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.1: Place mixed numbers and decimals on a number line.

Comparing and Ordering Decimals
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

6A.2: Show equivalent representations of a number by changing from one form to another form (e.g., standard form to expanded form, fraction to decimal, decimal to percent, improper fraction to mixed number).

Dividing Mixed Numbers
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Number Systems
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

6A.3: Differentiate how fractions are used (part of a whole, part of a set, location on a number line, and division of a whole number).

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
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 Fractions (Area Models)
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

6A.4: Analyze how the size of the whole affects the size of the fraction (e.g., 1/2 of a large pizza is not the same as 1/2 of a small pizza).

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

6A.5: Describe integers using familiar applications (e.g., a thermometer, above/below sea level).

Integers, Opposites, and Absolute Values

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: Determine whether a number is prime or composite.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models

6B.2: Identify all the whole number factors of a composite number.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models

6B.3: Explore and identify properties of square numbers.

Square Roots

6B.5: Explore and use divisibility rules.

Factor Trees (Factoring Numbers)

6B.6: Solve number sentences and word problems using addition and subtraction of fractions with unlike denominators.

Fractions with Unlike Denominators

6B.7: Solve number sentences and word problems using addition and subtraction of decimals.

Sums and Differences with Decimals

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

6C.3: Select and use appropriate operation(s) and tool(s) (e.g., mental math, pencil-and-paper, estimation, calculator, computer) to perform calculations on whole numbers, fractions, and decimals according to the context and nature of the computation.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

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

6D.1: Identify and express ratios using appropriate notation (i.e., a/b, a to b, a:b).

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

6D.2: Model the concept of percent using manipulatives or drawings.

Fraction, Decimal, Percent (Area and Grid Models)

7A: Students who meet the standard can measure and compare quantities using appropriate units, instruments, and methods. (Performance and conversion of measurements)

7A.1: Convert U.S. customary and metric measurements into larger or smaller units.

Cannonball Clowns (Number Line Estimation)
Unit Conversions

7B: Students who meet the standard can estimate measurements and determine acceptable levels of accuracy. (Estimation)

7B.3: Estimate the perimeter, area, and/or volume of regular and irregular shapes and objects.

Area of Triangles
Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

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 appropriate tools to measure, draw, or construct figures.

Segment and Angle Bisectors

7C.2: Develop and discuss strategies for determining area and perimeter of irregular shapes.

Area of Triangles
Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

7C.3: Develop and use formulas to determine the area of squares, rectangles, and right triangles.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Pythagorean Theorem with a Geoboard
Square Roots

7C.4: Read and interpret a scale on a map or a scale drawing using the idea of a constant ratio (e.g., 1" represents 1 mile), and use it to answer questions about actual measurement.

Points in the Coordinate Plane

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

8A.1: Describe, extend, and make generalizations about given geometric and numeric patterns.

Arithmetic and Geometric Sequences
Finding Patterns
Function Machines 1 (Functions and Tables)
Pattern Flip (Patterns)

8A.2: Describe a pattern, with at least two operations, verbally and symbolically, given a table of input/output numbers.

Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)

8A.3: Demonstrate equality of two expressions with variables (e.g., 28 + 35 = 35 + n).

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
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: Model problem situations with objects and equations to draw conclusions.

Reaction Time 1 (Graphs and Statistics)

8B.2: Represent and analyze patterns and functions using words, tables, and graphs.

Function Machines 1 (Functions and Tables)
Geometric Sequences
Graphing Skills
Introduction to Functions
Pattern Flip (Patterns)

8B.3: Demonstrate how the change in one quantity affects the other in a functional relationship involving whole numbers and unit fractions.

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations

8B.4: Identify, describe, and compare situations with constant and varying rates of change using words, tables, and graphs (e.g., two quantities that vary together are the length of the side of a square and its area).

Compound Interest

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: Solve problems with whole numbers using order of operations, equality properties, and appropriate field properties.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
Number Line Frog Hop (Addition and Subtraction)
Order of Operations
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

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: Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Classifying Quadrilaterals

9A.2: Classify two- or three-dimensional shapes according to their properties (e.g., regular and irregular, concave and convex, types of quadrilaterals, pyramids, and prisms).

Classifying Quadrilaterals

9A.3: Investigate and describe the results of subdividing and combining shapes.

Area of Triangles

9A.6: Identify and justify rotational symmetry in two- and three-dimensional shapes.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

9A.8: Identify, sketch, and build two- and three-dimensional shapes given attribute clues.

Classifying Quadrilaterals

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

10A.1: Represent given data using double bar graphs, double line graphs, and stem and leaf plots with and without technology.

Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

10A.2: Select an appropriate graph format to display given data.

Distance-Time Graphs
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

10A.3: Read, interpret, infer, predict, draw conclusions, and evaluate data from any graph.

Graphing Skills

10A.4: Determine mean, median, mode, minimum value, maximum value, and range, and discuss what each does to help interpret a given set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
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.1: Design investigations to address a question and consider how data-collection methods affect the nature of a data set.

Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

10B.2: Propose and justify conclusions and predictions that are based on data, and design studies to further investigate the conclusions or predictions.

Box-and-Whisker Plots
Polling: Neighborhood
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.2: Assign a value of zero to probabilities that are impossible and a value of one to probabilities that are certain.

Geometric Probability
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

10C.3: Express simple probabilities as a fraction between zero and one.

Independent and Dependent Events
Theoretical and Experimental Probability

10C.4: Predict the probability of outcomes of simple experiments and test the predictions.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability