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Math / G8 / M1 / TA / lesson 1

Exponential Notation

1 hour
Students know the reason for some bases requiring parentheses.
Math / G8 / M1 / TA / lesson 2

Multiplication of Numbers in Exponential Form

1 hour
Students write equivalent numerical and symbolic expressions using the first law of exponents.
Math / G8 / M1 / TA / lesson 3

Numbers in Exponential Form Raised to a Power

1 hour
Students write simplified, equivalent numeric, and symbolic expressions using this new knowledge of powers.
Math / G8 / M1 / TA / lesson 4

Applying Properties of Exponents to Generate Equivalent Expressions

1 hour
Students know that a number raised to the zeroth power is equal to one.
Math / G8 / M1 / TA / lesson 5

Negative Exponents and the Laws of Exponents

1 hour
Students know the definition of a number raised to a negative exponent.
Math / G8 / M1 / TA / lesson 6

Proofs of Laws of Exponents

1 hour
Students extend the previous laws of exponents to include all integer exponents.
Math / G8 / M1 / TB / lesson 7

Magnitude

1 hour
Students know the exponent of an expression provides information about the magnitude of a number.
Math / G8 / M1 / TB / lesson 8

Estimating Quantities

1 hour
Students use their knowledge of ratios, fractions, and laws of exponents to simplify expressions.
Math / G8 / M1 / TB / lesson 9

Scientific Notation

1 hour
In this lesson we learn how to write the number exactly, using scientific notation.
Math / G8 / M1 / TB / lesson 10

Operations with Numbers in Scientific Notation

1 hour
Practicing operations with numbers in scientific notation and standard notation.
Math / G8 / M1 / TB / lesson 11

Efficacy of Scientific Notation

1 hour
Students read, write, and perform operations on numbers expressed in scientific notation.
Math / G8 / M1 / TB / lesson 12

Choice of Unit

1 hour
Students determine appropriate units for various measurements and rewrite measurements based on new units.
Math / G8 / M1 / TB / lesson 13

Comparing and Interpreting Scientific Notation Using Technology

1 hour
Students compare numbers expressed in scientific notation.
Math / G8 / M2 / TA / lesson 1

Why Move Things Around?

1 hour
Students are introduced to vocabulary and notation related to rigid motions (e.g., transformation, image, map).
Math / G8 / M2 / TA / lesson 2

Definition of Translation and Three Basic Properties

1 hour
Students learn that translations preserve lengths of segments and degrees of angles.
Math / G8 / M2 / TA / lesson 3

Translating Lines

1 hour
Students learn that translations map parallel lines to parallel lines.
Math / G8 / M2 / TA / lesson 4

Definition of Reflection and Basic Properties

1 hour
Students know the definition of reflection and perform reflections across a line using a transparency.
Math / G8 / M2 / TA / lesson 5

Definition of Rotation and Basic Properties

1 hour
Students know how to rotate a figure a given degree around a given center.
Math / G8 / M2 / TA / lesson 6

Rotations of 180 Degrees

1 hour
Learning rotation of 180 degrees moves a point on the coordinate plane (a,b) to (-a,-b).
Math / G8 / M2 / TB / lesson 7

Sequencing Translations

1 hour
Students learn about the sequence of transformations (one move on the plane followed by another).
Math / G8 / M2 / TB / lesson 8

Sequencing Reflections and Translations

1 hour
Students learn that the reflection is its own inverse transformation.
Math / G8 / M2 / TB / lesson 9

Sequencing Rotations

1 hour
Sequences of rotations preserve lengths of segments as well as degrees of measures of angles.
Math / G8 / M2 / TB / lesson 10

Sequences of Rigid Motions

1 hour
Students describe a sequence of rigid motions that maps one figure onto another.
Math / G8 / M2 / TC / lesson 11

Definition of Congruence and Some Basic Properties

1 hour
Basic properties of congruence are similar to properties for all rigid motions (translations, rotations, reflections).
Math / G8 / M2 / TC / lesson 12

