Scope and Sequence Standards highlighted in green ... › a1d2 › 07 › 23 › 19 › 144549-fa87fa... · (8.EE.A.1) • Scientific Notation Lesson 1: Exponential Notation Lesson

Collierville Schools Eighth Grade Math Scope and Sequence

Standards highlighted in green represent the major content of the grade level. Unlighted standards represent supporting content standards of the grade level.

1st Quarter

Module 1: Integer Exponents and Scientific Notation

Standards Learning Targets New or Recently Introduced Terms Familiar Terms and Symbols

8.EE.A.1 Know and apply the properties of integer exponents to

Topic A: Exponential Notation and Properties of Integer Exponents

• Order of Magnitude • Base, Exponent, Power • Equivalent Fractions

• Expanded Form (of decimal

numbers) • Exponential Notation

• Integer

• Square and Cube (of a

number) • Whole Number

generate equivalent numerical expressions.

(8.EE.A.1) • Scientific Notation

Lesson 1: Exponential Notation

Lesson 2: Multiplication of Numbers

8.EE.A.3 Use numbers expressed in Exponential Form in the form of a single digit times and integer power of 10 to Lesson 3: Numbers in Exponential estimate very large or very small Form Raised to a Power quantities and to express how many times one is larger than the Lesson 4: Numbers Raised to the other. Zeroth Power

Lesson 5: Negative Exponents and

the Laws of Exponents 8.EE.A.4 Perform operations with numbers expressed in scientific notation, including

Lesson 6: Proofs of Laws of Exponents (optional)

problems where both decimal and scientific notation are used.

Topic B: Magnitude and Scientific

Use scientific notation and Notation (8.EE.A.3, 8.EE.A.4) choose units of appropriate size for measurement of very large or Lesson 7: Magnitude



very small quantities (e.g. use



millimeters per year for seafloor Lesson 8: Estimating Quantities spreading). Interpret scientific notation that has been generated Lesson 9: Scientific Notation by technology.

Lesson 10: Operations with Numbers in Scientific Notation

Lesson 11: Efficacy of Scientific Notation (optional)

Lesson 12: Choice of Unit

Lesson 13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology

Module 2: The Concept of Congruence


8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations:

Topic A: Definitions and Properties of the Basic Rigid Motions (8.G.A.1) (8.GA.2)

• Angle Preserving re

• Basic Rigid Motion

• Area and perimeter

• Parallel and perpendicular lines

• Ray, line, segment, angle

• Supplementary,

complementary, vertical, and adjacent angles

a. Lines are taken to lines, and line segments of line segments of

Lesson 1: Why Move Things Around? • Between

the same length. Lesson 2: Definition of Translation • Congruence and Three Basic Properties

• Congruent Lesson 3: Translating Lines



b. Angles are taken to angles of the same measure

c. Parallel lines are taken to parallel lines.

8.G.A.2 Describe the effect of dilations, translations, rotations, and reflections on two- dimensional figures using coordinates.

8.G.B.3 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

8G.B.4 Explain a proof of the Pythagorean Theorem and its converse.

Lesson 4: Definition of Reflection and Basic Properties

Lesson 5: Definition of Rotation and Basic Properties

Lesson 6: Rotations of 180 Degrees

Topic B: Sequencing the Basic Rigid Motions Not a TN Standard

Topic C: Congruence and Angle Relationships (8.G.B.3)

Lesson 11: Definition of Congruence and Some Basic Properties

Lesson 12: Angles Associated with Parallel Lines

• Directed Line Segment

• Distance Preserving

• Exterior Angle

• Reflection (description)

• Rotation (description)

• Sequence(Composition) of Transformations

• Transformation

• Translation (description)

• Transversal

• Vector

• Triangle, quadrilateral



8.G.B.5 Apply the Pythagorean Lesson 13: Angle Sum of a Triangle theorem to determine the unknown side lengths in right Lesson 14: More on the Angles of a triangles in real-world and Triangle mathematical problems in two and three dimensions.

