(8.MP) The Number System

(8.NS) Expressions and Equations

(8.EE) Functions

(8.F) Geometry

(8.G) Statistics and Probability

(8.SP)

Standard 8.MP.1

Make sense of problems and persevere in solving them. Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, "Does this make sense?" Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

Standard 8.MP.2

Reason abstractly and quantitatively. Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently as well as the ability to contextualize algebraic representations to make sense of the problem.

Standard 8.MP.3

Construct viable arguments and critique the reasoning of others. Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

Standard 8.MP.4

Model with mathematics. Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Standard 8.MP.5

Use appropriate tools strategically. Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

Standard 8.MP.6

Attend to precision. Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

Standard 8.MP.7

Look for and make use of structure. Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.For example, see 5 3(x y)^{2}as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Standard 8.MP.8

Look for and express regularity in repeated reasoning. Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

- The Number System (8.NS) - 8th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 - The Number System.

- Chapter 7 - Mathematical Foundation (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Rational and Irrational Numbers. - Chapter 7 - Student Workbook (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Rational and Irrational Numbers. Engage NY - Grade 8 Math Module 7: Introduction to Irrational Numbers Using Geometry (EngageNY)

Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form ofx2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general. - Grade 8 Unit 2: Exponents and Equations (Georgia Standards)

In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system; recognize that every rational number has a decimal representation that either terminates or repeats; recognize that irrational numbers must have decimal representations that neither terminate nor repeat; understand that the value of a square root can be approximated between integers and that nonperfect square roots are irrational; locate rational and irrational numbers on a number line diagram; use the properties of exponents to extend the meaning beyond counting-number exponents; recognize perfect squares and cubes, and understanding that non-perfect squares and non- perfect cubes are irrational.

- Approximating pi

The goal of this task is to explore some important aspects of approximating an irrational number with rational numbers. The irrational number chosen here is pi because it is one of the most interesting, well known, and grade appropriate irrational numbers. - Calculating and Rounding Numbers

This task is intended for instructional (rather than assessment) purposes, providing an opportunity to discuss technology as it relates to irrational numbers and calculations in general. The task gives a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding. - Calculating the square root of 2

This Illustrative Mathematics task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. - Comparing Rational and Irrational Numbers

This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers. It allows students to construct viable arguments by identifying and justifying the greater of two expressions in each part. - Converting Decimal Representations of Rational Numbers to Fraction Representations

This task requires students to represent several rational numbers in fraction form. - Converting Repeating Decimals to Fractions

The purpose of this task is to study some concrete examples of repeating decimals and find a way to convert them to fractions. - Estimating Square Roots

The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. - Identifying Rational Numbers

Given a set of numbers students must decide whether each number is rational or irrational. - Irrational Numbers on the Number Line

In this task students plot irrational numbers on the number line in order to reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers. This task could be used for assessment, or if elaborated a bit, could be used in an instructional setting. - Placing a square root on the number line

The purpose of the task is to make connections between the definition and properties of squares and square roots and ordering on the number line, as prescribed by standard 8.NS.2. - Repeating or Terminating?

The purpose of this task is to understand, in some concrete cases, why terminating decimal numbers can also be written as repeating decimals where the repeating part is all 9's.

- 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.

Standard 8.NS.1

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.Standard 8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^{2}).For example, by truncating the decimal expansion 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.Standard 8.NS.3

Understand how to perform operations and simplify radicals with emphasis on square roots.

- "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.

- Chapter 2 - Student Workbook (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 8 student workbook. It covers Proportional and Linear Relationships. - Chapter 7 - Mathematical Foundation (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Rational and Irrational Numbers. - Chapter 7 - Student Workbook (UMSMP)

This is Chapter 7 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Rational and Irrational Numbers. - Chapter 8 - Mathematical Foundation (UMSMP)

This is Chapter 8 of the Utah Middle School Math Grade 8 textbook. It provides a Mathematical Foundation for Integer Exponents, Scientific Notation and Volume. - Chapter 8 - Student Workbook (UMSMP)

This is Chapter 8 of the Utah Middle School Math Grade 8 student workbook. It focuses on Integer Exponents, Scientific Notation and Volume. Engage NY - Grade 8 Math Module 1: Integer Exponents and Scientific Notation (EngageNY)

In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for any integer exponent. Next, students work with numbers in the form of an integer multiplied by a power of 10 to express how many times as much one is than the other. This leads into an explanation of scientific notation and continued work performing operations on numbers written in this form. - Grade 8 Math Module 7: Introduction to Irrational Numbers Using Geometry (EngageNY)

Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form ofx2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general. - Grade 8 Unit 2: Exponents and Equations (Georgia Standards)

In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system; recognize that every rational number has a decimal representation that either terminates or repeats; recognize that irrational numbers must have decimal representations that neither terminate nor repeat; understand that the value of a square root can be approximated between integers and that nonperfect square roots are irrational; locate rational and irrational numbers on a number line diagram; use the properties of exponents to extend the meaning beyond counting-number exponents; recognize perfect squares and cubes, and understanding that non-perfect squares and non- perfect cubes are irrational. - Grade 8 Unit 3: Geometric Applications of Exponents (Georgia Standards)

In this unit students will distinguish between rational and irrational numbers; find or estimate the square and cubed root of non-negative numbers, including 0; interpret square and cubed roots as both points of a line segment and lengths on a number line; use the properties of real numbers (commutative, associative, distributive, inverse, and identity) and the order of operations to simplify and evaluate numeric and algebraic expressions involving integer exponents, square and cubed roots; work with radical expressions and approximate them as rational numbers; solve problems involving the volume of a cylinder, cone, and sphere; determine the relationship between the hypotenuse and legs of a right triangle; use deductive reasoning to prove the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in right triangles; determine if a triangle is a right triangle, Pythagorean triple; apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and solve problems involving the Pythagorean Theorem.

