Equivalent Expressions Using Exponents

Source: PBS Learning Media

Resource Type: Interactive & Activity Documents

Students will apply critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to get you to recognize patterns and determine a rule.

Skill: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) = 1/(3^3) = 1/27.

Georgia Standard: MGSE8.EE.1

Approximating Square Roots of Nonperfect Squares

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will identify rational and irrational numbers, compare sizes of irrational numbers, and estimate the value of irrational square roots.

Skills: Use square root and cube root symbols to represent solutions to equations. Recognize that x^2 = p (where p is a positive rational number and |x| < 25) has 2 solutions and x^3 = p (where p is a negative or positive rational number and |x| < 10) has one solution. Evaluate square roots of perfect squares < 625 and cube roots of perfect cubes > -1000 and < 1000.

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Use rational approximation of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., estimate π^2 to the nearest tenth). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Georgia Standards: MGSE8.EE.2, MGSE8.NS.1, MGSE8.NS.2

Comparing Powers of 10

Source: PBS Learning Media

Resource Type: Interactive & Activity Documents

Use powers of 10 to investigate scientific notation. This interactive exercise focuses on determining which of a series of numbers written in scientific notation is larger and by what magnitude then you need to use your critical thinking skills to determine methods for general cases.

Skills: Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g. use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g. calculators).

Georgia Standards: MGSE8.EE.3, MGSE8.EE.4

Bivariate Data and Analysis: Anthropological Studies

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will Investigate how skeletal populations can help determine the impact of slavery on the height and health of African American males. This video focuses on the measurements and equations Mark Mack is using to explore relationships between the length of the bones in the leg and height while discussing how statistics is a useful tool to analyze data and make inferences taking math out of the classroom and into real world problem solving.

Skills: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

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.

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.

Georgia Standards: MGSE8.EE.5, MGSE8.SP.2, MGSE8.SP.3

Slope and House Construction

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will list two or more instances of slope in everyday life, name a career that involves working with slope, define slope as height/length, and identify the steeper of two slopes.

Skills: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; 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.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Georgia Standards: MGSE8.EE.5, MGSE8.EE.6, MGSE8.F.2

Understanding Slope with Similar Triangles

Source: PBS Learning Media

Resource Type: Video & Activity Document

In this video, learn how similar triangles can be used to help explain the concept of slope. In the accompanying classroom activity, students apply the concept of similar triangles to explore the slope between different points on the coordinate plane. Students may already know that two points make a line. In the activity, they use similar right triangles to explore why the slope of a line is constant between any two points on that line. The activity begins with a review of two concepts: similar triangles and slope. Students then watch the video, which relating the two ideas, and break into partner groups to develop mathematical arguments relating slope and similarity.

Skill: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; 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.

Georgia Standard: MGSE8.EE.6

Understanding Solutions to Linear Equations

Source: PBS Learning Media

Resource Type: Video & Activity Document

In this video, Students explore linear equations in one variable with one solution, infinitely many solutions, or no solutions. In the accompanying classroom activity, students watch the video and then write and solve three equations: one with one solution, one with infinitely many solutions, and one with no solutions. They trade with a partner and solve each other’s equations.

Skills: Solve linear equations in one variable.

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).

Georgia Standards: MGSE8.EE.7, MGSE8.EE.7a

Solving Simultaneous Linear Equations

Source: PBS Learning Media

Resource Type: Video & Activity Document

In this video, students learn the elimination method for solving two simultaneous linear equations in a real-world context. In the accompanying classroom activity, students watch the video, solve a pair of simultaneous linear equations, and write a word problem to fit the equations. In order to facilitate introduction to and practice with the elimination method, students work with simple linear equations.

Skills: Analyze and solve pairs of simultaneous linear equations (systems of linear equations).

Solve systems of two linear 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.

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.

Georgia Standards: MGSE8.EE.8, MGSE8.EE.8b, MGSE8.EE.8c

Thinkport: Systems of Equations

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will learn about the role of math in architecture in this media gallery from MPT. In the accompanying classroom activity, students design a triangular roof and find equations for the lines that include the sides of the triangle. They verify that the point at which the two lines intersect satisfy both equations.

Skills: Analyze and solve pairs of simultaneous linear equations (systems of linear equations).

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.

Georgia Standards: MGSE8.EE.8, MGSE8.EE.8a

Source: PBS Learning Media

Resource Type: Videos & Activity Documents

Watch three demonstrations that highlight the functional relationships between a ball’s height and distance traveled in this media gallery from MPT. In the accompanying classroom activity, students create graphs to show the trajectory of a basketball as players pass it in different ways: with a linear chest pass, a U-shaped (parabolic) pass, and a V-shaped bounce pass. They then interpret a set of basketball-related graphs.

Skills: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).

Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Georgia Standards: MGSE8.F.1, MGSE8.F.5

Cooking with Bill Nye: Dependent and Independent Variables

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will identify an independent and a dependent variable in a real-world context and analyze the relationship between an independent and dependent variable, using graphs and tables.

Skill: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Georgia Standard: MGSE8.F.5

Interpreting Stories and Graphs

Source: PBS Learning Media

Resource Type: Interactive & Activity Documents

Students will demonstrate problem solving skills by interpreting and sketching graphs. This interactive exercise focuses on how line graphs can be used to represent mathematical data and provides an opportunity to translate actions from a story into graph form, and then asks students to write their own story to coincide with a line graph.