(Optional) Topic D: The Pythagorean Theorem (8.G.B.4, 8.G.B.5)

Lesson 15: Informal Proof of the Pythagorean Theorem

Lesson 16: Applications of the Pythagorean Theorem



Module 3: Similarity


8.G.A.2 Describe the effect of dilations, translations, rotations,

Topic A: Dilation (8.G.A.2) • Dilation

and reflections on two- dimensional figures using

Lesson 1: What Lies Behind "Same Shape"? • Scale Drawing

coordinates. Lesson 2: Properties of Dilations • Similar

Lesson 3: Examples of Dilations • Similarity Transformation

Lesson 4: Fundamental Theorem of Similarity (FTS) (optional) Lesson 5: First Consequences of FTS

Lesson 6: Dilations on a Coordinate • Angle –Preserving

Plane • Scale Drawing

8.G.A.3 Use informal arguments Lesson 7: Informal Proofs of

to establish facts about the angle Properties of Dilations (optional) sum and exterior angle of triangles, about the angles created when parallel lines are Topic B: Similar Figures (8.G.A.4, cut by a transversal, and the 8.G.A.5) angle-angle criterion for Lesson 8: Similarity similarity of triangles. 8.G.B.4 Explain a proof of the Pythagorean Theorem and its



converse.



Module 3: Similarity


8.G.A.2 Describe the effect of dilations, translations, rotations, and reflections on two- dimensional figures using coordinates. 8.G.A.3 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. 8.G.B.4 Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.5 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Topic B: Similar Figures (8.G.A.2, 8.G.A.3) Lesson 9: Basic Properties of

Similarity Lesson 10: Informal Proof of AA Criterion for Similarity Lesson 11: More About Similar Triangles (optional)

Lesson 12: Modeling Using Similarity (optional)

Topic C: The Pythagorean Theorem (8.G.B.4, 8.G.B.5)

Lesson 13: Proof of the Pythagorean Theorem

Lesson 14: The Converse of the Pythagorean Theorem

• Dilation

• Scale Drawing

• Similar

• Similarity Transformation

• Angle –Preserving

2nd Quarter







Module 4: Linear Equations

Standards Learning Targets New of Recently Introduced Terms Familiar Terms and Symbols

8. EE.C.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Topic A: Writing and Solving Linear Equations (8.EE.C.7)

Lesson 1: Writing Equations Using Symbols (optional) Lesson 2: Linear and Nonlinear Expressions in x (optional)

Lesson 3: Linear Equations in x

Lesson 4: Solving a Linear Equation

Lesson 5: Writing and Solving Linear Equations (optional)

Lesson 6: Solutions of Linear Equations

Lesson 7: Classification of Solutions

Lesson 8: Linear Equations in Disguise (optional)

Lesson 9: An Application of Linear Equations (optional)

• Average Speed

• Constant Speed

• Horizontal Line

• Linear Equation (description)

• Point-Slope Equation of a

Line

• Slope of a Line in a Cartesian Plane

• Slope- Intercept Equation

of a Line

• Slope of a System of Linear Equations (description)

• Standard Form of a Linear

Equation

• System of Linear Equations

• Vertical Line test

• X- intercept

• Coefficient

• Equation

• Like terms

• Linear Expression

• Solution

• Term

• Unit rate

• Variable



Topic B: Linear Equations in Two Variables and Their Graphs (8.EE.B.5)

Lesson 10: A Critical Look at Proportional Relationships

Lesson 11: Constant Rate

Lesson 12: Linear Equations in Two Variables (optional) Lesson 13: The Graph of a Linear Equation in Two Variables (optional)

Lesson 14: The Graph of a Linear Equation - Horizontal and Vertical


• X- intercept

• Y-intercept





Module 4 Continued: Linear Equations


8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two district points on a non-vertical line in the coordinate plane; know and derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8. EE.C.8 Analyze and solve systems of two linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear

Topic C: Slope and Equations of Lines (8.EE.B.5, 8.EE.B.6)

Lesson 15: The Slope of a Non- Vertical Line

Lesson 16: The Computation of the Slope of a Non-Vertical Line

Lesson 17: The line Joining Two Distinct Points of the graph y = mx +b

Lesson 18: There is Only One Line Passing Through a Given Point (optional)

Lesson 19: The Graph of a Linear Equation in Two Variables is a Line (optional)