- Ant and Elephant

In this problem students are comparing a very small quantity with a very large quantity using the metric system. - Ants versus humans

This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass. - Choosing appropriate units

The purpose of this task is to use scientific notation in the context of choosing units to report quantities. - Estimating Length Using Scientific Notation

This lesson unit is intended to help you assess how well students are able to estimate lengths of everyday objects, convert between decimal and scientific notation, and make comparisons of the size of numbers expressed in both decimal and scientific notation. - Extending the Definitions of Exponents, Variation 1

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. - Giantburgers

Every day 7% of Americans eat at Giantburger restaurants! The student's task is to decide whether this newspaper headline can be true. - How old are they?

In this task, students will use equations to solve a number puzzle about three people's ages - Orders of Magnitude

The purpose of this task is for students to develop a feel for large powers of ten, which is a critical component of working fluently with numbers in scientific notation. Note that this task develops "very large number sense"--strategies for helping students understand very small numbers are forthcoming. - Pennies to Heaven

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. - Raising to the zero and negative powers

The goal of this task is to use the quotient rule of exponents to help explain how to define the expressions ck for c>0 and k is greater than or equal to 0. This important definition is motivated and explained by the law of exponents: adopting the definitions for the expressions c0 and c-n given in the task allows us to maintain the intuitive product and quotient rules known for all positive exponents (which this task assumes students are familiar with).

Standard 8.EE.1

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.Standard 8.EE.2

Use square root and cube root symbols to represent solutions to equations of the formx^{2}=pandx^{3}= p, wherepis a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.Standard 8.EE.3

Use numbers expressed in the form of a single digit times a whole-number power of 10 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 times 10^{8}and the population of the world as 7 times 10^{9}, and determine that the world population is more than 20 times larger.Standard 8.EE.4

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use 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.

- 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.

- Chapter 2 - Mathematical Foundation (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Proportional and Linear Relationships. - Chapter 2 - Student Workbook (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 8 student workbook. It covers Proportional and Linear Relationships. Engage NY - Grade 8 Math Module 4: Linear Equations (EngageNY)

In 8th grade Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables. - Grade 8 Unit 5: Linear Functions (Georgia Standards)

In this unit students will graph proportional relationships; interpret unit rate as the slope; compare two different proportional relationships represented in different ways; use similar triangles to explain why the slope is the same between any two points on a non-vertical line; derive the equation y = mx for a line through the origin; derive the equation y = mx + b for a line intercepting the vertical axis at b; and interpret equations in y = mx + b form as linear functions.

- Bivariate Data and Analysis: Anthropological Studies

This lesson opens with a video from an anthropologist explaining how he uses bivariate data to examine the impact that slavery had on the slave's height and weight. Students then use his data in the classroom activity which has them study the relationship between tibia and femur measurements and a person's stature. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Coffee by the Pound

Given a statement about the price of coffee, students are asked to answer a number of questions about the cost per pound and draw a graph in the coordinate plane of the relationship between the number of pounds of coffee and the total cost. - Comparing Speeds in Graphs and Equations

This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. - DVD Profits, Variation 1

The first two problems in this task ask students to find the unit cost per DVD for making a million DVDs. Even though each additional DVD comes at a fixed price, the overall cost per DVD changes with the number of DVDs produced because of the startup cost of building the factory. - Different Areas?

The goal of this task is to motivate a discussion of similarity and slope via a counterintuitive geometric construction where it appears as if area is not conserved by cutting and reassembling a simple shape. - Equations of Lines

This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question. - Find the Change

This task is designed to help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. It may also produce a reasonable starting place for discussing point-slope form of a linear equation. - Folding a Square into Thirds

The purpose of this task is to find and solve a pair of linear equations which can be used to understand a common method of folding a square piece of origami paper into thirds. - GeoGebra: Derivation of the line

Use this file to see the derivation of the line y=mx. - Journey

In this task, students will read a description of a car journey and draw a distance-time graph to represent it. - Lines and Linear Equations

This lesson unit is intended to help educators assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation. - Peaches and Plums

This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope. - Proportional relationships, lines, and linear equations

The purpose of this task is to assess whether students understand certain aspects of the relationship between proportional relationships, lines, and linear equations. In particular, it requires students to find the slope of the line defined by the equation 4y=x and to write the equation of a line knowing its slope and y-intercept. - Shelves

In this task, students must figure out how many planks and bricks are needed to build a bookcase. - Slopes Between Points on a Line

The purpose of this task is to help students understand why the calculated slope will be the same for any two points on a given line. This is the first step in understanding and explaining why it will work for any line (not just the line shown). - Sore Throats, Variation 2

The purpose of this task is to show how the ideas in the RP and EE domains in 6th and 7th grade mature in 8th grade. Parts (a)-(c) could easily be asked of 7th grade students. Part (a) asks students to do what is described in 7.RP.2.a, Part (b) asks students to do what is described in 7.RP.2.c, and Part (c) is the 7th grade extension of the work students do in 6.EE.9. On the other hand, part (d) is 8th grade work. - Stuffing Envelopes

This task provides students with an opportunity to take the step from unit rates in a proportional relationship to the rate of change of a linear relationship. Students should already be familiar with proportional relationships from their work in prior grades. - Who Has the Best Job?

Given a table students are asked to make graphs representing the relationship between the time a student worked and the money they earned.

Standard 8.EE.5

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.Standard 8.EE.6

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 equationy = mxfor a line through the origin and the equationy=mx+bfor a line intercepting the vertical axis atb.

- Buying Chips and Candy

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.

- Chapter 1 - Mathematical Foundation (UMSMP)

This is Chapter 1 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Analyzing and Solving Linear Equations. - Chapter 1 - Student Workbook (UMSMP)

This is Chapter 1 of the Utah Middle School Math: Grade 8 student workbook. It covers analyzing and solving linear equations. Engage NY - Grade 8 Math Module 4: Linear Equations (EngageNY)

In 8th grade Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables. - Grade 8 Unit 2: Exponents and Equations (Georgia Standards)

In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system; recognize that every rational number has a decimal representation that either terminates or repeats; recognize that irrational numbers must have decimal representations that neither terminate nor repeat; understand that the value of a square root can be approximated between integers and that nonperfect square roots are irrational; locate rational and irrational numbers on a number line diagram; use the properties of exponents to extend the meaning beyond counting-number exponents; recognize perfect squares and cubes, and understanding that non-perfect squares and non- perfect cubes are irrational. - Grade 8 Unit 7: Solving Systems of Equations (Georgia Standards)

In this unit students will understand the solution to a system of equations is the point of intersection when the equations are graphed; understand the solution to a system of equations contains the values that satisfy both equations; find the solution to a system of equations algebraically; estimate the solution for a system of equations by graphing; understand that parallel lines have will have the same slope but never intersect; therefore, have no solution; understand the two lines that are co-linear share all of the same points; therefore, they have infinitely many solutions; and apply knowledge of systems of equations to real-world situations.

- Cell Phone Plans

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations. The students are required to find the solution algebraically to complete the task. - Classifying Solutions to Systems of Equations

This lesson unit is intended to help educators assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. - Coupon versus discount

This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented. - Expressions and Equations

A set of short tasks for grades 7 and 8 dealing with expressions and equations. - Fixing the Furnace

This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts. The solution can be determined in multiple ways, including either a graphical or algebraic approach. - Folding a Square into Thirds

The purpose of this task is to find and solve a pair of linear equations which can be used to understand a common method of folding a square piece of origami paper into thirds. - Hot Under The Collar

In this task students will compare two methods of converting temperature measurements from Celsius to Fahrenheit. - How Many Solutions?

Given an equation students are asked to find a second linear equation to create a system of equations that has one, two, none, or an infinity of solutions. - Lines and Linear Equations

This lesson unit is intended to help educators assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation. - Mixture Problems

Learning to think of a mixture as a kind of rate is an important step in learning to solve these types of problems. Any situation in which two or more different variables are combined to determine a third is a type of rate. Speed and time combine to give us distance. Wages and hours worked produce earnings. - Multiple Solutions

In this task, students will look at a number of equations and inequalities that have more than one solution. - Quinoa Pasta 1

This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns. - Sammy's Chipmunk and Squirrel Observations

This task provides a context for setting up a linear equation whose solution requires some algebraic manipulation. Because the numbers involved are not too large, students can also experiment with some small values and eventually find the solution this way; a first solution with a table is provided showing this method. On the other hand, the reasoning required without using an equation is complex enough that the simplicity and elegance of the algebraic approach can be highlighted. - Solving Equations

This task requires students to solve 5x+1=2x+7 in two ways: symbolically, the way you usually do with equations, and also with pictures of a balance. Show how each step you take symbolically is shown in the pictures. - Summer Swimming

The purpose of this task is for students to represent relationships between quantities in a context with equations and interpret the resulting system of equations in the context. This task has a wide array of uses: it could be an introductory task to systems of equations or used in assessment. - The Intersection of Two Lines

The purpose of this task is to introduce students to systems of equations. It takes skills and concepts that students know up to this point, such as writing the equation of a given line, and uses it to introduce the idea that the solution to a system of equations is the point where the graphs of the equations intersect (assuming they do). This task does not delve deeply into how to find the solution to a system of equations because it focuses more on the student's comparison between the graph and the system of equations. - The Sign of Solutions

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. - Two Lines

In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts, and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.

