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: Represent any large number using scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

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 using exponents.

Finding Factors with Area Models

6B.3: Classify numbers according to the number of whole number factors (e.g., square numbers have an odd number of factors).

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

6B.4: Demonstrate and describe the effects of multiplying or dividing by a fraction less than or greater than one.

Dividing Fractions
Dividing Mixed Numbers

6B.5: Simplify arithmetic expressions containing exponents using the field properties and the order of operations.

Order of Operations

6B.6: Justify rules of divisibility for 2, 5, and 10.

Factor Trees (Factoring Numbers)

6B.7: Solve multi-step number sentences and word problems with rational numbers using the four basic operations.

Dividing Mixed Numbers
Estimating Population Size
Improper Fractions and Mixed Numbers
Multiplying Decimals (Area Model)
Multiplying Mixed Numbers
Multiplying with 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.1: Select, use, and justify appropriate operations, methods, and tools to compute or estimate with integers and familiar rational numbers.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

6C.3: Analyze algorithms for computing with rational numbers and develop fluency in their use.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

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

6D.1: Work flexibly with fractions, decimals, and percents to solve number sentences and word problems (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5 x 10).

Multiplying Decimals (Area Model)
Multiplying with Decimals
Percent of Change
Percents and Proportions
Proportions and Common Multipliers
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

6D.2: Create and explain ratios and proportions that represent quantitative relationships.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers
Road Trip (Problem Solving)

6D.3: Create and explain a variety of equivalent ratios to represent a given situation.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

6D.4: Develop, use, analyze, and explain methods for solving numeric or word problems involving proportions.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

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

7A.2: Make simple measurements to determine indirect measures (e.g., determining the height of a flagpole using its shadow and similar right triangles).

Estimating Population Size

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

7B.1: Estimate angle measure, area, and volume using reasonable units and with acceptable levels of accuracy.

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 and use appropriate units and tools to measure volume, surface area, and mass/weight accurately for a given situation.

Balancing Blocks (Volume)
Beam to Moon (Ratios and Proportions)
Surface and Lateral Areas of Prisms and Cylinders

7C.2: Select an appropriate formula to determine the circumference and the area of circles.

Circumference and Area of Circles

7C.3: Select and explain an appropriate formula or strategy to find the surface area and volume of rectangular and triangular pyramids, cylinders and cones.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

7C.4: Solve simple problems involving rate, time, and distance.

Household Energy Usage
Road Trip (Problem Solving)

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

8A.1: Investigate, describe, and generalize a variety of patterns using variable or recursive techniques.

Arithmetic Sequences
Geometric Sequences

8A.2: Represent situations using variables.

Solving Algebraic Equations I

8A.3: Recognize and generate equivalent forms of simple algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
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.2: Graph two inequalities with a single variable, including the intersection or union of these 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

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 arithmetic and linear equations using the properties of equality and inequality.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

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.2: Solve simple problems involving quadratic relationships using technology for graphing.

Quadratics in Factored Form
Quadratics in Polynomial Form

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.3: Examine and describe line or rotational symmetry of objects in terms of transformations.

Holiday Snowflake Designer
Rock Art (Transformations)

9A.4: Draw transformations of figures in a plane to match specified criteria.

Circles
Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

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: Describe, classify, and justify relationships among types of two- and three-dimensional objects using their defining properties.

Classifying Quadrilaterals

9B.3: Classify and order quadrilaterals according to their properties.

Classifying Quadrilaterals

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

9C.2: Justify the area formulas for triangles, parallelograms, and trapezoids based on the formula for the area of a rectangle.

Area of Triangles
Perimeter and Area of Rectangles

9C.3: Make and test conjectures about the relationships between side length and angle measure in various triangles and quadrilaterals.

Classifying Quadrilaterals

9C.4: Justify the properties of angles formed by parallel lines cut by a transversal using appropriate terminology.

Triangle Angle Sum

9D: Students who meet the standard can use trigonometric ratios and circular functions to solve problems.

9D.2: Solve problems that involve the use of proportions and the Pythagorean theorem in similar right triangles with whole number side lengths.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

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 box and whiskers plots.

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

10A.2: Find, use, and interpret measures of center and spread, including interquartile range.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

10A.3: Construct an equivalent data representation given data in a different form.

Box-and-Whisker Plots
Correlation
Graphing Skills
Movie Reviewer (Mean and Median)
Polling: City
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
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: Select and use appropriate data gathering techniques.

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.2: Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability.

Geometric Probability
Independent and Dependent Events
Spin the Big Wheel! (Probability)

10C.3: Compute probabilities for simple compound events using methods such as organized lists and tree diagrams.

Permutations and Combinations