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 of rational numbers (integers, decimals, fractions).

1.1.1.a: Create a model when given a symbolic representation of a rational number.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Improper Fractions and Mixed Numbers

1.1.1.b: Write the rational number when given a model (e.g., number line, area model, situation, diagram, picture).

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Improper Fractions and Mixed Numbers

1.1.1.c: Identify and convert between equivalent forms of rational numbers (e.g., fractions to decimals, percents to fractions).

Percents, Fractions and Decimals

1.1.1.d: Identify prime, square, or composite numbers.

Finding Factors with Area Models

1.1.2: Understand the relative values of rational numbers.

1.1.2.a: Compare and order rational numbers using physical models or implementing strategies (e.g., like denominators, changing to the same form).

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

1.1.2.b: Locate symbolic representations of rational numbers on a model (e.g., a number line, fraction line, decimal grid, and circle graph).

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Improper Fractions and Mixed Numbers

1.1.3: Apply properties of addition and multiplication including inverse properties to the rational number system.

1.1.3.a: Use the inverse relationships between multiplication and division to simplify computations and solve problems.

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

1.1.3.b: Use the inverse properties of addition and multiplication to simplify computations with integers, fractions, and decimals.

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

1.1.4: Understand the concept of direct proportion.

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

Estimating Population Size

1.1.4.b: Explain the meaning of a proportion.

Estimating Population Size

1.1.4.c: Represent a new relationship from a given ratio (e.g., height of a totem pole, maypole).

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

1.1.4.d: Represent percentages less than 1% or greater than 100% using objects, pictures, and symbols.

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

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

Estimating Population Size

1.1.4.f: Solve problems involving proportions (e.g., determine the number and kinds of baked goods to bring to a bake sale based on proportions of different goods sold at previous bake sales).

Estimating Population Size

1.1.4.g: Use ratios to make predictions about proportions in a future situation.

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

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

1.1.5.a: Explain the meaning of addition and subtraction of integers using real-world models (e.g., reducing debt, temperature increase or decrease, yards gained and lost, movement of a hot-air balloon).

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

1.1.5.b: Create a problem situation involving addition or subtraction of integers.

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

1.1.5.c: Explain or show the meaning of addition or subtraction of integers.

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

1.1.5.d: Use technology to demonstrate addition and subtraction with integers.

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

1.1.6: Apply computational procedures with fluency for multiplication and division on non-negative rational numbers.

1.1.6.a: Find the product or quotient using nonnegative decimals and fractions with unlike denominators.

Dividing Fractions
Multiplying Fractions
Multiplying with Decimals

1.1.6.b: Apply percentages to solve a problem in a variety of situations (e.g., taxes, discounts, interest).

Percent of Change
Percents and Proportions
Polling: Neighborhood
Simple and Compound Interest

1.1.6.c: Use multiplication and division to solve real-world problems involving non-negative rational numbers.

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

1.1.6.d: Multiply non-negative decimal numbers to the hundredths place.

Multiplying with Decimals

1.1.7: Understand and apply strategies and tools to complete tasks involving addition and subtraction on integers and the four basic operations on non-negative rational numbers.

1.1.7.b: Convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator.

Percents, Fractions and Decimals

1.1.7.c: Use calculators to add and subtract with integers of two or more digits.

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

1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Analyze how a change in a linear dimension affects other linear measurements (perimeter, circumference) and area measurements.

1.2.1.a: Describe the relationships among linear dimensions (e.g., radius of a circle, length of a side or base, changes in the diameter affects the amount of deer hide needed to cover a drum face) and area of the figure (e.g., change the radius or length of a side, and check the change in area; describe that change).

Prisms and Cylinders - Activity A

1.2.1.b: Explain changing one, two, or three dimensions in a rectangular prism and how it affects the surface area and volume; give three examples.

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

1.2.1.c: Solve problems involving the effects of changes in one dimension on area (e.g., given a garden with certain dimensions, make the area of the garden x square units by changing only one dimension of the garden).

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

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

1.2.3.a: Select the appropriate measurement tool to match the precision needed (e.g., if needing measurement to the nearest 1/16 inch, select a ruler that has 1/32 increments).