Standard 8.EE.7

Solve linear equations and inequalities 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, ora=bresults (whereaandbare different numbers).- Solve single-variable linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and collecting like terms.
- Solve single-variable absolute value equations.
Standard 8.EE.8

Analyze and solve pairs of simultaneous 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.
- Solve systems of two linear equations in two variables graphically, approximating when solutions are not integers and estimate solutions by graphing the equations. Solve simple cases by inspection.
For example,3x + 2y = 5and3x + 2y = 6have no solution because3x + 2ycannot simultaneously be 5 and 6.- Solve real-world and mathematical problems leading to two linear equations in two variables graphically.
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.

- Functions (8.F) - 8th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Functions.

- Chapter 3 - Mathematical Foundation (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Representations of a Line. - Chapter 3 - Student Workbook (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 8 student workbook. It covers Representations of a Line. - Chapter 4 - Mathematical Foundation (UMSMP)

This is Chapter 4 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Functions. - Chapter 4 - Student Workbook (UMSMP)

This is Chapter 4 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Functions. - Chapter 5 - Mathematical Foundation (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Simultaneous Linear Equations. - Chapter 5 - Student Workbook (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Simultaneous Linear Equations. Engage NY - Grade 8 Math Module 5: Examples of Functions from Geometry (EngageNY)

In the first topic of this 15 day 8th grade module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two. Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions. Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line. They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line. Students compare linear functions and their graphs and gain experience with non-linear functions as well. In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres. - Grade 8 Unit 4: Functions (Georgia Standards)

In this unit students will recognize a relationship as a function when each input is assigned to exactly one unique output; reason from a context, a graph, or a table, after first being clear which quantity is considered the input and which is the output; produce a counterexample: an input value with at least two output values when a relationship is not a function; explain how to verify that for each input there is exactly one output; and translate functions numerically, graphically, verbally, and algebraically. - Grade 8 Unit 5: Linear Functions (Georgia Standards)

In this unit students will graph proportional relationships; interpret unit rate as the slope; compare two different proportional relationships represented in different ways; use similar triangles to explain why the slope is the same between any two points on a non-vertical line; derive the equation y = mx for a line through the origin; derive the equation y = mx + b for a line intercepting the vertical axis at b; and interpret equations in y = mx + b form as linear functions.

- Battery Charging

This task has students engaging in a simple modeling exercise, taking verbal and numerical descriptions of battery life as a function of time and writing down linear models for these quantities. To draw conclusions about the quantities, students have to find a common way of describing them. - Foxes and Rabbits

This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function by using the example of fox and rabbit populations. - Function Rules

The purpose of this task is to connect the a function described by a verbal rule with corresponding values in a table (one of six connections to be made between the four ways to represent a function, the other two being through its graph and through an expression). It also encourages students to think more broadly about functions as relating objects other than numbers, although this broad application is not intended to be assessed. Because of its ambiguity, this task would be more suitable for use in a classroom than for assessment. - Graphing Linear Equations: T-Charts

This teaching module takes the student step-by-step through graphing linear equations. They are shown how to graph by making a T chart, plotting points, and drawing the line. - Graphs and Functions

This lesson plan is designed to help the student understand how to plot functions on the Cartesian plane and how the graphing of functions leads to lines and parabolas. - Introducing Functions

The goal of this task is to motivate the definition of a function by carefully analyzing some different relationships. In some of these relationships, one quantity can be determined in terms of the other while in others this is not possible. In this way, students are led to see what is special about a function, namely that to each input there corresponds one and only one output. - Introduction to Functions

This lesson introduces students to functions and how they are represented as rules and data tables. They also learn about dependent and independent variables. - Introduction to Linear Functions

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions. - Pennies to Heaven

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. - The Customers

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context. Instructors might prepare themselves for variations on the problems that the students might wander into (e.g., whether one person could have two home phone numbers) and how such variants affect the correct responses. - US Garbage, Version 1

In this task, the rule of the function is more conceptual: We assign to a year (an input) the total amount of garbage produced in that year (the corresponding output). Even if we didn't know the exact amount for a year, it is clear that there will not be two different amounts of garbage produced in the same year. Thus, this makes sense as a "rule" even though there is no algorithmic way to determine the output for a given input except looking it up in the table. - Vertical Line Test

This interactive applet asks the student to connect points on a plane in order to build a function and then test it to see if it's valid.

- 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. - Student Task: Linear Graphs

In this task, students are asked to match equations with linear graphs. - Student Task: Short Tasks - Functions

A set of short tasks for grade 8 dealing with functions. - 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.

Standard 8.F.1

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. (Function notation is not required in grade 8.)Standard 8.F.2

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.Standard 8.F.3

Interpret the equationy = mx + bas defining a linear function, whose graph is a straight line; give examples of functions that are not linear.For example, the function A = s^{2}giving the area of a square as a 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.

