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.A: Number Sense

4.1.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.A.1.b: Percents

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

4.1.A.1.d: Roots

Operations with Radical Expressions

4.1.A.1.e: Absolute values

Comparing and Ordering Integers
Real Number Line - Activity A

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

Beam to Moon (Ratios and Proportions)
Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Part:Part and Part:Whole Ratios
Percents and Proportions
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Probability Simulations
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons
Theoretical and Experimental Probability

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

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

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

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals

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

Square Roots

4.1.B: Numerical Operations

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

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

4.1.B.1.b: Mental math

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

4.1.B.1.c: Calculator

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

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

Square Roots

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

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Percents and Proportions
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons

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

Order of Operations

4.1.C: Estimation

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

Square Roots

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

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals

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.A: Geometric Properties

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

4.2.A.1.a: Complementary and supplementary angles

Investigating Angle Theorems - Activity A

4.2.A.1.b: Vertical angles

Investigating Angle Theorems - Activity A

4.2.A.1.c: Bisectors and perpendicular bisectors

Concurrent Lines, Medians, and Altitudes

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

Investigating Parallel Lines and Planes

4.2.A.1.e: Intersection of plane with cube, cylinder, cone, and sphere

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

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

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

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

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

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity A
Parallelogram Conditions
Special Quadrilaterals

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

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

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

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

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Proportions and Common Multipliers

4.2.A.4.c: Models of 3D objects

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.A.5: Use logic and reasoning to make and support conjectures about geometric objects.

Biconditional Statement
Conditional Statement

4.2.B: Transforming Shapes

4.2.B.1: Understand and apply transformations.

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

Dilations
Reflections
Rotations, Reflections and Translations

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

Dilations
Reflections
Rotations, Reflections and Translations

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

Reflections
Rotations, Reflections and Translations
Translations

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

Dilations

4.2.B.2: Use iterative procedures to generate geometric patterns.

4.2.B.2.c: Construction of initial stages

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

4.2.B.2.d: Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski’s Triangle)

Finding Patterns

4.2.C: Coordinate Geometry

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

Points in the Coordinate Plane - Activity A

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

Dilations
Parabolas - Activity A
Rotations, Reflections and Translations
Translations

4.2.D: Units of Measurement

4.2.D.3: Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements.

Triple Beam Balance

4.2.D.4: Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.

Triple Beam Balance

4.2.D.6: Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).

Density Experiment: Slice and Dice
Density Laboratory
Determining Density via Water Displacement
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

4.2.E: Measuring Geometric Objects

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

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

Special Quadrilaterals

4.2.E.1.b: Estimation of area using grids of various sizes

Area of Parallelograms - Activity A
Rectangle: Perimeter and Area

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

Dilations
Perimeter, Circumference, and Area - Activity B

4.2.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).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

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

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

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

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

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.E.3.c: Impact of a dilation on the surface area and volume of a three-dimensional figure

Dilations

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.A: Patterns

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

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

4.3.A.1.b: Finite and infinite sequences

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

4.3.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

4.3.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.A.1.e: Generating sequences by using calculators to repeatedly apply a formula

Arithmetic Sequences
Geometric Sequences

4.3.B: Functions and Relationships

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

4.3.B.1.a: Equations involving two variables

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

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

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope - Activity B

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

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

4.3.C: Modeling

4.3.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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A

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

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

Using Algebraic Equations

4.3.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
Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Geometric Sequences
Half-life
Simple and Compound Interest

4.3.D: Procedures

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

4.3.D.1.a: Absolute value

Inequalities Involving Absolute Values
Quadratic and Absolute Value Functions
Real Number Line - Activity A

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

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

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

4.3.D.3: Solve simple linear inequalities.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

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

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

Order of Operations

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

Using Algebraic Equations
Using Algebraic Expressions

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

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

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
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.A: Data Analysis

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

4.4.A.1.a: Type of display most appropriate for given data

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

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

Box-and-Whisker Plots

4.4.A.1.c: Scatter plot

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

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

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

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

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

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

Describing Data Using Statistics

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

Populations and Samples

4.4.B: Probability

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

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Probability Simulations
Theoretical and Experimental Probability

4.4.B.2: Determine probabilities of compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

4.4.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).

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

4.4.B.4: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.

4.4.B.4.a: Frequency, relative frequency

Populations and Samples

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

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

4.4.C: Discrete Mathematics-Systematic Listing and Counting

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

4.4.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
Permutations and Combinations

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

Permutations and Combinations