Review Activities and Games

These resources are intended for review and practice after initial instruction of the standards.

Strand: MATHEMATICAL PRACTICES (8.MP)

Strand: NUMBER SYSTEM (8.NS)
Know that there are numbers that are not rational, and approximate them by rational numbers (Standards 8.NS.1–3).
• Approximating Square Roots of Nonperfect Squares
Students will learn a strategy for how to approximate the square root of a nonperfect square in this video and classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Building a Number Line
This lesson and activity will examine different number sets on a number line. Students will identify and plot integers, counting numbers, rational and irrational numbers on a number line. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Repeating Decimal Rings
In this interactive activity you will explore the patterns that occur when expanding seventh and thirteenth fractions into decimals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Repeating Decimals
This lesson unit is intended to help educators assess how well students are able to translate between decimal and fraction notation, particularly when the decimals are repeating, create and solve simple linear equations to find the fractional equivalent of a repeating decimal, and understand the effect of multiplying a decimal by a power of 10.

Strand: EXPRESSIONS AND EQUATIONS (8.EE)
Work with radical and integer exponents (Standards 8.EE.1–4).
• "Ponzi" Pyramid Schemes
The student's task is to find the fatal catch in this sure-fire money making scheme.
• 100 People
In the 1990s researchers calculated that if there were just 100 people in the world, there would be 20 children, 25 people would not have food and shelter, 17 people would speak Chinese, and 8 would speak English. In this task, students are asked to estimate the real numbers, given that there are approximately seven billion people in the world.
• A Million Dollars
In this task, students will figure out questions such as: How much does a million Dollars in Dollar bills weigh? How many burgers can you buy for a million Dollars?
• Scientific Notation
Defining scientific notation and the conversion of extreme numbers into scientific notation is the focus of the animated Math Shorts video. After viewing it the students practice using scientific notation to write numbers and also create real-world problems for other students to solve. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Slope and House Construction
A video with This Old House's carpenter demonstrates how the use of slope is critical in the building of a house. The students then practice working with slope to not only build a playground slide, but identify other real-world uses of slope. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Writing Expressions and Equations video
How to write an equation using what we know to solve a problem we don't know.
Understand the connections between proportional relationships, lines, and linear relationships (Standards 8.EE.5–6).
• Bike Ride
In this task, students interpret a distance/time graph describing a bike ride.
• Graphing Linear Equations - Full Body Style
This Teaching Channel video and lesson plan shows students graphing a line given slope-intercept on a giant coordinate plane. (4 minutes)
• Manipulating Graphs
This video demonstrates how to use the slope-intercept of a line to the graph of that line. The classroom activity has them demonstrate their understanding by finding equations for a set of lines through the origin. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Slope and House Construction
A video with This Old House's carpenter demonstrates how the use of slope is critical in the building of a house. The students then practice working with slope to not only build a playground slide, but identify other real-world uses of slope. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Solving Systems of Equations by Graphing
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Systems of Linear Equations by Graphing
This is a video introduction and explanation of the topic.
• Stairway Slope
Students learn how to use stairs to understand and calculate the slope of a line. The classroom activity then has students use the real-world situation of a wheelchair and a the slope of a ramp to calculate the length needed for the ramp. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations (Standards 8.EE.7–8)
In this task, students will write equations to solve problems about buying bags of chips and candy bars.
• IXL Game: Linear Functions
Designed for eighth graders, this game will help the student understand linear functions, specifically how to graph a line from an equation. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Manipulating Graphs
This video demonstrates how to use the slope-intercept of a line to the graph of that line. The classroom activity has them demonstrate their understanding by finding equations for a set of lines through the origin. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
• Rate Problems
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Repeating Decimals
This lesson unit is intended to help educators assess how well students are able to translate between decimal and fraction notation, particularly when the decimals are repeating, create and solve simple linear equations to find the fractional equivalent of a repeating decimal, and understand the effect of multiplying a decimal by a power of 10.
• Simultaneous Linear Equations
This website offers students instruction on various methods of solving simultaneous equations and practice examples for each method.
• Solving Equations video
Answers the questions "what are equations?" and "how do we solve them?"