Angles Associated with Parallel Lines

1 hour
Presenting arguments to conclude about angles formed when parallel lines are cut by a transversal.
Math / G8 / M2 / TC / lesson 13

Angle Sum of a Triangle

1 hour
Students present informal arguments to draw conclusions about the angle sum of a triangle.
Math / G8 / M2 / TC / lesson 14

More on the Angles of a Triangle

1 hour
Students know a third informal proof of the angle sum theorem.
Math / G8 / M2 / TD / lesson 15

Informal Proof of the Pythagorean Theorem

1 hour
Introduction to the Pythagorean theorem and showing an informal proof of the theorem.
Math / G8 / M2 / TD / lesson 16

Applications of the Pythagorean Theorem

1 hour
Students use the Pythagorean theorem to determine missing side lengths of right triangles.
Math / G8 / M3 / TA / lesson 1

“What Lies Behind Same Shape”?

1 hour
Students know that dilations magnify and shrink figures.
Math / G8 / M3 / TA / lesson 2

Properties of Dilations

1 hour
Students learn how to use a compass and a ruler to perform dilations.
Math / G8 / M3 / TA / lesson 3

Examples of Dilations

1 hour
Students know that dilations map circles to circles and ellipses to ellipses.
Math / G8 / M3 / TA / lesson 4

Fundamental Theorem of Similarity (FTS)

1 hour
Students experimentally verify the properties related to the fundamental theorem of similarity (FTS).
Math / G8 / M3 / TA / lesson 5

First Consequences of FTS

1 hour
Students verify the converse of the fundamental theorem of similarity experimentally.
Math / G8 / M3 / TA / lesson 6

Dilations on the Coordinate Plane

1 hour
Students describe the effect of dilations on two-dimensional figures using coordinates.
Math / G8 / M3 / TA / lesson 7

Informal Proofs of Properties of Dilations

1 hour
Students know an informal proof of why dilations are angle-preserving transformations.
Math / G8 / M3 / TB / lesson 8

Similarity

1 hour
Students define similarity and why dilation alone is not enough to determine similarity.
Math / G8 / M3 / TB / lesson 9

Basic Properties of Similarity

1 hour
Similarity is both a symmetric and a transitive relation.
Math / G8 / M3 / TB / lesson 10

Informal Proof of AA Criterion for Similarity

1 hour
Students know an informal proof of the angle-angle (AA) criterion for similar triangles.
Math / G8 / M3 / TB / lesson 11

More About Similar Triangles

1 hour
Students present informal arguments as to whether or not two triangles are similar.
Math / G8 / M3 / TB / lesson 12

Modeling Using Similarity

1 hour
Students see how the mathematics they have learned in this module relates to real-world problems.
Math / G8 / M3 / TC / lesson 13

Proof of the Pythagorean Theorem

1 hour
The following proof of the Pythagorean theorem is based on the fact similarity is transitive.
Math / G8 / M3 / TC / lesson 14

The Converse of the Pythagorean Theorem (Intro)

1 hour
Students apply the Pythagorean Theorem and its converse to solve problems.
Math / G8 / M4 / TA / lesson 1

Writing Equations Using Symbols

1 hour
Students write mathematical statements using symbols to represent numbers.
Math / G8 / M4 / TA / lesson 2

Linear and Nonlinear Expressions in x

1 hour
Distinguishing linear expressions from nonlinear expressions because we will soon be solving linear equations.
Math / G8 / M4 / TA / lesson 3

Linear Equations in x

1 hour
Students know that a linear equation is a statement of equality between two expressions.
Math / G8 / M4 / TA / lesson 4

Solving a Linear Equation

1 hour
Validate the use of the properties of equality by having students share their thoughts.
Math / G8 / M4 / TA / lesson 5

Writing and Solving Linear Equations

1 hour
Students apply knowledge of geometry to writing and solving linear equations.
Math / G8 / M4 / TA / lesson 6

Solutions of a Linear Equation

1 hour
Students learn that not every linear equation has a solution.
Math / G8 / M4 / TA / lesson 7

Classification of Solutions

1 hour
Conditions for a linear equation has a unique solution, no solution, or infinitely many solutions.
Math / G8 / M4 / TA / lesson 8

