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
 Constructing Parallel and Perpendicular Lines
 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.a: Congruent angles or line segments

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines

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

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.