8.N: Number Sense and Operations

8.N.1: Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents.

Comparing and Ordering Decimals
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Integers, Opposites, and Absolute Values
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Rational Numbers, Opposites, and Absolute Values
Sums and Differences with Decimals

8.N.2: Define, compare, order, and apply frequently used irrational numbers, such as Square root of 2 and pi.

Circumference and Area of Circles
Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.N.3: Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.

Household Energy Usage

8.N.4: Represent numbers in scientific notation, and use them in calculations and problem situations.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

8.N.6: Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

8.N.7: Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots.

Order of Operations

8.N.8: Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 = 1); and the notion o

Adding Fractions (Fraction Tiles)
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
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

8.N.9: Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2.

Solving Two-Step Equations
Square Roots

8.N.10: Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

8.P: Patterns, Relations, and Algebra

8.P.1: Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.

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

8.P.5: Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Elevator Operator (Line Graphs)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

8.P.6: Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b.

Solving Equations on the Number Line
Using Algebraic Equations

8.P.7: Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.

Absolute Value with Linear Functions
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
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.P.8: Explain and analyze-both quantitatively and qualitatively, using pictures, graphs, charts, or equations-how a change in one variable results in a change in another variable in functional relationships, e.g., C = pi d, A = pi r² (A as a function of r), A rectangle = lw (A rectangle as a function of l and w).

Absolute Value with Linear Functions
Introduction to Exponential Functions
Points, Lines, and Equations
Translating and Scaling Functions

8.P.9: Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.

Direct and Inverse Variation

8.P.10: Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.

Function Machines 1 (Functions and Tables)

8.G: Geometry

8.G.1: Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons.

Polygon Angle Sum
Triangle Angle Sum

8.G.3: Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.

Concurrent Lines, Medians, and Altitudes

8.G.4: Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.

Circles
Distance Formula
Investigating Angle Theorems
Isosceles and Equilateral Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

8.G.6: Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations.

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

8.G.8: Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.

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

8.M: Measurement

8.M.1: Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.

Unit Conversions

8.M.2: Given the formulas, convert from one system of measurement to another. Use technology as appropriate.

Unit Conversions

8.M.3: Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders

8.M.4: Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.

Beam to Moon (Ratios and Proportions)
Dilations
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Perimeters and Areas of Similar Figures
Proportions and Common Multipliers
Similar Figures

8.M.5: Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density.

Household Energy Usage

8.D: Data Analysis, Statistics, and Probability

8.D.1: Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling.

Polling: City
Polling: Neighborhood
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

8.D.2: Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts. Differentiate between continuous and discrete data and ways to represent them.

Box-and-Whisker Plots
Compound Inequalities
Correlation
Graphing Skills
Histograms
Least-Squares Best Fit Lines
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

8.D.3: Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets 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

8.D.4: Use tree diagrams, tables, organized lists, basic combinatorics ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.

Permutations and Combinations