Triple Beam Balance

1.2.3.b: Explain how the unit selected for a situation can affect the precision of the measurement (e.g., when you have a ruler that has only 1/10 increments, you cannot measure something to the nearest hundredth with confidence of precision).

Triple Beam Balance

1.2.3.c: Explain how measurement systems allow for different levels of precision (e.g., millimeters give more precise measurement than centimeters).

Triple Beam Balance

1.2.5: Apply formulas to find measurements of circles, triangles, and rectangular prisms.

1.2.5.a: Apply formulas to determine missing measurements for circles, rectangular prisms, and triangles.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Investigating Angle Theorems - Activity A
Perimeter, Circumference, and Area - Activity B
Polygon Angle Sum - Activity A
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones
Triangle Angle Sum - Activity A

1.2.5.b: Explain how to use a formula for finding the area and circumference of a circle (e.g, calculate the area needed to cover a drum face).

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

1.2.5.c: Find and compare the volumes of rectangular prisms that have a given volume (e.g., if two rectangular prisms have the same volume and one has twice the height of the other, determine how the areas of their bases compare).

Prisms and Cylinders - Activity A

1.2.5.d: Justify the standard formula for finding the area of a right triangle (e.g., 1/2 of a rectangle).

Area of Parallelograms - Activity A
Rectangle: Perimeter and Area

1.2.5.e: Use given dimensions to determine surface area and volume.

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

1.2.6: Understand and apply strategies to obtain reasonable estimates of circle measurements, right triangles, and surface area for rectangular prisms.

1.2.6.c: Use common approximations of pi (3.14; 22/7) to calculate the approximate circumference and the area of circles.

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

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

1.3.1: Understand the concept of similarity.

1.3.1.a: Identify corresponding sides and angles of two similar figures.

Similar Figures - Activity A

1.3.1.b: Determine and justify if two figures are similar using the definition of similarity.

Similar Figures - Activity A

1.3.1.c: Differentiate between similar and congruent figures, either geometric figures or real-world objects, and justify the conclusion.

Constructing Congruent Segments and Angles
Similar Figures - Activity A

1.3.1.d: Explain how a scale drawing is an example of similarity.

Similar Figures - Activity A

1.3.2: Apply understanding of the characteristics of rectangular prisms and circles.

1.3.2.b: Draw rectangular prisms and circles with specified properties (e.g., circumference of an 18-centimeter quadrilateral having equal sides but no right angles; a triangle with no equal sides).

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

1.3.2.c: Use the properties of rectangular prisms and circles to solve problems (e.g., determine which of two rectangular prismshaped boxes will hold the most cans of food at the food drive and explain how the geometric characteristics affect capacity).

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

1.3.2.d: Compare two rectangular prisms based on their characteristics (e.g., compare the geometric characteristics of two rectangular prisms with different dimensions and the same volume).

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

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

1.3.3.a: Identify the coordinates of the fourth point to make a rectangle given three points.

Special Quadrilaterals

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

Points in the Coordinate Plane - Activity A

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

Points in the Coordinate Plane - Activity A

1.3.3.d: Identify objects or the location of objects on a coordinate grid using coordinates or labels.

Points in the Coordinate Plane - Activity A

1.3.3.f: Use ordered pairs to describe the location of objects on a grid.

Points in the Coordinate Plane - Activity A

1.3.4: Understand and apply combinations of translations (slides) and reflections (flips) to two-dimensional figures.

1.3.4.a: Identify and explain whether a shape has been translated (slid) or reflected (flipped) with or without a grid.

Reflections
Rotations, Reflections and Translations

1.3.4.b: Use transformations to create congruent figures and shapes in multiple orientations.

Constructing Congruent Segments and Angles
Dilations
Reflections
Rotations, Reflections and Translations

1.3.4.c: Find the coordinate pairs for a translation or a reflection across an axis given a shape on a coordinate grid.

Reflections
Rotations, Reflections and Translations

1.3.4.d: Match a shape with its image following one or two transformations (sliding or flipping).

