6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

6.A: Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.

6.A.3: Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms.

Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

6.B: Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.

6.B.3a: Solve practical computation problems involving whole numbers, integers and rational numbers.

Adding on the Number Line
Cargo Captain (Multi-digit Subtraction)
Dividing Mixed Numbers
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

6.B.3b: Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems.

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

6.B.3c: Identify and apply properties of real numbers including pi, squares, and square roots.

Square Roots

6.C: Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.

6.C.3a: Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.

Beam to Moon (Ratios and Proportions)
Comparing and Ordering Decimals
Direct and Inverse Variation
Estimating Population Size
Estimating Sums and Differences
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Geometric Probability
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Sums and Differences with Decimals
Time Estimation
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

6.C.3b: Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Toy Factory (Set Models of Fractions)

6.D: Solve problems using comparison of quantities, ratios, proportions and percents.

6.D.3: Apply ratios and proportions to solve practical problems.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

7.A: Measure and compare quantities using appropriate units, instruments and methods.

7.A.3a: Measure length, capacity, weight/mass and angles using sophisticated instruments (e.g., compass, protractor, trundle wheel).

Beam to Moon (Ratios and Proportions)
Measuring Trees

7.A.3b: Apply the concepts and attributes of length, capacity, weight/mass, perimeter, area, volume, time, temperature and angle measures in practical situations.

Area of Parallelograms
Beam to Moon (Ratios and Proportions)
Fido's Flower Bed (Perimeter and Area)
Measuring Trees
Perimeter and Area of Rectangles
Prisms and Cylinders
Similar Figures

7.C: Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.

7.C.3b: Use concrete and graphic models and appropriate formulas to find perimeters, areas, surface areas and volumes of two- and three-dimensional regions.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

8.A: Describe numerical relationships using variables and patterns.

8.A.3a: Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.

Chocomatic (Multiplication, Arrays, and Area)
Order of Operations
Solving Two-Step Equations
Square Roots
Using Algebraic Equations

8.A.3b: Solve problems using linear expressions, equations and inequalities.

Absolute Value with Linear Functions
Compound Inequalities
Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Multiplying Exponential Expressions
Operations with Radical Expressions
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

8.B: Interpret and describe numerical relationships using tables, graphs and symbols.

8.B.3: Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.

Arithmetic and Geometric Sequences

8.D: Use algebraic concepts and procedures to represent and solve problems.

8.D.3a: Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities.

Circles
Compound Interest
Linear Inequalities in Two Variables
Solving Equations on the Number Line

8.D.3b: Propose and solve problems using proportions, formulas and linear functions.

Absolute Value with Linear Functions
Arithmetic Sequences
Beam to Moon (Ratios and Proportions)
Compound Interest
Direct and Inverse Variation
Estimating Population Size
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Probability
Linear Functions
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Slope-Intercept Form of a Line

8.D.3c: Apply properties of powers, perfect squares and square roots.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.A: Demonstrate and apply geometric concepts involving points, lines, planes and space.

9.A.3a: Draw or construct two- and three- dimensional geometric figures including prisms, pyramids, cylinders and cones.

Segment and Angle Bisectors
Surface and Lateral Areas of Pyramids and Cones

9.A.3b: Draw transformation images of figures, with and without the use of technology.

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

9.A.3c: Use concepts of symmetry, congruency, similarity, scale, perspective, and angles to describe and analyze two- and three-dimensional shapes found in practical applications (e.g., geodesic domes, A-frame houses, basketball courts, inclined planes, art forms, blueprints).

Circles

9.B: Identify, describe, classify and compare relationships using points, lines, planes and solids.

9.B.3: Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Similar Figures
Special Parallelograms

9.D: Use trigonometric ratios and circular functions to solve problems.

9.D.3: Compute distances, lengths and measures of angles using proportions, the Pythagorean theorem and its converse.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Road Trip (Problem Solving)

10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

10.A: Organize, describe and make predictions from existing data.

10.A.3a: Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data.

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

10.A.3b: Compare the mean, median, mode and range, with and without the use of technology.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

10.A.3c: Test the reasonableness of an argument based on data and communicate their findings.

Box-and-Whisker Plots

10.B: Formulate questions, design data collection methods, gather and analyze data and communicate findings.

10.B.3: Formulate questions (e.g., relationships between car age and mileage, average incomes and years of schooling), devise and conduct experiments or simulations, gather data, draw conclusions and communicate results to an audience using traditional methods and contemporary technologies.

Box-and-Whisker Plots
Conditional Statements
Correlation
Describing Data Using Statistics
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots
Time Estimation