• Solving Linear Equations in One Variable
This lesson unit is intended to help educators assess how well students are able to solve linear equations in one variable with rational number coefficients, collect like terms, expand expressions using the distributive property, and categorize linear equations in one variable as having one, none, or infinitely many solutions.
• Solving Real-Life Problems: Baseball Jerseys
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, interpret and evaluate the data generated and identify the break-even point, checking it for confirmation, and communicate their reasoning clearly.
• Solving Systems of Linear Equations by Elimination
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Systems of Linear Equations by Substitution
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.

Strand: FUNCTIONS (8.F)
Define, evaluate, and compare functions (Standards 8.F.1–3)
• Comparing Algorithms: Guess My Rule
Use a function machine to play a game where you guess three mystery algorithms, then check to see if you're correct. In the activity you test function rules and find relationships between those rules and graphs. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Comparing Exponential, Quadratic, and Linear Functions
This interactive requires the student to examine functional relationships to determine whether they are quadratic, exponential, or linear. The classroom activity for the lesson shows the student 3 graphs and has them determine what sort of function they reflect. They also solve word problems using the interactive activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Coordinates and the Cartesian Plane
This lesson helps students understand functions and the domain and range of a set of data points.
• Exploring Linear Functions: Representational Relationships
This lesson plan helps students better understand linear functions by allowing them to manipulate values and get a visual representation of the result.
• Exploring Reasoning and Proof
Questions requiring geometric reasoning are applied to the icing of a cake in this Annenberg interactive. Students must estimate the amount of frosting needed to cover a whole cake. The classroom activity focuses on pattern recognition and geometric reasoning. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Function Machine
Students learn how a function machine works in this interactive from Annenberg and then use them to answer questions. Students must then apply function rules to problems, plot points on graphs, and solve rules problems. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Functional Relationships Between Quantities: Calculating Fuel Consumption
This lesson consists of interactive visualizations to help students examine the relationship between a car's mpg to gallons per mile. They can use the interactive slider to see how the relationship changes as a car's efficiency is changed. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
• IXL Game: Nonlinear functions
Designed for eighth graders this game will help the student understand linear functions, specifically how to identify linear and nonlinear functions. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Interpreting Distance-Time Graphs
This lesson unit is intended to help educators assess how well students are able to interpret distance and time graphs.
• Linear Function Machine
By putting different values into the linear function machine students will explore simple linear functions.
• Manipulating Graphs
This video demonstrates how to use the slope-intercept of a line to the graph of that line. The classroom activity has them demonstrate their understanding by finding equations for a set of lines through the origin. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
• Sequencer
By using this applet students are able to create sequences by changing the values of starting numbers, multipliers, and add-ons.
In this task, students are asked to match equations with linear graphs.
• Teacher Desmos: LEGO Prices
In this activity, students use sliders to explore the relationship between price and number of pieces for various Star Wars LEGO sets and to make several predictions based on that model. Students will also interpret the parameters of their equation in context.
• Teacher Desmos: Linear Functions Collection
A collection of activities designed for algebra students studying linear functions as tables, graphs, and equations.
• Teacher Desmos: Marbleslides Lines
In this activity, students will transform lines so that the marbles go through the stars. Students will test their ideas by launching the marbles, and have a chance to revise before trying the next challenge.
Use functions to model relationships between quantities (Standards 8.F.4–5).
• Comparing Algorithms: Guess My Rule
Use a function machine to play a game where you guess three mystery algorithms, then check to see if you're correct. In the activity you test function rules and find relationships between those rules and graphs. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Comparing Exponential, Quadratic, and Linear Functions
This interactive requires the student to examine functional relationships to determine whether they are quadratic, exponential, or linear. The classroom activity for the lesson shows the student 3 graphs and has them determine what sort of function they reflect. They also solve word problems using the interactive activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
This Teaching Channel video demonstrates a lesson where students analyze patterns and represent functions. (9 minutes)
• Finding Patterns to Make Predictions
This activity asks students to identify and contemplate mathematical patterns that we see around us. They are asked to represent them in a table and predict the pattern to the 7th, 9th, and nth terms. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Functional Relationships Between Quantities: Calculating Fuel Consumption
This lesson consists of interactive visualizations to help students examine the relationship between a car's mpg to gallons per mile. They can use the interactive slider to see how the relationship changes as a car's efficiency is changed. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Graphing Equations in Slope Intercept Form
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Graphing Equations in Slope Intercept Form Video
This is a video introduction to the topic.
• Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
• Intercepts of Linear Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Intercepts of Linear Equations video
This video introduces the topic.
• Interpreting Distance-Time Graphs
This lesson unit is intended to help educators assess how well students are able to interpret distance and time graphs.
• Linear Function Machine
By putting different values into the linear function machine students will explore simple linear functions.
• Linear Functions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Linear Functions video
This video compares proportional and non-proportional linear functions.
• Modeling Situations With Linear Equations
This lesson unit is intended to help educators assess how well students use algebra in context, and in particular, how well students explore relationships between variables in everyday situations, find unknown values from known values, find relationships between pairs of unknowns, and express these as tables and graphs, as well as find general relationships between several variables, and express these in different ways by rearranging formulae.
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
• Non-Linear Functions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Non-linear Functions video
This video introduces non-linear functions.
• Parallel Lines
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Parallel Lines video
This video explains the concept.
In this task, students will help Bill to find the best price for buying printed jerseys for the baseball team.
In this task, students are asked to match equations with linear graphs.
In this task, students use equations to solve a problem with a restaurant check.

Strand: GEOMETRY (8.G)
Understand congruence and similarity using physical models, transparencies, or geometry software (Standards 8.G.1–5).
• Calculating Distance Using the Pythagorean Theorem
In this interactive students must find the distance between two points on a plane by use the Pythagorean Theorum. They then use this skill to complete an activity involving an amusement park. They create a map of a park and then figure out the distance between attractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Circle Sandwich
The purpose of this task is to apply knowledge about triangles, circles, and squares in order to calculate and compare two different areas.
• Comparing Volumes of Cylinders, Spheres, and Cones
This interactive explains how to calculate the volumes of cylinders, cones and spheres. Students then apply this understanding to an activity where cylinders, cones and spheres are filled with water so that their volumes can be compared. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Escaramuza: Symmetry, Reflection, Rotation
The real-life equestrian event known as Escaramuza is used to teach students how to diagram 2D representations on an x-y graph and then reflect and rotate the figure. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Geometry in Tessellations
In this lesson students will learn about lines, angles, planes, and experiment with the area and perimeter of polygons.
• Identifying Unknown Transformations
This applet allows the student to drag a shape and then observe the changes to its behavior. They then determine whether the alteration is due to reflection, a rotation, or a translation/slide transformation.
• Introduction to Fractals: Infinity, Self-Similarity and Recursion
This lesson is designed to help students understand aspects of fractals, specifically self-similarity and recursion.
• Reflection
In this animated video from UEN (Utah Education Network) students learn about one type of movement for geometric shapes - reflection. In the accompanying activity students demonstrate understanding by creating a geometric figure on a plane and then reflecting it into another quadrant. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Rotation
In this animated Math Shorts video from the Utah Education Network, learn about rotation, which describes how a geometric shape turns around a point, called the center of rotation. In the accompanying classroom activity, students are given two rotations from a handout and work in pairs to try to determine whether one figure is a rotation of the other figure around the given point. Note: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Rotation Symmetry
Exploring this interactive students are able to predict and find the angle of rotation for various figures by using rotation symmetry. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Scaling
An interactive from Annenberg asks students to scale a picture by using the math strategies of multiplicative and additive relationships. Students then use those strategies to compare photocopies and rectangles in different scales. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
A set of short tasks for grades 7 & 8 dealing with geometry.
• Translation
This lesson opens with an animated short from the Utah Education Network to explain the concept of translation when a geometric figure changes location on a plane. Students are then asked to solve practice translation problems and explain their solution. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Translations, Reflections, and Rotations
Students are introduced to the concepts of translation, reflection and rotation in this lesson plan.
Understand and apply the Pythagorean Theorem and its converse (Standards 8.G.6–8).