Lesson 20: Every Line is a Graph of a Linear Equation (optional)

Lesson 21: Some Facts About Graphs of a Linear Equation (optional)

Lesson 22: Constant Rates Revisited

• Average Speed

• Constant Speed

• Horizontal Line

• Linear Equation (description)

• Point-Slope Equation of a

Line

• Slope of a Line in a Cartesian Plane

• Slope- Intercept Equation

of a Line

• Slope of a System of Linear Equations (description)

• Standard Form of a Linear

Equation

• System of Linear Equations

• Coefficient

• Equation

• Like terms

• Linear Expression

• Solution

• Term

• Unit rate

• Variable



equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y= 5 and 3x +2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

8.G.B.5 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in the real-world and mathematical problems in two and three dimensions.

Lesson 23: The Defining Equation of a Line (optional)

Topic D: System of Linear Equations and Their Solutions (8.EE.B.5, 8.EE.C.8)

Lesson 24: Introduction to Simultaneous Equations

Lesson 25: Geometric Interpretation of the Solutions of a Linear System

Lesson 26: Characterization of Parallel Lines

Lesson 27: Nature of Solutions of System of Linear Equations

Lesson 28: Another Computational Method of Solving a Linear System

Lesson 29: Word Problems

Lesson 30: Conversion Between Celsius and Fahrenheit (optional)

Topic E: Pythagorean Theorem (8.G.B.5, 8.EE.C.8)

Lesson 31: System of Equations

(optional) Pythagorean Triples


• X- intercept

• Y-intercept



3rd Quarter

Module 5: Examples of Functions from Geometry


8.F.A.1 Understand that a Topic A: Functions

• Cone

• Cylinder

• Equation Form of a Linear

Function

• Function

• Graph of a Linear Function

• Lateral Edge of a Prism

• Lateral Edge and Face of a

Pyramid

• Linear Function

• Solid Sphere or Ball

• Sphere

function is a rule that assigns to (8.F.A.1, 8.F.A.2, 8.F.A.3) each input exactly one output. The graph of a function is the set Lesson 1:The Concept of a Function of ordered pairs consisting of an input and the corresponding Lesson 2: Formal Definition of a output. (Function is not required in 8th grade.)

Function

8.F.A.2 Compare properties of

Lesson 3: Linear Functions and Proportionality • Area

two functions each represented in a different way (algebraically,

Lesson 4: More Examples of • Linear equation

graphically, numerically in tables, or by verbal descriptions).

Functions • Nonlinear equation

For example, given a linear function represented by a table of

Lesson 5: Graphs of Functions and Equations • Rate of change

values and another linear function represented by an

Lesson 6: Graphs of Linear Functions • Solids

algebraic expression, determine which function has the greater

and Rate of Change • Volume

rate of change. Lesson 7: Comparing Linear Functions and Graphs 8.F.A.3 Know and interpret the equation y = mx + b as defining a Lesson 8: Graphs of Simple linear function, whose graph is a Nonlinear Functions straight line; give examples of functions that are not linear. For example, the function A=s2

Topic B: Volume (8.G.C.7)

giving the area of a square as a Lesson 9: Examples of Functions



function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.G.C.7 Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.

from Geometry Lesson 10: Volumes of Familiar Solids-Cones and Cylinders

Lesson 11: Volume of a Sphere



Module 6 : Linear Functions


8.F.B.4 Construct a function to Topic A: Linear Functions

• Association

• Bivariate Data Set

• Column Relative Frequency

• Row Relative Frequency

• Scatter Plot

• Two –Way Frequency

Table

• Variable

model a linear relationship (8.F.B.4, 8.F.B.5) between two quantities. Determine the rate of change Lesson 1: Modeling Linear and initial value of the function Relationships from a description of a relationship or from two (x, y) Lesson 2: Interpreting Rate of values, including reading these from a table or from a graph.

Change and Initial Value • Categorical variable

Interpret the rate of change Lesson 3: Representations of a Line and initial value of a linear • Intercept or Initial value function in terms of the Lesson 4: Increasing and Decreasing situation it models and in terms of its graph or a table of values.