- 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. - Conjecturing About Functions

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. - Student Task: Baseball Jerseys

In this task, students will help Bill to find the best price for buying printed jerseys for the baseball team. - Student Task: Linear Graphs

In this task, students are asked to match equations with linear graphs. - Student Task: Meal Out

In this task, students use equations to solve a problem with a restaurant check. - Student Task: Short Tasks - Functions

A set of short tasks for grade 8 dealing with functions.

- Chapter 2 - Mathematical Foundation (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Proportional and Linear Relationships. - Chapter 2 - Student Workbook (UMSMP)

This is Chapter 2 of the Utah Middle School Math: Grade 8 student workbook. It covers Proportional and Linear Relationships. - Chapter 3 - Mathematical Foundation (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Representations of a Line. - Chapter 3 - Student Workbook (UMSMP)

This is Chapter 3 of the Utah Middle School Math: Grade 8 student workbook. It covers Representations of a Line. - Chapter 4 - Mathematical Foundation (UMSMP)

This is Chapter 4 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Functions. - Chapter 4 - Student Workbook (UMSMP)

This is Chapter 4 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Functions. - Chapter 5 - Mathematical Foundation (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Simultaneous Linear Equations. - Chapter 5 - Student Workbook (UMSMP)

This is Chapter 5 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Simultaneous Linear Equations. Engage NY - Grade 8 Math Module 6: Linear Functions (EngageNY)

In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the possible relationships of bivariate data. This module is important in setting a foundation for students work in algebra in Grade 9. - Grade 8 Unit 6: Linear Models and Tables (Georgia Standards)

In this unit students will identify the rate of change and the initial value from tables, graphs, equations, or verbal descriptions; write a model for a linear function; sketch a graph when given a verbal description of a situation; analyze scatter plots; informally develop a line of best fit; use bivariate data to create graphs and linear models; and recognize patterns and interpret bivariate data.

- Baseball Cards

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. - Bike Race

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving. - Chicken and Steak, variation 1

This task presents a real world situation that can be modeled with a linear function best suited for an instructional context. - Chicken and Steak, variation 2

This task is intended strictly for instructional purposes with the goal of building understandings of linear relationships within a meaningful and, hopefully, somewhat familiar context. - Delivering the Mail, Assessment Variation

This task involves constructing a linear function and interpreting its parameters in a context. Thus, this task has a medium level of complexity - Distance

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown. - Distance Across the Channel

This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation - Downhill

This task provides an opportunity to compare and contrast the graph of a function and what it represents with a drawing of the hill and the vertical and horizontal distances traversed with each mile down the slope. - Graphs and Functions

This lesson plan is designed to help the student understand how to plot functions on the Cartesian plane and how the graphing of functions leads to lines and parabolas. - Heart Rate Monitoring

In this task, students are asked to draw a graph that represents heart rate as a function of time from a verbal description of that function. Then they use the graph to draw conclusions about the context, for instance they have to understand that a heart rate greater than 100 beats per minute occurs when the graph is above the line y=100. - High School Graduation

While not a full-blown modeling problem, this task does address some aspects of modeling as described in Standard for Mathematical Practice 4. - Introduction to Functions

This lesson introduces students to functions and how they are represented as rules and data tables. They also learn about dependent and independent variables. - Lines and Linear Equations

This lesson unit is intended to help educators assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation. - Modeling with a Linear Function

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions. - Riding by the Library

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable. - Tides

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents. - Video Streaming

Given a scenario of monthly plans for video streaming students must determine what type of functions model this situation.

Standard 8.F.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.Standard 8.F.5

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.

- Geometry (8.G) - 8th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Geometry.

- Chapter 10 - Mathematical Foundation (UMSMP)

This is Chapter 10 of the Utah Middle School Math Grade 8 textbook. It provides a Mathematical Foundation for Angles, Triangles and Distance. - Chapter 10 - Student Workbook (UMSMP)

This is Chapter 10 of the Utah Middle School Math Grade 8 student workbook. It focuses Angles, Triangles and Distance. - Chapter 9 - Mathematical Foundation (UMSMP)

This is Chapter 9 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Transformations, Congruence and Similarity. - Chapter 9 - Student Workbook (UMSMP)

This is Chapter 9 of the Utah Middle School Math: Grade 8 student workbook. It focuses on these topics: Transformations, Congruence and Similarity. Engage NY - Grade 8 Math Module 2: The Concept of Congruence (EngageNY)

In this Grade 8 module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem. - Grade 8 Math Module 3: Similarity (EngageNY)

In 8th grade Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles. The module begins with the definition of dilation, properties of dilations, and compositions of dilations. One overarching goal of this module is to replace the common idea of same shape, different sizes with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles. - Grade 8 Unit 1: Transformations, Congruence, and Similarity (Georgia Standards)

In this unit students will develop the concept of transformations and the effects that each type of transformation has on an object; explore the relationship between the original figure and its image in regards to their corresponding parts being moved an equal distance which leads to concept of congruence of figures; learn to describe transformations with both words and numbers; relate rigid motions to the concept of symmetry and to use them to prove congruence or similarity of two figures; physically manipulate figures to discover properties of similar and congruent figures; and focus on the sum of the angles of a triangle and use it to find the measures of angles formed by transversals (especially with parallel lines), find the measures of exterior angles of triangles, and to informally prove congruence.