• Calculating Distance Using the Pythagorean Theorem
In this interactive students must find the distance between two points on a plane by use the Pythagorean Theorum. They then use this skill to complete an activity involving an amusement park. They create a map of a park and then figure out the distance between attractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Circle Sandwich
The purpose of this task is to apply knowledge about triangles, circles, and squares in order to calculate and compare two different areas.
• IXL Game: Pythagorean theorem
This game will help eighth graders understand the pythagorean theorem via word problems. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Pythagorean Explorer
This applet challenges the student to find the length of the third side of a triangle when given the two sides and the right angle.
• Pythagorean Theorem
In this lesson students will be able to use the Pythagorean Theorem to find side lengths of right triangles, the areas of right triangles, and the perimeter and areas of triangles.
• Squaring the Triangle
Students can manipulate the sides of a triangle in this applet in order to better understand the Pythagorean Theorem.
In this task, students will create a design using rotations and reflections.
• Student Task: Circles and Squares
In this task, students must solve a problem about circles inscribed in squares
The Hopewell people were Native Americans whose culture flourished in the central Ohio Valley about 2000 years ago. They constructed earthworks using right triangles. In this task, the student will look at some of the geometrical properties of a Hopewell earthwork.
In this task, students will need to work out the actual dimensions of TV screens, which are sold according to their diagonal measurements.
• Student Task: Proofs Of The Pythagorean Theorem?
In this task, students will look at three different attempts to prove the Pythagorean theorem and determine which is the best "proof".
In this task, the student will investigate Pythagorean Triples.
A set of short tasks for grades 7 & 8 dealing with geometry.
During the Edo period (1603-1867) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to worshippers. Here is one such problem for students to investigate.
• The Pythagorean Theorem and 18th-Century Cranes
A video from Annenberg Learner Learning Math shows how the Pythagorean Theorem was useful in the reconstruction of an 18th century crane. The classroom activity asks students to apply the theorem and understand its usefulness in construction and design. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• The Pythagorean Theorem: Square Areas
This lesson unit is intended to help educators assess how well students are able to use the area of right triangles to deduce the areas of other shapes, use dissection methods for finding areas, organize an investigation systematically and collect data, and deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem.)
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (Standard 8.G.9).
• Comparing Volumes of Cylinders, Spheres, and Cones
This interactive explains how to calculate the volumes of cylinders, cones and spheres. Students then apply this understanding to an activity where cylinders, cones and spheres are filled with water so that their volumes can be compared. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Flower Vases
The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.
• Modeling: Making Matchsticks
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods, interpret and evaluate the data generated, and communicate their reasoning clearly.
In this task, students will determine how many matchsticks can be made from a tree with a trunk with a base radius of 1 foot and a height of 80 feet.
In this task, students will find the volumes of different shaped drinking glasses.
A set of short tasks for grades 7 & 8 dealing with geometry.
During the Edo period (1603-1867) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to worshippers. Here is one such problem for students to investigate.
• The Largest Container: Problems Using Volume and Shape
By using a single sheet of paper this interactive leads students to construct shapes, calculate volume, and think about the relationships between different shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Strand: STATISTICS AND PROBABILITY (8.SP)
Investigate patterns of association in bivariate data (Standards 8.SP.1–4).
• Create a Graph
This applet allows students to create bar, line, area, pie, and XY graphs.
• IXL Game: Linear Functions: Slope of a Graph
This game will help eighth graders learn to find the slope of a graph. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Lesson Starter: Populated Communities
Students will use statistics and probability knowledge, as well as critical thinking skills, to solve problems.
• Linear Regression and Correlation
In this lesson students will plot data onto a scatter plot and then determine the line of best fit for the data sets.
• Multi-Function Data Flyer
The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
• Scatter Plot
An understanding of how a scatter plot works is the focus of this interactive. Students interpret a scatter plot representing the relationship of height to arm length. They then create their own plot by measuring foot and forearm lengths. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Simple Plot
The applet in this lesson plan allows the student to plot ordered pairs and understand functions.
In this task students will user a scatter graph to investigate a possible connection between the length and width of bird's eggs.