Dilations
Reflections
Rotations, Reflections and Translations

1.3.4.e: Use combinations of translations and reflections to draw congruent figures.

Constructing Congruent Segments and Angles
Reflections
Rotations, Reflections and Translations

1.3.4.f: Use ordered pairs to describe the location of an object on a coordinate grid after a translation and reflection.

Points in the Coordinate Plane - Activity A
Reflections
Rotations, Reflections and Translations

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

1.4.2: Understand and apply the procedures for determining the probabilities of multiple trials.

1.4.2.a: Calculate the probabilities of independent or mutually exclusive outcomes or events.

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

1.4.2.b: Calculate the probability of an event given the probability of its complement.

Geometric Probability - Activity A

1.4.2.c: Create a game that has an equal probability for all players to win.

Geometric Probability - Activity A

1.4.2.e: 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.f: Predict the probability of outcomes of experiments and test the predictions.

Geometric Probability - Activity A
Probability Simulations

1.4.4: Understand how variations in data may affect the choice of data analysis techniques used.

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

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

1.4.4.b: Describe the effects of extreme values on means in a population.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.c: Explain the difference between median or mean as a measure of central tendency in a given situation (e.g., when an extreme value skews the mean).

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

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

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.e: Find the range of a set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots

1.4.4.f: Explain what the range adds to measures of central tendency.

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

1.4.5: Understand and apply various data display techniques including box-andwhisker plots.

1.4.5.b: Determine the appropriate representation for given data.

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

1.4.5.c: Construct bar graphs, circle graphs, line graphs, box-and-whisker and scatter plots using collected data.

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

1.4.5.d: Use scatter plots to describe trends and interpret relationships.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

1.4.5.e: Read and interpret data from box-andwhisker plots and determine when using this type of graph is appropriate.

Box-and-Whisker Plots

1.4.5.f: Describe statistical information given a box-and-whisker plot (e.g., median, range, interquartile range).

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

1.4.5.g: Compare different graphical representations of the same data.

Box-and-Whisker Plots
Histograms
Line Plots
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

1.4.6: Evaluate how different representations of the same set of data can support different points of view.

1.4.6.a: Critique the use of data and data displays for univariate data.

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

1.4.6.d: Explain how different representations of the same set of data can support different points of view.

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

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

1.5.1: Apply understanding of linear relationships to analyze patterns, sequences, and situations.

1.5.1.a: Identify patterns that are linear relations and provide missing terms.

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

1.5.1.b: Describe the relationship between the terms in a sequence and their positions in the sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

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

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

1.5.1.e: Make predictions using linear relationships in situations.

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

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

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

1.5.1.g: Create a representation of a linear relationship given a rule.

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

1.5.2: Apply understanding of linear patterns in a table, graph, or situation to develop a rule.

1.5.2.a: Describe the rule and/or construct a table to represent a pattern with combinations of two arithmetic operations in the rule.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

1.5.2.b: Write an expression or equation with a single variable representing a situation or real-world problem.

Using Algebraic Equations
Using Algebraic Expressions

1.5.2.c: Write a story about a situation that represents a given linear equation, expression, or graph.

Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

1.5.2.d: Describe the rule or construct a table to represent a pattern with combinations of two arithmetic operations in the rule.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

1.5.2.e: Use technology to determine the rule for a linear relationship.

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

1.5.3: Understand relationships between quantities using squares and square roots.

1.5.3.b: Simplify square roots of square numbers (e.g., the square root of 9 is 3).

Square Roots

1.5.3.c: Demonstrate understanding of square roots with physical models and examples.

Square Roots

1.5.4: Apply understanding of equations, tables, and graphs to represent situations involving linear relationships.

1.5.4.a: Represent linear relationships through expressions, equations, tables, and graphs of situations involving nonnegative rational numbers.

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Using Tables, Rules and Graphs

1.5.4.b: Graph data to demonstrate relationships in familiar contexts (e.g., conversions, perimeter, area, volume, and scaling).

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

1.5.4.c: Develop a situation that corresponds to a given equation or expression.

Using Algebraic Equations

1.5.4.d: Create a table or graph given a description of, or an equation for, a situation involving a linear relationship.

