6A: Students who meet the standard can demonstrate knowledge and use of numbers and their many representations in a broad range of theoretical and practical settings. (Representations)

6A.2: Represent, order, compare, and graph integers.

Adding and Subtracting Integers
Adding on the Number Line
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6A.3: Identify fractional pieces that have the same value but different shapes.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

6A.4: Compare and order fractions and decimals efficiently and find their approximate position on a number line.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Equivalent Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

6B: Students who meet the standard can investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships. (Operations and properties)

6B.1: Write prime factorizations of numbers.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

6B.2: Determine the least common multiple and the greatest common factor of a set of numbers.

Pattern Flip (Patterns)

6B.3: Demonstrate the meaning of multiplication of fractions (e.g., 1/2 x 3 is 1/2 of a group of three objects).

Multiplying Fractions
Multiplying Mixed Numbers

6B.4: Simplify simple arithmetic expressions with rational numbers using the field properties and the order of operations.

Adding on the Number Line
Order of Operations
Simplifying Algebraic Expressions I

6B.5: Recognize and use the inverse relationships of addition and subtraction, multiplication and division to simplify computations and solve problems.

Factor Trees (Factoring Numbers)
Function Machines 3 (Functions and Problem Solving)
Modeling One-Step Equations
Solving Two-Step Equations

6B.6: Solve multiplication number sentences and word problems with whole numbers and familiar fractions.

Critter Count (Modeling Multiplication)

6C: Students who meet the standard can compute and estimate using mental mathematics, paper-and-pencil methods, calculators, and computers. (Choice of method)

6C.1: Select and use appropriate operations, methods, and tools to compute or estimate using whole numbers with natural number exponents.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

6C.2: Analyze algorithms for computing with whole numbers, familiar fractions, and decimals and develop fluency in their use.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
Dividing Fractions
Dividing Mixed Numbers
Equivalent Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Target Sum Card Game (Multi-digit Addition)

6D: Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents.

6D.1: Solve number sentences and word problems using percents.

Fraction, Decimal, Percent (Area and Grid Models)
Percent of Change
Percents and Proportions

6D.2: Demonstrate and explain the meaning of percents, including greater than 100 and less than 1.

Fraction, Decimal, Percent (Area and Grid Models)

6D.4: Analyze situations to determine whether ratios are appropriate to solve problems.

Estimating Population Size

6D.5: Determine equivalent ratios.

Fraction, Decimal, Percent (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

7C: Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. (Progression from selection of appropriate tools and methods to application of measurements

7C.1: Select and justify an appropriate formula to find the area of triangles, parallelograms, and trapezoids.

Area of Triangles

7C.2: Select an appropriate formula or strategy to find the surface area and volume of rectangular and triangular prisms.

Balancing Blocks (Volume)
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

7C.3: Develop and use formulas for determining the area of triangles, parallelograms, and trapezoids.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

7C.4: Develop and use the formula for determining the volume of a rectangular and triangular prism.

Balancing Blocks (Volume)
Prisms and Cylinders
Pyramids and Cones

7C.5: Calculate the surface area of a cube, rectangular prism, and triangular prism.

Surface and Lateral Areas of Prisms and Cylinders

7C.6: Develop and use formulas for determining the circumference and area of circles.

Circumference and Area of Circles

8A: Students who meet the standard can describe numerical relationships using variables and patterns. (Representations and algebraic manipulations)

8A.1: Investigate, extend, and describe arithmetic and geometric sequences of numbers whether presented in numeric or pictorial form.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Flip (Patterns)

8A.3: Express properties of numbers and operations using variables (e.g., the commutative property is m + n = n + m).

Solving Algebraic Equations I
Solving Algebraic Equations II

8A.4: Simplify algebraic expressions involving like terms.

Addition of Polynomials
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

8B: Students who meet the standard can interpret and describe numerical relationships using tables, graphs, and symbols. (Connections of representations including the rate of change)

8B.1: Graph simple inequalities on a number line.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

8B.2: Create a table of values that satisfy a simple linear equation and plot the points on the Cartesian plane.

