Skip to main content Skip to main navigation Skip to footer
Login
Student Login
Educator Login
Sign Up For Free
Gizmos home page Gizmos home page
Gizmos home page
  • Find Gizmos
    
                                                
    See Full Search Results
    • FREE Gizmos
    • NEW Releases
    • STEM Cases
    • Browse by Standard
    • Browse by Grade & Topic
    • Browse by Core Curriculum
  • About Gizmos
    • What's a Gizmo?
    • About STEM Cases
    • What are Gizmos Investigations?
    • Take a Tour
    • Supporting All Students
    • How to Get Gizmos
    • Testimonials
    • K-5 Science
  • Research
    • The Impact of Gizmos on Student Achievement
    • The Research Behind Gizmos
  • Support
    • Professional Development Overview
    • Meet the Team
    • Course Catalog
    • Help Center
    • Site Status
  • Resources
    • Popular Gizmos Collections
    • Educator Resource Hub
    • Success Stories
    • Insights
  • Get More Info
    • Sign Up for Free
    • Request Purchasing Info
    • Request a Demo
    • Request a Pilot
    • Contact Support
  • Login
    • Student Login
    • Educator Login
  • Sign Up For Free
  • Home
  • Find Gizmos
  • Browse by Core Curriculum
  • Glencoe/McGraw-Hill Textbooks
  • Common Core Course 3: Pre-Algebra (2015)

Common Core Course 3: Pre-Algebra (2015)

1: Real Numbers

1.1: Rational Numbers

Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview


Lesson Info
Launch Gizmo

1.3: Multiply and Divide Monomials

Screenshot of Dividing Exponential Expressions

Dividing Exponential Expressions

Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo

1.4: Powers of Monomials

Screenshot of Multiplying Exponential Expressions

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo

1.6: Scientific Notation

Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits

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


Lesson Info
Launch Gizmo

1.7: Compute with Scientific Notation

Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits

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


Lesson Info
Launch Gizmo

1.8: Roots

Screenshot of Square Roots

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


Lesson Info
Launch Gizmo

1.9: Estimate Roots

Screenshot of Ordering and Approximating Square 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


Lesson Info
Launch Gizmo

1.10: Compare Real Numbers

Screenshot of Ordering Percents, Fractions, and Decimals Greater Than 1

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Ordering and Approximating Square 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


Lesson Info
Launch Gizmo

2: Equations in One Variable

2.2: Solve Two-Step Equations

Screenshot of Modeling and Solving Two-Step Equations

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


Lesson Info
Launch Gizmo
Screenshot of Solving Two-Step Equations

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo

3: Equations in Two Variables

3.2: Slope

Screenshot of 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


Lesson Info
Launch Gizmo

3.3: Equations in y=mx Form

Screenshot of Slope-Intercept Form 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


Lesson Info
Launch Gizmo

3.4: Slope-Intercept Form

Screenshot of Slope-Intercept Form 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


Lesson Info
Launch Gizmo

3.5: Graph a Line Using Intercepts

Screenshot of Point-Slope Form of a Line

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


Lesson Info
Launch Gizmo

3.7: Solve Systems of Equations by Graphing

Screenshot of Solving Linear Systems (Standard Form)

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


Lesson Info
Launch Gizmo

3.8: Solve Systems of Equations Algebraically

Screenshot of Solving Linear Systems (Slope-Intercept Form)

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 (x, y) point to be a solution of one equation, or of a system of two equations. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Solving Linear Systems (Standard Form)

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


Lesson Info
Launch Gizmo
Screenshot of Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Matrices and Special Solutions)

Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview


Lesson Info
Launch Gizmo

4: Functions

4.1: Represent Relationships

Screenshot of Introduction to 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


Lesson Info
Launch Gizmo
Screenshot of Points, Lines, and Equations

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


Lesson Info
Launch Gizmo

4.2: Relations

Screenshot of Introduction to 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


Lesson Info
Launch Gizmo

4.3: Functions

Screenshot of Introduction to 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


Lesson Info
Launch Gizmo

4.4: Linear Functions

Screenshot of Linear 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


Lesson Info
Launch Gizmo

4.6: Construct Functions

Screenshot of Translating and Scaling Functions

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview


Lesson Info
Launch Gizmo

4.8: Quadratic Functions

Screenshot of Quadratics in Factored Form

Quadratics in Factored Form

Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Quadratics in Polynomial Form

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Quadratics in Vertex Form

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo

5: Triangles and the Pythagorean Theorem

5.3: Angles of Triangles

Screenshot of Triangle Angle Sum

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


Lesson Info
Launch Gizmo
Screenshot of Triangle Inequalities

Triangle Inequalities

Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview


Lesson Info
Launch Gizmo

5.4: Polygons and Angles

Screenshot of Polygon Angle Sum

Polygon Angle Sum

Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview


Lesson Info
Launch Gizmo

5.5: The Pythagorean Theorem

Screenshot of 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


Lesson Info
Launch Gizmo
Screenshot of Pythagorean Theorem with a Geoboard

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


Lesson Info
Launch Gizmo

5.7: Distance on the Coordinate Plane

Screenshot of Distance Formula

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


Lesson Info
Launch Gizmo

6: Transformations

6.1: Translations

Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


Lesson Info
Launch Gizmo

6.2: Reflections

Screenshot of Reflections

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


Lesson Info
Launch Gizmo

6.3: Rotations

Screenshot of Rotations, Reflections, and 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


Lesson Info
Launch Gizmo

6.4: Dilations

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


Lesson Info
Launch Gizmo

7: Congruence and Similarity

7.1: Congruence and Transformations

Screenshot of Holiday Snowflake Designer

Holiday Snowflake Designer

Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Quilting Bee (Symmetry)

