Math - Eighth Grade

8th Grade
Instructional Tasks

Stand alone tasks are organized to support learning of content standards. These tasks can be used as initial instruction or to support students who are struggling with a particular topic.

 

Strand: MATHEMATICAL PRACTICES (8.MP)
Back to top

 

Strand: NUMBER SYSTEM (8.NS)
Know that there are numbers that are not rational, and approximate them by rational numbers (Standards 8.NS.1–3).
  • Approximating 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.
Back to top

 

Strand: EXPRESSIONS AND EQUATIONS (8.EE)
Work with radical and integer exponents (Standards 8.EE.1–4).
  • 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).
Understand the connections between proportional relationships, lines, and linear relationships (Standards 8.EE.5–6).
  • 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.
Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations (Standards 8.EE.7–8)
  • 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.
Back to top

 

Strand: FUNCTIONS (8.F)
Define, evaluate, and compare functions (Standards 8.F.1–3)
  • 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.
Use functions to model relationships between quantities (Standards 8.F.4–5).
  • 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.
Back to top

 

Strand: GEOMETRY (8.G)
Understand congruence and similarity using physical models, transparencies, or geometry software (Standards 8.G.1–5).
  • 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.
Understand and apply the Pythagorean Theorem and its converse (Standards 8.G.6–8).
  • 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.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (Standard 8.G.9).
  • 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.
Back to top

 

Strand: STATISTICS AND PROBABILITY (8.SP)
Investigate patterns of association in bivariate data (Standards 8.SP.1–4).
  • 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.
Back to top

 

Utah Education NetworkUtah State Office of EducationThe 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.