to describe a linear relationship.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

1.5.2.c: Use technology to determine the rule for a linear pattern or sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

1.5.3: Express relationships between quantities using equality and inequality symbols.

1.5.3.a: Express relationships between quantities including integers, and non-negative decimals and fractions using =, "not equal to", <, >, "less than or equal to" and "greater than or equal to".

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

1.5.3.b: Describe a situation represented by an equation or inequality involving integers and/or non-negative decimals and fractions.

Using Algebraic Equations

1.5.3.c: Write a simple equation or inequality using rational numbers and integers to represent a given situation.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4: Use variables to write expressions, linear equations, and inequalities that represent situations involving integers and non-negative decimals and fractions.

1.5.4.a: Write an expression, equation, or inequality using variables to represent a given situation.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.b: Describe a situation that corresponds to a given expression, equation, or inequality.

Using Algebraic Equations

1.5.4.c: Describe a situation involving a linear relationship that matches a given graph.

Arithmetic Sequences
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.4.d: Translate among different representations of linear equations, using symbols, graphs, tables, diagrams, or written descriptions.

Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.4.e: Explain the meaning of a variable in a formula, expression, equation, or inequality.

Using Algebraic Equations
Using Algebraic Expressions

1.5.5: Apply algebraic properties to evaluate expressions and formulas using order of operations.

1.5.5.c: Write an expression with a variable that represents a given situation and determine the value of the expression given a value for the variable.

Using Algebraic Equations
Using Algebraic Expressions

1.5.6: Apply a variety of properties to solve one-step and two-step equations with one variable.

1.5.6.a: Solve single variable one-step or two-step equations and checks the solution.

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

1.5.6.b: Write and solve a single-variable one- or two-step equation for a given situation.

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

1.5.6.c: Explain or show the meaning of the solution to an equation.

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

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Analyze numerical, measurement, geometric, probability, statistical, and/or algebraic information from a variety of sources.

3.1.1.a: Analyze mathematical information or results.

Biconditional Statement
Conditional Statement

3.1.1.b: Compare mathematical information represented in tables, charts, graphs, text, diagrams, figures, or pictures.

Biconditional Statement
Conditional Statement
Populations and Samples

3.1.1.d: Differentiate between valid and invalid analysis of mathematical information or results.

Biconditional Statement
Conditional Statement

3.3: Verify results.

3.3.1: Justify results using evidence.

3.3.1.a: Justify results using evidence and information from the problem situation and/or known facts, patterns, and relationships.

Introduction to Functions

3.3.2: Evaluate reasonableness of results.

3.3.2.b: Verify that the solution to a real-world problem makes sense in relation to the situation.

Biconditional Statement
Conditional Statement

4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.1: Gather information.

4.1.2: Extract numerical, measurement, geometric, probability, statistical, and/or algebraic information from multiple sources.

4.1.2.a: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, line graphs, circle graphs, histograms, scatter plots, stem-and-leaf plots, box-and-whisker plots, diagrams, and/or models for a purpose.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

4.2: Organize, represent, and share information.

4.2.2: Represent numerical, measurement, geometric, probability, statistical, and/or algebraic information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using tables, charts, histograms, scatter plots, stem-and-leaf plots, box-and-whisker plots, pictures, models, drawings, or other appropriate forms including title, labels, appropriate and consistent scales, and accurate display of data.

Box-and-Whisker Plots
Histograms
Scatter Plots - Activity A
Stem-and-Leaf Plots