Defining a Line with Two Points
Linear Functions
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

1.5.4.e: Describe a situation involving a linear or non-linear relationship that matches a given graph (e.g., time-distance, timeheight).

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

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

Using Algebraic Equations
Using Algebraic Expressions

1.5.5: Understand and apply procedures to evaluate expressions and formulas considering order of operations.

1.5.5.b: Explain the simplification of expressions and equations using order of operations.

Order of Operations
Solving Equations By Graphing Each Side
Using Algebraic Equations

1.5.5.c: Evaluate expressions and formulas considering order of operations.

Order of Operations

1.5.5.f: Write expressions or equations for a situation.

Using Algebraic Equations
Using Algebraic Expressions

1.5.6: Understand and apply a variety of strategies to solve two-step equations with one variable.

1.5.6.b: Solve two-step equations with one variable on only one side of the equal sign (e.g., 2x + 4 = 12).

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 information from a variety of sources to interpret and compare information.

3.1.1.a: Explain and compare conclusions reached from data (e.g., from newspapers, web sites, opinion polls).

Populations and Samples

3.1.1.b: Use graphs to describe trends, compare, and interpret relationships from data (e.g., from newspapers, web sites, opinion polls).

Populations and Samples
Solving Using Trend Lines

3.2: Make predictions, inferences, conjectures, and draw conclusions.

3.2.1: Apply prediction and inference skills to make or evaluate conjectures.

3.2.1.a: Predict the probability of future events based on empirical data.

Geometric Probability - Activity A

3.2.3: Analyze procedures and results in various situations.

3.2.3.a: Describe how additional data added to data sets may affect the computations of measures of central tendency in various situations.

Describing Data Using Statistics
Mean, Median and Mode

3.3: Verify results.

3.3.1: Analyze procedures and information used to justify results using evidence.

3.3.1.c: Apply estimation strategies prior to computing addition and subtraction of integers and operations on non-negative rational numbers to determine reasonableness of answers.

Adding and Subtracting Integers
Estimating Population Size
Estimating Sums and Differences

3.3.2: Analyze thinking and mathematical ideas using models, known facts, patterns, relationships, or counter examples.

3.3.2.a: Explain how different representations of the same set of data can support different points of view.

Describing Data Using Statistics

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

4.1: Gather information.

4.1.2: Understand how to extract information from multiple sources using reading, listening, and observation.

4.1.2.a: Create a table or graph given a description of, or an equation for, a situation involving a linear or non-linear relationship.

Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

4.2: Organize, represent, and share information.

4.2.1: Apply organizational skills for a given purpose.

4.2.1.a: Identify, 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

4.2.2: Apply communication skills to clearly and effectively express or present ideas and situations using mathematical language or notation.

4.2.2.a: Identify data that may represent sampling errors and explain why the sample (and the display) might be biased.

Polling: Neighborhood

4.2.2.b: Explain when estimation might be used rather than computation.

Estimating Sums and Differences

5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

5.1: Relate concepts and procedures within mathematics.

5.1.1: Apply concepts and procedures from a variety of mathematical areas in a given problem or situation.

5.1.1.b: Given a set of data, compare various representations (e.g., box-and-whisker, bar, circle graph) for a given situation.

Describing Data Using Statistics
Populations and Samples

5.1.2: Apply different mathematical models and representations to the same situation.

5.1.2.a: Explain how different representations of the same set of data can support different points of view.

Describing Data Using Statistics

5.2: Relate mathematical concepts procedures to other disciplines.

5.2.1: Analyze mathematical patterns and ideas to extend mathematical thinking and modeling to other disciplines.

5.2.1.g: Mix paint in the correct proportions to create a particular color.

Estimating Population Size
Polling: Neighborhood
Similar Figures - Activity A

5.3: Relate mathematical concepts and procedures to real-world situations.

5.3.1: Understand that mathematics is used in daily life and extensively outside the classroom.

5.3.1.b: Use properties of polygons and circles to solve real-world problems (e.g., find the amount of fencing needed for a pasture).

Chords and Arcs