Linear Equations in Disguise

1 hour
Students learn some equations may not look like linear equations are, in fact, linear.
Math / G8 / M4 / TA / lesson 9

An Application of Linear Equations

1 hour
The purpose of this lesson is to expose students to applications of linear equations.
Math / G8 / M4 / TB / lesson 10

A Critical Look at Proportional Relationships

1 hour
Students use linear equations in two variables to answer questions about distance and time.
Math / G8 / M4 / TB / lesson 11

Constant Rate

1 hour
Students graph points on a coordinate plane related to constant rate problems.
Math / G8 / M4 / TB / lesson 12

Linear Equations in Two Variables

1 hour
Students use a table to find solutions to a linear equation.
Math / G8 / M4 / TB / lesson 13

The Graph of a Linear Equation in Two Variables

1 hour
As students provide solutions, organize them in an x-y table.
Math / G8 / M4 / TB / lesson 14

The Graph of a Linear Equation—Horizontal and Vertical Lines

1 hour
Graphing and exploring the connection between ax+by=c and x=c.
Math / G8 / M4 / TC / lesson 15

The Slope of a Non-Vertical Line

1 hour
Students interpret the unit rate as the slope of a graph.
Math / G8 / M4 / TC / lesson 16

The Computation of the Slope of a Non-Vertical Line

1 hour
Students use the slope formula to compute the slope of a non-vertical line.
Math / G8 / M4 / TC / lesson 17

The Line Joining Two Distinct Points of the Graph

1 hour
Students transform the standard form of an equation into y=-a/b x+c/b.
Math / G8 / M4 / TC / lesson 18

Only One Line Passing Through a Point with a Slope

1 hour
Students graph equations in the form of y=mx+b using information about slope and y-intercept point.
Math / G8 / M4 / TC / lesson 19

Graph of Linear Equation in Two Variables Is a Line

1 hour
Students graph linear equations on the coordinate plane.
Math / G8 / M4 / TC / lesson 20

Every Line Is a Graph of a Linear Equation

1 hour
Students write the linear equation whose graph is a given line.
Math / G8 / M4 / TC / lesson 21

Some Facts About Graphs of Linear Equations in Two Variables

1 hour
Students know the traditional forms of the slope formula and slope-intercept equation.
Math / G8 / M4 / TC / lesson 22

Constant Rates Revisited

1 hour
Constant rate problems are linear equation in two variables where graph slope is constant rate.
Math / G8 / M4 / TC / lesson 23

The Defining Equation of a Line

1 hour
Two equations ax+by=c and a'x+b'y=c' graph as the same line when one is nonzero.
Math / G8 / M4 / TD / lesson 24

Introduction to Simultaneous Equations

1 hour
Students learn the notation for simultaneous equations.
Math / G8 / M4 / TD / lesson 25

Geometric Interpretation of the Solutions of a Linear System

1 hour
Sketching graphs of two linear equations finding the point of intersection. Identifying lines as solution.
Math / G8 / M4 / TD / lesson 26

Characterization of Parallel Lines

1 hour
The Discussion is an optional proof of the theorem about parallel lines.
Math / G8 / M4 / TD / lesson 27

Nature of Solutions of a System of Linear Equations

1 hour
Students know a strategy for solving a system of linear equations algebraically.
Math / G8 / M4 / TD / lesson 28

Another Computational Method of Solving a Linear System

1 hour
Students learn the elimination method for solving a system of linear equations.
Math / G8 / M4 / TD / lesson 29

Word Problems

1 hour
Students write word problems into systems of linear equations.
Math / G8 / M4 / TD / lesson 30

Conversion Between Celsius and Fahrenheit

1 hour
Consistency using repeated reasoning leading them to the general equation for conversion between Celsius, Fahrenheit.
Math / G8 / M4 / TE / lesson 31

System of Equations Leading to Pythagorean Triples

1 hour
System of equations to find three numbers, a, b, c, (a2 + b2 = c2).
Math / G8 / M5 / TA / lesson 1