Skill: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Georgia Standard: MGSE8.F.5

Geometry of Shapes in Kapa Design

Source: PBS Learning Media

Resource Type: Video & Activity Documents

Students will explore the beauty of geometrical shapes and find the patterns that a Hawaiian kapa quilt maker incorporates into her designs in this video from the Center for Asian American Media.

Skills: Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Georgia Standards: MGSE8.G.1, MGSE8.G.2

Esacaramuza: Coordinates, Reflection, Rotation

Source: PBS Learning Media

Resource Type: Video & Activity Documents

Student will use footage from a real-life equestrian event to draw a two-dimensional diagram and learn to reflect a representation of it on a coordinate graph in this video from Center for Asian American Media.

Skills: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Georgia Standards: MGSE8.G.2, MGSE8.G.3, MGSE8.G.4

Rotation and Dilation

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will watch an animated demonstration of rotating and dilating a triangle on the coordinate plane. In the accompanying classroom activity, students watch the video; draw rotations and dilations of a triangle; and identify center of rotation, angle of rotation, and scale factors in classmates drawings.

Skill: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

Georgia Standard: MGSE8.G.3

Translations and Reflections

Source: PBS Learning Media

Resource Type: Video & Activity Document

Students will watch an animated demonstration of translating and reflecting a triangle on the coordinate plane in this video from KCPT. In the accompanying classroom activity, students watch the video and then consider the effect of translating and reflecting on the coordinates of the vertices of the triangle. Next, they draw translations and reflections of a triangle and identify the number of units and direction of translation as well as the lines of reflection in classmates drawings.

Skill: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

Georgia Standard: MGSE8.G.3

Rotational Symmetry

Source: PBS Learning Media

Resource Type: Interactive & Activity Document

Students visualize how objects behave when they are rotated around a centrally located rotation point. This interactive exercise looks at angles of rotation and rotational symmetry of a variety of figures.

Skill: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Georgia Standard: MGSE8.G.4

Thinkport: Mapping Sculptures

Source: PBS Learning Media

Resource Type: Video & Activity Document

In this video from MPT, student's learn how sculptor Mary Ann Mears uses angle measurement and geometric relationships when determining angles in scale models. In the accompanying classroom activity, students apply what they learn in the video as they solve problems in which they are given clues about two of the angles in a triangle and must determine the third. Clues involve measurements of interior and exterior angles in the triangle.

Skill: 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. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.

Georgia Standard: MGSE8.G.5

Taco Cart: A Pythagorean Journey

Source: PBS Learning Media

Resource Type: Interactive, Video, & Activity Document

Students will use distance and speed of travel to solve a real-life problem. This interactive exercise focuses on using what you know about the Pythagorean theorem and rate of change to make a prediction about whether Ben or Dan will get their tacos first and then requires completing the calculations to see if your prediction was accurate.

Skill: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Georgia Standard: MGSE8.G.7

Using the Pythagorean Theorem on the Cartesian Graph

Source: PBS Learning Media

Resource Type: Interactive & Activity Documents

In this interactive, students use logic and mathematical skill to place animals at the correct points on a Cartesian graph representing the cardinal directions. Then, they use the Pythagorean theorem to determine the distances between points. The riddles in the interactive, including one requiring an understanding of rate, have randomized values so that students can place points at different locations and calculate different distances. The activity provides a review of concepts related to determining the distances between points on a Cartesian graph using the Pythagorean theorem and a response sheet to help students work with the interactive.

Skills: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Georgia Standards: MGSE8.G.7, MGSE8.G.8

Meatballs: Volumes of Spheres and Cylinders

Source: PBS Learning Media

Resource Type: Interactive, Video, & Activity Document

Students will Use problem solving skills to find out if the pot will overflow when Dan adds meatballs to his pasta sauce. This interactive exercise focuses on using the volume equations for cylinders and spheres to figure out the multistep problem of how many meatballs it would take to fill the space left in the pot.

Skill: Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Georgia Standard: MGSE8.G.9

Popcorn Picker: Volumes of Solid Shapes

Source: PBS Learning Media

Resource Type: Interactive, Video, & Activity Document

Students will experiment with the volume of two cylinders made from the same size paper. This interactive exercise focuses on using what you know about cylinders to make a prediction about their volume and then requires calculating the actual volume to see if your prediction was accurate.

Skill: Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Georgia Standard: MGSE8.G.9

You Pour, I Choose: Volumes of Cylinders

Source: PBS Learning Media

Resource Type: Interactive, Video, & Activity Document

Students will compare the volume of varied cylindrical glasses filled to different heights. This interactive exercise focuses on using what you know about cylinders to make a prediction about their volume and then requires calculating the actual volume to see if your prediction was accurate.

Skill: Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Georgia Standard: MGSE8.G.9

Scatter Plot

Source: PBS Learning Media

Resource Type: Interactive & Activity Document

Students consider the graphical relationship between arm span and height. This interactive exercise focuses on taking measurements, adding them to a table, and then plotting them so you can interpret the graph.

Skills: 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.

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.

Georgia Standards: MGSE8.SP.1, MGSE8.SP.2

Thinkport: Two-Way Tables and Associations

Source: PBS Learning Media

Resource Type: Interactive & Activity Documents

Students will explore possible associations between students’ grade level and their preferences for using land behind a middle school with this interactive from MPT. They display frequencies and relative frequencies in a two-way table and interpret the results. Next, they apply what they learned as they use an interactive from MPT to explore possible associations between students’ grade and their preferences for using land behind a middle school.

Skill: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

Georgia Standard: MGSE8.SP.4