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1 hour

Students know the reason for some bases requiring parentheses.

1 hour

Students write equivalent numerical and symbolic expressions using the first law of exponents.

1 hour

Students write simplified, equivalent numeric, and symbolic expressions using this new knowledge of powers.

1 hour

Students know that a number raised to the zeroth power is equal to one.

1 hour

Students know the definition of a number raised to a negative exponent.

1 hour

Students extend the previous laws of exponents to include all integer exponents.

1 hour

Students know the exponent of an expression provides information about the magnitude of a number.

1 hour

Students use their knowledge of ratios, fractions, and laws of exponents to simplify expressions.

1 hour

In this lesson we learn how to write the number exactly, using scientific notation.

1 hour

Practicing operations with numbers in scientific notation and standard notation.

1 hour

Students read, write, and perform operations on numbers expressed in scientific notation.

1 hour

Students determine appropriate units for various measurements and rewrite measurements based on new units.

1 hour

Students compare numbers expressed in scientific notation.

1 hour

Students are introduced to vocabulary and notation related to rigid motions (e.g., transformation, image, map).

1 hour

Students learn that translations preserve lengths of segments and degrees of angles.

1 hour

Students learn that translations map parallel lines to parallel lines.

1 hour

Students know the definition of reflection and perform reflections across a line using a transparency.

1 hour

Students know how to rotate a figure a given degree around a given center.

1 hour

Learning rotation of 180 degrees moves a point on the coordinate plane (a,b) to (-a,-b).

1 hour

Students learn about the sequence of transformations (one move on the plane followed by another).

1 hour

Students learn that the reflection is its own inverse transformation.

1 hour

Sequences of rotations preserve lengths of segments as well as degrees of measures of angles.

1 hour

Students describe a sequence of rigid motions that maps one figure onto another.

1 hour

Basic properties of congruence are similar to properties for all rigid motions (translations, rotations, reflections).

1 hour

Presenting arguments to conclude about angles formed when parallel lines are cut by a transversal.

1 hour

Students present informal arguments to draw conclusions about the angle sum of a triangle.

1 hour

Students know a third informal proof of the angle sum theorem.

1 hour

Introduction to the Pythagorean theorem and showing an informal proof of the theorem.

1 hour

Students use the Pythagorean theorem to determine missing side lengths of right triangles.

1 hour

Students know that dilations magnify and shrink figures.

1 hour

Students learn how to use a compass and a ruler to perform dilations.

1 hour

Students know that dilations map circles to circles and ellipses to ellipses.

1 hour

Students experimentally verify the properties related to the fundamental theorem of similarity (FTS).

1 hour

Students verify the converse of the fundamental theorem of similarity experimentally.

1 hour

Students describe the effect of dilations on two-dimensional figures using coordinates.

1 hour

Students know an informal proof of why dilations are angle-preserving transformations.

1 hour

Students define similarity and why dilation alone is not enough to determine similarity.

1 hour

Similarity is both a symmetric and a transitive relation.

1 hour

Students know an informal proof of the angle-angle (AA) criterion for similar triangles.

1 hour

Students present informal arguments as to whether or not two triangles are similar.

1 hour

Students see how the mathematics they have learned in this module relates to real-world problems.

1 hour

The following proof of the Pythagorean theorem is based on the fact similarity is transitive.

1 hour

Students apply the Pythagorean Theorem and its converse to solve problems.

1 hour

Students write mathematical statements using symbols to represent numbers.

1 hour

Distinguishing linear expressions from nonlinear expressions because we will soon be solving linear equations.

1 hour

Students know that a linear equation is a statement of equality between two expressions.

1 hour

Validate the use of the properties of equality by having students share their thoughts.

1 hour

Students apply knowledge of geometry to writing and solving linear equations.

1 hour

Students learn that not every linear equation has a solution.

1 hour

Conditions for a linear equation has a unique solution, no solution, or infinitely many solutions.

1 hour

Students learn some equations may not look like linear equations are, in fact, linear.

1 hour

The purpose of this lesson is to expose students to applications of linear equations.

1 hour

Students use linear equations in two variables to answer questions about distance and time.

1 hour

Students graph points on a coordinate plane related to constant rate problems.

1 hour

Students use a table to find solutions to a linear equation.

1 hour

As students provide solutions, organize them in an x-y table.

1 hour

Graphing and exploring the connection between ax+by=c and x=c.

1 hour

Students interpret the unit rate as the slope of a graph.

1 hour

Students use the slope formula to compute the slope of a non-vertical line.

1 hour

Students transform the standard form of an equation into y=-a/b x+c/b.

1 hour

Students graph equations in the form of y=mx+b using information about slope and y-intercept point.

1 hour

Students graph linear equations on the coordinate plane.

1 hour

Students write the linear equation whose graph is a given line.

1 hour

Students know the traditional forms of the slope formula and slope-intercept equation.

1 hour

Constant rate problems are linear equation in two variables where graph slope is constant rate.

1 hour

Two equations ax+by=c and a'x+b'y=c' graph as the same line when one is nonzero.

1 hour

Students learn the notation for simultaneous equations.

1 hour

Sketching graphs of two linear equations finding the point of intersection. Identifying lines as solution.

1 hour

The Discussion is an optional proof of the theorem about parallel lines.

1 hour

Students know a strategy for solving a system of linear equations algebraically.

1 hour

Students learn the elimination method for solving a system of linear equations.

1 hour

Students write word problems into systems of linear equations.

1 hour

Consistency using repeated reasoning leading them to the general equation for conversion between Celsius, Fahrenheit.

1 hour

System of equations to find three numbers, a, b, c, (a2 + b2 = c2).

1 hour

Students use proportions to analyze the reasoning involved.

1 hour

Students know that a function assigns to each input exactly one output.

1 hour

Students relate constant speed and proportional relationships to linear functions using information from a table.

1 hour

Examine and recognize real-world functions as discrete functions, such as the cost of a book.

1 hour

Understanding the graph of a function is identical to the graph of a certain equation.

1 hour

Students use rate of change to determine if a function is a linear function.

1 hour

Using rate of change to compare functions, determining which has a greater rate of change.

1 hour

Students determine whether an equation is linear or nonlinear by examining the rate of change.

1 hour

Students write rules to express functions related to geometry.

1 hour

Students know the volume formulas for cones and cylinders.

1 hour

Students apply the formula for the volume of a sphere to real-world and mathematical problems.

1 hour

Students interpret linear functions based on the context of a problem.

1 hour

Students interpret the constant rate of change and initial value of a line in context.

1 hour

Graphing a line specified by two points of a linear relationship, providing the linear function.

1 hour

Students describe qualitatively the functional relationship between two types of quantities by analyzing a graph.

1 hour

Students qualitatively describe the functional relationship between two types of quantities by analyzing a graph.

1 hour

Students understand that a trend in a scatterplot does not establish cause-and-effect.

1 hour

Students identify and describe unusual features in scatter plots, such as clusters and outliers.

1 hour

Students informally fit a straight line to data displayed in a scatter plot.

1 hour

Students make predictions based on the equation of a line fit to data.

1 hour

Students interpret slope and the initial value in a data context.

1 hour

Students recognize and justify that a linear model can be used to fit data.

1 hour

Students draw nonlinear functions that are consistent with a verbal description of a nonlinear relationship.

1 hour

Students organize bivariate categorical data into a two-way table.

1 hour

Students consider whether conclusions are reasonable based on a two-way table.

1 hour

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