- 3D Transmographer

This lesson contains an applet that allows students to explore translations, reflections, and rotations. - A Scaled Curve

The goal of this task is to motivate and prepare students for the formal definition of dilations and similarity transformations. While these notions are typically applied to triangles and quadrilaterals, having students engage with the concepts in a context where they don't have as much training (these more "random" curves) lead students to focus more on the properties of the transformations than the properties of the figure. - A Triangle's Interior Angles

The task gives students to demonstrate several Practice Standards. Practice Standards SMP2 (Reason abstractly and quantitatively), SMP7 (Look for and make use of structure), and SMP8 (look for and express regularity in repeated reasoning) are all illustrated by the process of taking an initial solved problem -- in this case, the argument for the single given triangle -- and looking for the key structures that allow them to repeat that reasoning for a more abstract general setting. - Are These Shapes Congruent?

This cool interactive will allow students to conceptualize whether two shapes are congruent my twisting and turning them. The student then applies an understanding of congruency by diagramming and building shapes on a graph in the accompanying 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. - Are They Similar?

This goal of this task is to provide experience applying transformations to show that two polygons are similar. - Congruence of Alternate Interior Angles via Rotations

This goal of this task is to experiment with rigid motions to help visualize why alternate interior angles (made by a transverse connecting two parallel lines) are congruent: this result can then be used to establish that the sum of the angles in a triangle is 180 degrees. - Congruent Rectangles

This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent. - Congruent Segments

When given two line segments with the same length this task asks students to describe a sequence of reflections that exhibits a congruence between them. - Congruent Triangles

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation. - Creating Similar Triangles

The purpose of this task is to apply rigid motions and dilations to show that triangles are similar. - Cutting a rectangle into two congruent triangles

This task shows the congruence of two triangles in a particular geometric context arising by cutting a rectangle in half along the diagonal. - Different Areas?

The goal of this task is to motivate a discussion of similarity and slope via a counterintuitive geometric construction where it appears as if area is not conserved by cutting and reassembling a simple shape. - Effects of Dilations on Length, Area, and Angles

The purpose of this task is for students to study the impact of dilations on different measurements: segment lengths, area, and angle measure. - Escaramuza: 2D Drawing

The real-life equestrian event known as Escaramuza is used to help student make 2D drawings to make triangles. 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: Coordinates, Reflection, Rotation

A real-life equestrian event known as Escaramuza is used to demonstrate how to draw a two-dimensional diagram and then represent it on a coordinate plane. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Find the Angle

The task is an example of a direct but non-trivial problem in which students have to reason with angles and angle measurements (and in particular, their knowledge of the sum of the angles in a triangle) to deduce information from a picture. - Find the Missing Angle

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade. - Is this a rectangle?

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. - Origami Silver Rectangle

The purpose of this task is to apply geometry in order analyze the shape of a rectangle obtained by folding paper. The central geometric ideas involved are reflections (used to model the paper folds), analysis of angles in triangles, and the Pythagorean Theorem. - Partitioning a Hexagon

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations. - Point Reflection

The purpose of this task is for students to apply a reflection to a single point. - Reflecting a rectangle over a diagonal

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions. - Reflecting reflections

The goal of this task is to give students an opportunity to experiment with reflections of triangles on a coordinate grid. - Reflections, Rotations, and Translations

The goal of this task is to use technology to visualize what happens to angles and side lengths of a polygon (a triangle in this case) after a reflection, rotation, or translation. - Rigid motions and congruent angles

The goal of this task is to use rigid motions to establish some fundamental results about angles made by intersecting lines. Both vertical angles and alternate interior angles are treated. - Same Size, Same Shape?

The purpose of the task is to help students transition from the informal notion of congruence as "same size, same shape" that they learn in elementary school and begin to develop a definition of congruence in terms of rigid transformations. - 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. - Similar Triangles I

The goal of this task is to prepare students for the angle-angle criterion for triangle similarity. Since the sum of the three angles in a triangle is always 180 degrees, having two pairs of congruent corresponding angles in two triangles tells us that the third pair of corresponding angles is also congruent. - Similar Triangles II

The goal of the task is to provide an informal argument for the AA criterion for triangle similarity, appropriate for an 8th grade audience. - Street Intersections

The purpose of this task is to apply facts about angles (including congruence of vertical angles and alternate interior angles for parallel lines cut by a transverse) in order to calculate angle measures in the context of a map. - Tile Patterns I: octagons and squares

This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons. - Tile Patterns II: hexagons

In this task one of the most important examples of a tiling, with regular hexagons, is studied in detail. This provides students an opportunity to use what they know about the sum of the angles in a triangle and also the sum of angles which make a line. - Triangle congruence with coordinates

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. - Triangle's Interior Angles

This problem has students argue that the interior angles of the given triangle sum to 180 degrees, and then generalize to an arbitrary triangle via an informal argument. The original argument requires students to make use the angle measure of a straight angle, and about alternate interior angles formed by a transversal cutting a pair of parallel lines.

- 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. - Student Task: Short Tasks - Geometry

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.