The Concept of a Function

1 hour
Students use proportions to analyze the reasoning involved.
Math / G8 / M5 / TA / lesson 2

Formal Definition of a Function

1 hour
Students know that a function assigns to each input exactly one output.
Math / G8 / M5 / TA / lesson 3

Linear Functions and Proportionality

1 hour
Students relate constant speed and proportional relationships to linear functions using information from a table.
Math / G8 / M5 / TA / lesson 4

More Examples of Functions

1 hour
Examine and recognize real-world functions as discrete functions, such as the cost of a book.
Math / G8 / M5 / TA / lesson 5

Graphs of Functions and Equations

1 hour
Understanding the graph of a function is identical to the graph of a certain equation.
Math / G8 / M5 / TA / lesson 6

Graphs of Linear Functions and Rate of Change

1 hour
Students use rate of change to determine if a function is a linear function.
Math / G8 / M5 / TA / lesson 7

Comparing Linear Functions and Graphs

1 hour
Using rate of change to compare functions, determining which has a greater rate of change.
Math / G8 / M5 / TA / lesson 8

Graphs of Simple Nonlinear Functions

1 hour
Students determine whether an equation is linear or nonlinear by examining the rate of change.
Math / G8 / M5 / TB / lesson 9

Examples of Functions from Geometry

1 hour
Students write rules to express functions related to geometry.
Math / G8 / M5 / TB / lesson 10

Volumes of Familiar Solids―Cones and Cylinders

1 hour
Students know the volume formulas for cones and cylinders.
Math / G8 / M5 / TB / lesson 11

Volume of a Sphere

1 hour
Students apply the formula for the volume of a sphere to real-world and mathematical problems.
Math / G8 / M6 / TA / lesson 1

Modeling Linear Relationships

1 hour
Students interpret linear functions based on the context of a problem.
Math / G8 / M6 / TA / lesson 2

Interpreting Rate of Change and Initial Value

1 hour
Students interpret the constant rate of change and initial value of a line in context.
Math / G8 / M6 / TA / lesson 3

Representations of a Line

1 hour
Graphing a line specified by two points of a linear relationship, providing the linear function.
Math / G8 / M6 / TA / lesson 4

Increasing and Decreasing Functions

1 hour
Students describe qualitatively the functional relationship between two types of quantities by analyzing a graph.
Math / G8 / M6 / TA / lesson 5

Increasing and Decreasing Functions (Continued)

1 hour
Students qualitatively describe the functional relationship between two types of quantities by analyzing a graph.
Math / G8 / M6 / TB / lesson 6

Scatter Plots

1 hour
Students understand that a trend in a scatterplot does not establish cause-and-effect.
Math / G8 / M6 / TB / lesson 7

Patterns in Scatter Plots

1 hour
Students identify and describe unusual features in scatter plots, such as clusters and outliers.
Math / G8 / M6 / TB / lesson 8

Informally Fitting a Line

1 hour
Students informally fit a straight line to data displayed in a scatter plot.
Math / G8 / M6 / TC / lesson 9

Determining the Equation of a Line Fit to Data

1 hour
Students make predictions based on the equation of a line fit to data.
Math / G8 / M6 / TC / lesson 10

Linear Models

1 hour
Students interpret slope and the initial value in a data context.
Math / G8 / M6 / TC / lesson 11

Using Linear Models in a Data Context

1 hour
Students recognize and justify that a linear model can be used to fit data.
Math / G8 / M6 / TD / lesson 12

Nonlinear Models in a Data Context (Optional)

1 hour
Students draw nonlinear functions that are consistent with a verbal description of a nonlinear relationship.
Math / G8 / M6 / TD / lesson 13

Summarizing Bivariate Categorical Data in a Two-Way Table

1 hour
Students organize bivariate categorical data into a two-way table.
Math / G8 / M6 / TD / lesson 14

Association Between Categorical Variables

1 hour
Students consider whether conclusions are reasonable based on a two-way table.
Math / G8 / M7 / TA / lesson 1

The Pythagorean Theorem

1 hour
This lesson assumes knowledge of the theorem and its basic applications.