4.1: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

4.1.8 A: Number Sense

4.1.8 A.1: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well):

4.1.8 A.1.a: Rational numbers

Rational Numbers, Opposites, and Absolute Values

4.1.8 A.1.b: Percents

Percent of Change
Percents, Fractions, and Decimals

4.1.8 A.1.d: Roots

Operations with Radical Expressions
Square Roots

4.1.8 A.1.e: Absolute values

Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

4.1.8 A.3: Understand and use ratios, rates, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Geometric Probability
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram

4.1.8 A.4: Compare and order numbers of all named types.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

4.1.8 A.5: Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.

Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

4.1.8 A.7: Construct meanings for common irrational numbers, such as pi and the square root of 2.

Circumference and Area of Circles

4.1.8 B: Numerical Operations

4.1.8 B.1: Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with:

4.1.8 B.1.a: Pencil-and-paper

Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Multiplying with Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals

4.1.8 B.1.b: Mental math

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Estimating Sums and Differences
Multiplying Fractions
Multiplying Mixed Numbers
Percents, Fractions, and Decimals
Sums and Differences with Decimals

4.1.8 B.1.c: Calculator

Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Multiplying with Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals

4.1.8 B.3: Find square and cube roots of numbers and understand the inverse nature of powers and roots.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

4.1.8 B.4: Solve problems involving proportions and percents.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

4.1.8 B.5: Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

Order of Operations

4.1.8 C: Estimation

4.1.8 C.1: Estimate square and cube roots of numbers.

Square Roots

4.1.8 C.2: Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

Estimating Sums and Differences

4.2: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

4.2.8 A: Geometric Properties

4.2.8 A.1: Understand and apply concepts involving lines, angles, and planes.

4.2.8 A.1.a: Complementary and supplementary angles

Investigating Angle Theorems

4.2.8 A.1.b: Vertical angles

Investigating Angle Theorems
Triangle Angle Sum

4.2.8 A.1.c: Bisectors and perpendicular bisectors

Concurrent Lines, Medians, and Altitudes
Segment and Angle Bisectors
Slope

4.2.8 A.1.d: Parallel, perpendicular, and intersecting planes

Parallel, Intersecting, and Skew Lines

4.2.8 A.2: Understand and apply the Pythagorean theorem.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

4.2.8 A.3: Understand and apply properties of polygons.

4.2.8 A.3.a: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

Classifying Quadrilaterals
Parallelogram Conditions
Perimeter and Area of Rectangles
Special Parallelograms

4.2.8 A.3.c: Sum of measures of interior angles of a polygon

Polygon Angle Sum
Triangle Angle Sum

4.2.8 A.4: Understand and apply the concept of similarity.

4.2.8 A.4.a: Using proportions to find missing measures

Beam to Moon (Ratios and Proportions)
Proportions and Common Multipliers

4.2.8 A.4.b: Scale drawings

Perimeters and Areas of Similar Figures

4.2.8 A.6: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).

4.2.8 A.6.b: Midpoint of a line segment

Segment and Angle Bisectors

4.2.8 A.7: Create two-dimensional representations (e.g., nets or projective views) for the surfaces of three-dimensional objects.

3D and Orthographic Views
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

4.2.8 B: Transforming Shapes

4.2.8 B.1: Understand and apply transformations.

4.2.8 B.1.a: Finding the image, given the pre-image, and vice-versa

Dilations
Reflections
Rock Art (Transformations)

4.2.8 B.1.b: Sequence of transformations needed to map one figure onto another

Rock Art (Transformations)

4.2.8 B.1.c: Reflections, rotations, and translations result in images congruent to the pre-image

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

4.2.8 B.1.d: Dilations (stretching/shrinking) result in images similar to the pre-image

Dilations
Similar Figures

4.2.8 C: Coordinate Geometry

4.2.8 C.1: Use coordinates in four quadrants to represent geometric concepts.

City Tour (Coordinates)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

4.2.8 C.2: Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).

Absolute Value with Linear Functions
Circles
Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