Standard 8.G.1

Verify experimentally the 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.
Standard 8.G.2

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.Standard 8.G.3

Observe that orientation of the plane is preserved in rotations and translations, but not with reflections. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.Standard 8.G.4

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.Standard 8.G.5

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 sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

- The Number System (8.NS) - 8th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 - The Number System.

- Chapter 10 - Mathematical Foundation (UMSMP)

This is Chapter 10 of the Utah Middle School Math Grade 8 textbook. It provides a Mathematical Foundation for Angles, Triangles and Distance. - Chapter 10 - Student Workbook (UMSMP)

This is Chapter 10 of the Utah Middle School Math Grade 8 student workbook. It focuses Angles, Triangles and Distance.

- Grade 8 Unit 3: Geometric Applications of Exponents (Georgia Standards)

In this unit students will distinguish between rational and irrational numbers; find or estimate the square and cubed root of non-negative numbers, including 0; interpret square and cubed roots as both points of a line segment and lengths on a number line; use the properties of real numbers (commutative, associative, distributive, inverse, and identity) and the order of operations to simplify and evaluate numeric and algebraic expressions involving integer exponents, square and cubed roots; work with radical expressions and approximate them as rational numbers; solve problems involving the volume of a cylinder, cone, and sphere; determine the relationship between the hypotenuse and legs of a right triangle; use deductive reasoning to prove the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in right triangles; determine if a triangle is a right triangle, Pythagorean triple; apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and solve problems involving the Pythagorean Theorem.

- A rectangle in the coordinate plane

This task provides an opportunity to apply the Pythagorean theorem to multiple triangles in order to determine the length of the hypotenuse; the converse of the Pythagorean theorem is also required in order to conclude that certain angles are right angles. - Applying the Pythagorean Theorem in a mathematical context

This task reads "Three right triangles surround a shaded triangle; together they form a rectangle measuring 12 units by 14 units. The figure below shows some of the dimensions but is not drawn to scale. Is the shaded triangle a right triangle? Provide a proof for your answer." - Converse of the Pythagorean Theorem

This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. - Finding isosceles triangles

This task looks at some triangles in the coordinate plane and how to reason that these triangles are isosceles. - Finding the distance between points

The goal of this task is to establish the distance formula between two points in the plane and its relationship with the Pythagorean Theorem. - Glasses

This task gives students an opportunity to work with volumes of cylinders, spheres and cones. - Is this a rectangle?

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. - Points from Directions

This task provides a slightly more involved use of similarity, requiring students to translate the given directions into an accurate picture, and persevere in solving a multi-step problem: They must calculate segment lengths, requiring the use of the Pythagorean theorem, and either know or derive trigonometric properties of isosceles right triangles. - Running on the Football Field

Students need to reason as to how they can use the Pythagorean Theorem to find the distance ran by Ben Watson and Champ Bailey. The focus here should not be on who ran a greater distance, but on seeing how you can set up right triangles to apply the Pythagorean Theorem to this problem. - Sizing up Squares

The goal of this task is for students to check that the Pythagorean Theorem holds for two specific examples. Although the work of this task does not provide a proof for the full Pythagorean Theorem, it prepares students for the area calculations they will need to make as well as the difficulty of showing that a quadrilateral in the plane is a square. - Spiderbox

The purpose of this task is for students to work on their visualization skills and to apply the Pythagorean Theorem. - Two Triangles' Area

This task requires the student to draw pictures of the two triangles and also make an auxiliary construction in order to calculate the areas (with the aid of the Pythagorean Theorem). Students need to know, or be able to intuitively identify, the fact that the line of symmetry of the isosceles triangle divides the base in half, and meets the base perpendicularly.

- 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. - Student Task: Aaron's Designs

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 - Student Task: Hopewell Geometry

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. - Student Task: Jane's TV

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". - Student Task: Pythagorean Triples

In this task, the student will investigate Pythagorean Triples. - Student Task: Short Tasks - Geometry

A set of short tasks for grades 7 & 8 dealing with geometry. - Student Task: Temple 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.)

Standard 8.G.6

Explore and explain a proof of the Pythagorean Theorem and its converse.Standard 8.G.7

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

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

- 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. - Student Task: Matchsticks

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. - Student Task: Glasses

In this task, students will find the volumes of different shaped drinking glasses. - Student Task: Short Tasks - Geometry

A set of short tasks for grades 7 & 8 dealing with geometry. - Student Task: Temple 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.

- Grade 8 Unit 3: Geometric Applications of Exponents (Georgia Standards)

In this unit students will distinguish between rational and irrational numbers; find or estimate the square and cubed root of non-negative numbers, including 0; interpret square and cubed roots as both points of a line segment and lengths on a number line; use the properties of real numbers (commutative, associative, distributive, inverse, and identity) and the order of operations to simplify and evaluate numeric and algebraic expressions involving integer exponents, square and cubed roots; work with radical expressions and approximate them as rational numbers; solve problems involving the volume of a cylinder, cone, and sphere; determine the relationship between the hypotenuse and legs of a right triangle; use deductive reasoning to prove the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in right triangles; determine if a triangle is a right triangle, Pythagorean triple; apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and solve problems involving the Pythagorean Theorem.