Function Machines 2 (Functions, Tables, and Graphs)
Points, Lines, and Equations
Slope-Intercept Form of a Line

8B.3: Describe verbally, symbolically, and graphically, a simple relationship presented by a set of ordered pairs of numbers.

Introduction to Functions
Points, Lines, and Equations

8C: Students who meet the standard can solve problems using systems of numbers and their properties. (Problem solving; number systems, systems of equations, inequalities, algebraic functions)

8C.1: Identify and explain incorrect uses of the commutative, associative, and distributive properties.

Chocomatic (Multiplication, Arrays, and Area)
Square Roots

8C.3: Identify and provide examples of inverse operations.

Function Machines 3 (Functions and Problem Solving)

8D: Students who meet the standard can use algebraic concepts and procedures to represent and solve problems. (Connection of 8A, 8B, and 8C to solve problems)

8D.1: Create, model, and solve algebraic equations using concrete materials.

Absolute Value Equations and Inequalities
Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

9A: Students who meet the standard can demonstrate and apply geometric concepts involving points, lines, planes, and space. (Properties of single figures, coordinate geometry and constructions)

9A.1: Plot and read ordered pairs of numbers in all four quadrants.

City Tour (Coordinates)
Points in the Coordinate Plane

9A.2: Describe sizes, positions, and orientations of shapes under transformations, including dilations.

Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures

9A.3: Perform simple constructions (e.g., equal segments, angle and segment bisectors, or perpendicular lines, inscribing a hexagon in a circle) with a compass and straightedge or a mira.

Segment and Angle Bisectors

9A.4: Determine and describe the relationship between pi, the diameter, the radius, and the circumference of a circle.

Circumference and Area of Circles

9A.5: Determine unknown angle measures using angle relationships and properties of a triangle or a quadrilateral.

Classifying Quadrilaterals
Polygon Angle Sum
Triangle Angle Sum

9B: Students who meet the standard can identify, describe, classify and compare relationships using points, lines, planes, and solids. (Connections between and among multiple geometric figures)

9B.1: Determine the relationships between the number of vertices or sides in a polygon, the number of diagonals, and the sum of its angles.

Polygon Angle Sum
Triangle Angle Sum

9B.2: Solve problems that involve vertical, complementary, and supplementary angles.

Investigating Angle Theorems
Triangle Angle Sum

9B.3: Analyze quadrilaterals for defining characteristics.

Classifying Quadrilaterals
Special Parallelograms

9B.4: Create a three-dimensional object from any two-dimensional representation of the object, including multiple views, nets, or technological representations.

Surface and Lateral Areas of Prisms and Cylinders

9C: Students who meet the standard can construct convincing arguments and proofs to solve problems. (Justifications of conjectures and conclusions)

9C.1: Make, test, and justify conjectures about various quadrilateral and triangle relationships, including the triangle inequality.

Classifying Quadrilaterals

10A: Students who meet the standard can organize, describe and make predictions from existing data. (Data analysis)

10A.1: Construct, read, interpret, infer, predict, draw conclusions, and evaluate data from various displays, including circle graphs.

Box-and-Whisker Plots
Correlation
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Stem-and-Leaf Plots

10B: Students who meet the standard can formulate questions, design data collection methods, gather and analyze data and communicate findings. (Data Collection)

10B.2: Collect data over time with or without technology.

Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)

10C: Students who meet the standard can determine, describe and apply the probabilities of events. (Probability including counting techniques)

10C.1: Record probabilities as fractions, decimals, or percents.

Estimating Population Size
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

10C.2: Demonstrate that the sum of all probabilities equals one.

Theoretical and Experimental Probability

10C.3: Determine empirical probabilities from a set of data provided.

Independent and Dependent Events

10C.4: Set up a simulation to model the probability of a single event.

Geometric Probability
Independent and Dependent Events
Theoretical and Experimental Probability

10C.5: Discuss the effect of sample size on the empirical probability compared to the theoretical probability.

Polling: City

10C.6: List outcomes by a variety of methods (e.g., tree diagram).

Permutations and Combinations

10C.7: Determine theoretical probabilities of simple events.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability