Core Curriculum Content Standards

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.

4.1.8 C: Estimation

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

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

Estimating Sums and Differences

4.2.8 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

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

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

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

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").

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

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).

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

4.3.8 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)

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

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)

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

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

Modeling One-Step Equations

Solving Algebraic Equations II

Solving Two-Step Equations

4.4.8 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

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)

4.4.8 C.1.b: Factorial notation

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

Correlation last revised: 3/1/2018

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