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Vermont - Mathematics: 8th Grade
Common Core State Standards | Adopted: 2010
CCSS.Math.Content.8.NS: : The Number System
CCSS.Math.Content.8.NS.A: : Know that there are numbers that are not rational, and approximate them by rational numbers.
CCSS.Math.Content.8.NS.A.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.
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
CCSS.Math.Content.8.NS.A.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., pi²).
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
![Screenshot of Square Roots](/Assets/img/blank.gif)
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
CCSS.Math.Content.8.EE: : Expressions and Equations
CCSS.Math.Content.8.EE.A: : Work with radicals and integer exponents.
CCSS.Math.Content.8.EE.A.1: : Know and apply the properties of integer exponents to generate equivalent numerical expressions.
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
CCSS.Math.Content.8.EE.A.2: : Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.
![Screenshot of Square Roots](/Assets/img/blank.gif)
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
CCSS.Math.Content.8.EE.A.3: : Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
![Screenshot of Number Systems](/Assets/img/blank.gif)
Number Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
CCSS.Math.Content.8.EE.A.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.
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
CCSS.Math.Content.8.EE.B: : Understand the connections between proportional relationships, lines, and linear equations.
CCSS.Math.Content.8.EE.B.5: : Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
CCSS.Math.Content.8.EE.B.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 equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
CCSS.Math.Content.8.EE.C: : Analyze and solve linear equations and pairs of simultaneous linear equations.
CCSS.Math.Content.8.EE.C.7: : Solve linear equations in one variable.
CCSS.Math.Content.8.EE.C.7.a: : Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
CCSS.Math.Content.8.EE.C.7.b: : Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
CCSS.Math.Content.8.EE.C.8: : Analyze and solve pairs of simultaneous linear equations.
CCSS.Math.Content.8.EE.C.8.a: : 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.
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Cat and Mouse (Modeling with Linear Systems) - Metric](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
CCSS.Math.Content.8.EE.C.8.b: : Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Cat and Mouse (Modeling with Linear Systems) - Metric](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
CCSS.Math.Content.8.EE.C.8.c: : Solve real-world and mathematical problems leading to two linear equations in two variables.
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Cat and Mouse (Modeling with Linear Systems) - Metric](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
CCSS.Math.Content.8.F: : Functions
CCSS.Math.Content.8.F.A: : Define, evaluate, and compare functions.
CCSS.Math.Content.8.F.A.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.
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
CCSS.Math.Content.8.F.A.3: : Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
CCSS.Math.Content.8.F.B: : Use functions to model relationships between quantities.
CCSS.Math.Content.8.F.B.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.
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Cat and Mouse (Modeling with Linear Systems) - Metric](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time Graphs - Metric](/Assets/img/blank.gif)
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs - Metric](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
CCSS.Math.Content.8.F.B.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.
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Distance-Time Graphs](/Assets/img/blank.gif)
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time Graphs - Metric](/Assets/img/blank.gif)
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
![Screenshot of Distance-Time and Velocity-Time Graphs - Metric](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
CCSS.Math.Content.8.G: : Geometry
CCSS.Math.Content.8.G.A: : Understand congruence and similarity using physical models, transparencies, or geometry software.
CCSS.Math.Content.8.G.A.1: : Verify experimentally the properties of rotations, reflections, and translations:
CCSS.Math.Content.8.G.A.1.a: : Lines are taken to lines, and line segments to line segments of the same length.
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
CCSS.Math.Content.8.G.A.1.b: : Angles are taken to angles of the same measure.
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
CCSS.Math.Content.8.G.A.1.c: : Parallel lines are taken to parallel lines.
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
CCSS.Math.Content.8.G.A.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.
![Screenshot of Reflections](/Assets/img/blank.gif)
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
CCSS.Math.Content.8.G.A.3: : Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
CCSS.Math.Content.8.G.A.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.
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
CCSS.Math.Content.8.G.A.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.
![Screenshot of Constructing Parallel and Perpendicular Lines](/Assets/img/blank.gif)
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
![Screenshot of Proving Triangles Congruent](/Assets/img/blank.gif)
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
CCSS.Math.Content.8.G.B: : Understand and apply the Pythagorean Theorem.
CCSS.Math.Content.8.G.B.6: : Explain a proof of the Pythagorean Theorem and its converse.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
CCSS.Math.Content.8.G.B.7: : Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
CCSS.Math.Content.8.G.B.8: : Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
![Screenshot of Distance Formula](/Assets/img/blank.gif)
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
CCSS.Math.Content.8.G.C: : Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
CCSS.Math.Content.8.G.C.9: : Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
![Screenshot of Measuring Volume](/Assets/img/blank.gif)
Measuring Volume
Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
CCSS.Math.Content.8.SP: : Statistics and Probability
CCSS.Math.Content.8.SP.A: : Investigate patterns of association in bivariate data.
CCSS.Math.Content.8.SP.A.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.
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
CCSS.Math.Content.8.SP.A.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.
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
CCSS.Math.Content.8.SP.A.3: : Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
![Screenshot of Correlation](/Assets/img/blank.gif)
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
Correlation last revised: 8/22/2022
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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Start teaching with 20-40 Free Gizmos. See the full list.
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