Functions • Numerical variable

8.F.B.5Describe qualitatively

Lesson 5: Increasing and Decreasing Functions

• Scatter plot

the functional relationship between two quantities by

Topic B: Bivariate Numerical Data

• Slope

analyzing a graph (e.g., where (8.SP.A.1, 8.SP.A.2) the function is increasing or decreasing, linear or Lesson 6: Scatter Plots nonlinear). Sketch a graph that exhibits the qualitative features Lesson 7: Patterns in Scatter Plots of a function that has been described verbally. Lesson 8: Informally Fitting a Line



8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and informally assess the model fit by judging the closeness of the data points to the line.

8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

Lesson 9: Determining the Equation of a Line Fit to Data

Topic C: Linear and Nonlinear Models (8.SP.A.1, 8.SP.A.2, 8.SP.A.3)

Lesson 10: Linear Models

Lesson 11: using Linear Models in a Data Context

Lesson 12: Nonlinear Models in a Data Context (optional)

Topic D: Bivariate Categorical Data

Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table

Lesson 14: Association Between Categorical Variables



8.SP.B.4 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

Compound Events (8.SP.B.4): Compound Events are not addressed in the 8th Grade Eureka Curriculum.

Please refer to Grade 7 Module 5 Lesson 6-7.

Module 7: Introduction to Irrational Numbers to Using Geometry


8.NS.A.1 Know that numbers that are not rational are called

Topic A: Square and Cube Roots (8.NS.A.1, 8.NS.A.2, 8.EE.A.2) • Cube Root • Decimal Expansion

irrational. Understand informally that every number has a decimal

Lesson 1: The Pythagorean Theorem • Decimal Expansion • Finite Decimals

expansion; for rational numbers show that the decimal expansion

Lesson 2: Square Roots • Decimal Expansion of a • Number Line

repeats eventually or terminates,



and covert a decimal expansion which repeats eventually or terminates into a rational number.

8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers locating them approximately on a number line diagram. Estimate the value of irrational expressions such as π2. For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1.4 and 1.5, and explain how to continue on to get better approximations.

8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

8.G.B.4 Explain a proof of the Pythagorean Theorem and its converse.

Lesson 3: Existence and Uniqueness of Square Roots and Cube Roots (optional)

Lesson 4: Simplifying Square Roots (optional)

Lesson 5: Solving Equations and Radicals

Topic B: Decimal Expansions of Numbers (8.NS.A.1, 8.NS.A.2, 8.EE.A.2)

Lesson 6: Finite and Infinite Decimals

Lesson 7: Infinite Decimals

Lesson 8: The Long Division Algorithm

Lesson 9: Decimal Expansions of Fractions, Part1

Lesson 10: Converting Repeating Decimals to Fractions

Lesson 11: The Decimal Expansions of Some Irrational Numbers

Lesson 12: Decimal Expansions of fractions, Part 2 (optional)

Negative Number

• Decimal Expansion of a

Positive Real Number

• Decimal System

• Irrational Number

• The nth Decimal Digit of a

Decimal Expansion

• The nth Finite Decimal of a

Decimal Expansion

• Perfect Square

• Rational Approximation

• Real Number

• A Square Root of a

Number

• The Square Root of a

Number

• Rate of Change

• Rational Number

• Volume



8.G.B.5 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.B.6 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Lesson13: Comparing Irrational Numbers

Lesson 14: Decimal Expansion of π

Topic C: The Pythagorean Theorem (8.G.B.4, 8.G.B.5, 8.G.B.6)

Lesson 15: Pythagorean Theorem, Revisited

Lesson 16: Converse of the Pythagorean Theorem

Lesson 17: Distance on the Coordinate Plane

• Truncated Cone



4th Quarter

8.G.B.5 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.C.7 Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.

Lesson 18: Applications of the Pythagorean Theorem

Topic D: Application of Radicals and Roots (8.G.B.5, 8.G.C.7)

Lesson 19: Cones and Spheres

Lesson 20: Truncated Cones

Lesson 21: Volume of Composite Solids

• Truncated Cone

Documents

Scope and Sequence Standards highlighted in green ... › a1d2 › 07 › 23 › 19 › 144549-fa87fa... · (8.EE.A.1) • Scientific Notation Lesson 1: Exponential Notation Lesson