- Comparing Snow Cones

This task asks students to use formulas for the volumes of cones, cylinders, and spheres to solve a real-world problem. - Glasses

This task gives students an opportunity to work with volumes of cylinders, spheres and cones. - Shipping Rolled Oats

Given different scenarios, students will generate dimensions of boxes and calculate the different surface areas.

Standard 8.G.9

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

- Statistics and Probability (8.SP) - 8th Grade Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Statistics and Probability.

- Chapter 6 - Mathematical Foundation (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Statistics: Investigate patterns of Association in Bivariate Data. - Chapter 6 - Student Workbook (UMSMP)

This is Chapter 6 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Statistics: Investigate patterns of Association in Bivariate Data. Engage NY - Grade 8 Math Module 6: Linear Functions (EngageNY)

In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the possible relationships of bivariate data. This module is important in setting a foundation for students work in algebra in Grade 9. - Grade 8 Unit 6: Linear Models and Tables (Georgia Standards)

In this unit students will identify the rate of change and the initial value from tables, graphs, equations, or verbal descriptions; write a model for a linear function; sketch a graph when given a verbal description of a situation; analyze scatter plots; informally develop a line of best fit; use bivariate data to create graphs and linear models; and recognize patterns and interpret bivariate data.

- Animal Brains

The purpose of this task is for students to create scatterplots, and think critically about associations and outliers in data as well as informally fit a trend line to data. This task provides an example of how students could informally fit a line to bivariate data without using technology to "magically" make the line appear. - Birds' Eggs

This task asks students to glean contextual information about bird eggs from a collection of measurements of said eggs organized in a scatter plot. In particular, students are asked to identify a correlation and use it to make interpolative predictions, and reason about the properties of specific eggs via the graphical presentation of the data. - Bivariate Data and Analysis: Anthropological Studies

This lesson opens with a video from an anthropologist explaining how he uses bivariate data to examine the impact that slavery had on the slave's height and weight. Students then use his data in the classroom activity which has them study the relationship between tibia and femur measurements and a person's stature. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. - Hand span and height

Do taller people tend to have bigger hands? To investigate this question, each student will measure his or her hand span (in cm) and height (in inches) and record these values in a table given. - Laptop Battery Charge

This task uses a situation that is familiar to students to solve a problem they probably have all encountered before: How long will it take until an electronic device has a fully charged battery? The goal of the task is to find and use a linear model answer this question. - Music and Sports

Is there an association between whether a student plays a sport and whether he or she plays a musical instrument? This task asks students to answer two questions about this and record answers on a table. They then create a graph that would help visualize the association, if any, between playing a sport and playing a musical instrument. - Sample Assessment Task: Golf Balls in Water

This sample task requires that students model approximately linear data with a linear function. To do so, they must use contextual information and construct representations of linear relationships as well as interpret parameters of the linear models in the context. Use the navigation at the upper right of this page to access the task. - Scatter Plot

The applet included in this lesson allows the student to enter ordered pairs and plot them. - Texting and Grades I

This task asks the question "what is the relationship between the number of text messages high school students send and their academic achievement?" In a random sample of 52 students from a school students were asked how many text messages were sent and their grade point average (GPA) during the most recent marking period. The data is summarized in a scatter plot of the number of text messages sent versus the GPA. For this task students must describe the relationship between number of text messages sent and GPA and discuss both the overall pattern and any deviations from the pattern. - US Airports, Assessment Variation

This is one of two assessment tasks illustrating the similarities and differences between the 8th grade standards in Functions and in Statistics and Probability. This one uses a linear function to model a relationship between two quantities that show statistical variation and do not have an exact linear relationship. - Univariate and Bivariate Data

This lesson helps students understand these two types of data and choose the best type of graph or measure appropriate to each. - What's Your Favorite Subject?

Given a table of data, students are asked whether there is there an association between a favorite academic subject and their grade for students at a school. They must support their answer by calculating appropriate relative frequencies using the given data.

- 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. - Student Task: Bird's Eggs

In this task students will user a scatter graph to investigate a possible connection between the length and width of bird's eggs. - Student Task: Birds' Eggs

In this task, students use a scatter graph to look for patterns in the size of birds' eggs. - Student Task: Scatter Diagram

In this task, students will use a scatter diagram to compare the results of two school tests. - Student Task: Short Tasks - Statistics and Probability

A set of short tasks for grades 7 and 8 reinforcing statistics and probability. - Student Task: Sugar Prices

In this task, students must use a graph showing the prices and weights of bags of sugar to find the bag offering the best value for money.

Standard 8.SP.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.Standard 8.SP.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.Standard 8.SP.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.(Calculating equations for a linear model is not expected in grade 8.)Standard 8.SP.4

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

The Online Core Resource pages are a collaborative project between the Utah State Board of Education and the Utah Education Network. If you would like to recommend a high quality resource, contact Trish French (Elementary) or Lindsey Henderson (Secondary). If you find inaccuracies or broken links contact resources@uen.org.