4.2.8 D: Units of Measurement

4.2.8 D.1: Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4'3" plus 7'10" equals 12'1").

Unit Conversions

4.2.8 E: Measuring Geometric Objects

4.2.8 E.1: Develop and apply strategies for finding perimeter and area.

4.2.8 E.1.a: Geometric figures made by combining triangles, rectangles and circles or parts of circles

Area of Parallelograms
Area of Triangles

4.2.8 E.1.c: Impact of a dilation on the perimeter and area of a 2-dimensional figure

Dilations

4.2.8 E.2: Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).

Pyramids and Cones

4.2.8 E.3: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.

4.2.8 E.3.a: Volume - prism, cone, pyramid

Prisms and Cylinders
Pyramids and Cones

4.2.8 E.3.b: Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)

Surface and Lateral Areas of Prisms and Cylinders

4.3: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

4.3.8 A: Patterns

4.3.8 A.1: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.

4.3.8 A.1.a: Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences

4.3.8 A.1.c: Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns

4.3.8 A.1.d: Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)

Arithmetic and Geometric Sequences
Geometric Sequences

4.3.8 B: Functions and Relationships

4.3.8 B.1: Graph functions, and understand and describe their general behavior.

4.3.8 B.1.a: Equations involving two variables

Absolute Value with Linear Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

4.3.8 B.1.b: Rates of change (informal notion of slope)

Slope

4.3.8 B.2: Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.

Compound Interest

4.3.8 C: Modeling

4.3.8 C.1: Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

Translating and Scaling Functions

4.3.8 C.2: Use patterns, relations, symbolic algebra, and linear functions to model situations.

4.3.8 C.2.a: Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities

Compound Interest
Multiplying with Decimals
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

4.3.8 C.2.b: Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

Arithmetic Sequences
Compound Interest
Geometric Sequences

4.3.8 D: Procedures

4.3.8 D.1: Use graphing techniques on a number line.

4.3.8 D.1.a: Absolute value

Absolute Value Equations and Inequalities
Compound Inequalities
Rational Numbers, Opposites, and Absolute Values

4.3.8 D.2: Solve simple linear equations informally, graphically, and using formal algebraic methods.

4.3.8 D.2.a: Multi-step, integer coefficients only (although answers may not be integers)

Point-Slope Form of a Line
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

4.3.8 D.2.b: Simple literal equations (e.g., A = lw)

Area of Triangles

4.3.8 D.2.c: Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology

Solving Equations by Graphing Each Side
Solving Two-Step Equations

4.3.8 D.3: Solve simple linear inequalities.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

4.3.8 D.4: Create, evaluate, and simplify algebraic expressions involving variables.

4.3.8 D.4.a: Order of operations, including appropriate use of parentheses

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

4.3.8 D.4.b: Distributive property

Equivalent Algebraic Expressions II
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Equations

4.3.8 D.4.c: Substitution of a number for a variable

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

4.3.8 D.4.d: Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa

Solving Equations on the Number Line
Using Algebraic Equations

4.3.8 D.5: Understand and apply the properties of operations, numbers, equations, and inequalities.

4.3.8 D.5.a: Additive inverse

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Solving Algebraic Equations I

4.3.8 D.5.b: Multiplicative inverse

Solving Algebraic Equations I

4.3.8 D.5.c: Addition and multiplication properties of equality

Modeling One-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

4.4: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

4.4.8 A: Data Analysis

4.4.8 A.1: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).

4.4.8 A.1.a: Type of display most appropriate for given 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)
Stem-and-Leaf Plots

4.4.8 A.1.b: Box-and-whisker plot, upper quartile, lower quartile

Box-and-Whisker Plots

4.4.8 A.1.e: Finding the median and mean (weighted average) using frequency data.

Populations and Samples
Reaction Time 1 (Graphs and Statistics)

4.4.8 A.1.f: Effect of additional data on measures of central tendency

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

4.4.8 A.2: Make inferences and formulate and evaluate arguments based on displays and analysis of data sets.

Box-and-Whisker Plots
Polling: City
Real-Time Histogram

4.4.8 A.3: Estimate lines of best fit and use them to interpolate within the range of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

4.4.8 A.4: Use surveys and sampling techniques to generate data and draw conclusions about large groups.

Correlation
Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples

4.4.8 B: Probability

4.4.8 B.1: Interpret probabilities as ratios, percents, and decimals.

Estimating Population Size
Independent and Dependent Events

4.4.8 B.2: Determine probabilities of compound events.

Independent and Dependent Events
Theoretical and Experimental Probability

4.4.8 B.3: Explore the probabilities of conditional events (e.g., if there are seven marbles in a bag, three red and four green, what is the probability that two marbles picked from the bag, without replacement, are both red).

Independent and Dependent Events

4.4.8 B.5: Estimate probabilities and make predictions based on experimental and theoretical probabilities.

Independent and Dependent Events

4.4.8 B.6: Play and analyze probability-based games, and discuss the concepts of fairness and expected value.

Probability Simulations
Theoretical and Experimental Probability

4.4.8 C: Discrete Mathematics-Systematic Listing and Counting

4.4.8 C.1: Apply the multiplication principle of counting.

4.4.8 C.1.a: Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class)

Permutations and Combinations

4.4.8 C.1.b: Factorial notation

Permutations and Combinations

4.4.8 C.1.c: Concept of combinations (e.g., number of possible delegations of 3 out of 23 students)

Permutations and Combinations