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- enVision Mathematics Grade 8 (Georgia Edition) (2021)
enVision Mathematics Grade 8 (Georgia Edition) (2021)
1: Real Numbers
1.1: Rational Numbers as Decimals
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
1.3: Compare and Order Real Numbers
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
1.4: Evaluate Square Roots and Cube Roots
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
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
1.6: Use Properties of Integer Exponents
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
1.7: More Properties of Integer Exponents
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
1.9: Understand Scientific Notation
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
1.10: Operations with Numbers in Scientific Notation
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
2: Analyze and Solve Linear Equations
2.2: Solve Equations with Variables on Both Sides
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
2.3: Solve Multistep Equations
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
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
2.4: Equations with No Solutions or Infinitely Many Solutions
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
GA-1: Justify Solution Steps Using Properties of Equality
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
GA-2: Solve Equations and Inequalities with Multiple Variables
Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
2.6: Connect Proportional Relationships and Slope
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
2.7: Analyze Linear Equations: y = mx
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
2.8: Understand the y-Intercept of a Line
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
2.9: Analyze Linear Equations: y = mx + b
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
3: Use Functions to Model Relationships
3.1: Understand Relations and Functions
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
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
3.2: Connect Representations of Functions
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
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
3.4: Construct Functions to Model Linear Relationships
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
GA-3: Write Linear Functions in Different Forms
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
GA-4: Graph Linear Functions
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
3.5: Intervals of Increase and Decrease
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
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
4: Investigate Bivariate Data
4.1: Construct and Interpret Scatter Plots
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
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
4.2: Analyze Linear Associations
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
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
4.3: Use Linear Models to Make Predictions
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
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
5: Analyze and Solve Systems of Linear Equations
5.2: Solve Systems by Graphing
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
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
5.3: Solve Systems by Substitution
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
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
5.4: Solve Systems by Elimination
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
GA-5: Parallel and Perpendicular Lines
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
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
6: Congruence and Similarity
6.1: Analyze Translations
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
6.2: Analyze Reflections
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
6.3: Analyze Rotations
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
6.4: Compose Transformations
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
6.5: Understand Congruent Figures
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
6.6: Describe Dilations
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
6.7: Understand Similar Figures
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
6.9: Interior and Exterior Angles of Triangles
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
6.10: Angle-Angle Triangle Similarity
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
7: Understand and Apply the Pythagorean Theorem
7.1: Understand the Pythagorean Theorem
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
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
7.2: Understand the Converse of the Pythagorean Theorem
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
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
7.3: Apply the Pythagorean Theorem to Solve Problems
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
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
7.4: Find Distance in the Coordinate Plane
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
8: Solve Problems Involving Surface Area and Volume
8.1: Find Surface Area of Three-Dimensional Figures
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder 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
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
8.2: Find Volume of Cylinders
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
8.3: Find Volume of Cones
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
8.4: Find Volume of Spheres
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
How Free Gizmos Work
Start teaching with 20-40 Free Gizmos. See the full list.
Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
Free Gizmos change each semester. The new collection will be available January 1 and July 1.
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.
Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
STEM Cases take between 30-90 minutes for students to complete, depending on the case.
Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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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