Quilting Bee (Symmetry)

Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview


Lesson Info
Launch Gizmo

7.2: Congruence

Screenshot of Congruence in Right Triangles

Congruence in Right Triangles

Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Proving Triangles Congruent

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


Lesson Info
Launch Gizmo

7.3: Similarity and Transformations

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of 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


Lesson Info
Launch Gizmo
Screenshot of Similarity in Right Triangles

Similarity in Right Triangles

Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview


Lesson Info
Launch Gizmo

7.4: Properties of Similar Polygons

Screenshot of 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


Lesson Info
Launch Gizmo
Screenshot of Similarity in Right Triangles

Similarity in Right Triangles

Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview


Lesson Info
Launch Gizmo

7.7: Area and Perimeter of Similar Figures

Screenshot of Perimeters and Areas of Similar Figures

Perimeters and Areas of Similar Figures

Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview


Lesson Info
Launch Gizmo

8: Volume and Surface Area

8.1: Volume of Cylinders

Screenshot of Prisms and 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


Lesson Info
Launch Gizmo

8.2: Volume of Cones

Screenshot of Pyramids and 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


Lesson Info
Launch Gizmo

8.4: Surface Area of Cylinders

Screenshot of Surface and Lateral Areas of Prisms and Cylinders

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


Lesson Info
Launch Gizmo

8.5: Surface Area of Cones

Screenshot of Surface and Lateral Areas of Pyramids and Cones

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


Lesson Info
Launch Gizmo

9: Scatter Plots and Data Analysis

9.1: Scatter Plots

Screenshot of Trends in Scatter Plots

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


Lesson Info
Launch Gizmo

9.2: Lines of Best Fit

Screenshot of Least-Squares Best Fit Lines

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


Lesson Info
Launch Gizmo
Screenshot of Trends in Scatter Plots

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


Lesson Info
Launch Gizmo

9.4: Descriptive Statistics

Screenshot of Box-and-Whisker Plots

Box-and-Whisker Plots

Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Mean, Median, and Mode

Mean, Median, and Mode

Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview


Lesson Info
Launch Gizmo

9.5: Measures of Variation

Screenshot of Box-and-Whisker Plots

Box-and-Whisker Plots

Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Sight vs. Sound Reactions

Sight vs. Sound Reactions

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Time Estimation

Time Estimation

Try to estimate the passage of time by selecting a time interval, clicking the Start button, and clicking Stop when you think the interval has passed. The estimate and percent error are recorded. Compare different techniques for estimating time, as well as the average error for long time intervals versus shorter intervals. 5 Minute Preview


Lesson Info
Launch Gizmo

9.6: Analyze Data Distributions

Screenshot of Sight vs. Sound Reactions

Sight vs. Sound Reactions

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Time Estimation

Time Estimation

Try to estimate the passage of time by selecting a time interval, clicking the Start button, and clicking Stop when you think the interval has passed. The estimate and percent error are recorded. Compare different techniques for estimating time, as well as the average error for long time intervals versus shorter intervals. 5 Minute Preview


Lesson Info
Launch Gizmo

How Free Gizmos Work

Gizmos icon

Start teaching with 20-40 Free Gizmos. See the full list.

Lesson materials list icon

Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.

Time icon

All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.

Refresh icon

Free Gizmos change each semester. The new collection will be available January 1 and July 1.

Sign Up for Free

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.

Realtime reporting icon

Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap

Time icon

STEM Cases take between 30-90 minutes for students to complete, depending on the case.

Save icon

Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.

Grades icon

Multiple grade-appropriate versions, or levels, exist for each STEM Case.

Handbook icon

Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.

STEM Case Help & Resources Sign Up for Free

Want More?

Check out these quick links.

  • Sign up for a FREE Trial!
  • Take a Tour
  • Get Help

Find Your Solution

Start playing, exploring and learning today with a free account. Or contact us for a quote or demo.

Sign Up For Free Get a Quote
Find Your Solution
Gizmos logo Brought to you by ExploreLearning

© 2025 ExploreLearning. All rights reserved. Gizmo and Gizmos are registered trademarks of ExploreLearning. STEM Cases, Handbooks and the associated Realtime Reporting System are protected by US Patent No. 10,410,534

Other Products

Reflex icon Frax icon Science4Us icon
Find Gizmos
  • FREE Gizmos
  • NEW Releases
  • STEM Cases
  • Browse by Standard
  • Browse by Grade & Topic
  • Browse by Core Curriculum
About Gizmos
  • What's a Gizmo?
  • About STEM Cases
  • What are Gizmos Investigations?
  • Take a Tour
  • Supporting All Students
  • How to Get Gizmos
  • Testimonials
  • K-5 Science
Research
  • The Impact of Gizmos on Student Achievement
  • The Research Behind Gizmos
Support
  • Professional Development Overview
  • Meet the Team
  • Course Catalog
  • Help Center
  • Site Status
Resources
  • Popular Gizmos Collections
  • Educator Resource Hub
  • Success Stories
  • Insights
Get More Info
  • Sign Up for Free
  • Request Purchasing Info
  • Request a Demo
  • Request a Pilot
  • Contact Support

Get Connected

  • Support Form
  • Toll-Free 866-882-4141
  • Local +1-434-293-7043
  • Newsletter Sign-Up
  • Facebook
  • Twitter
  • YouTube
  • Instagram

Other Products

Reflex icon Frax icon Science4Us icon

© 2025 ExploreLearning. All rights reserved. Gizmo and Gizmos are registered trademarks of ExploreLearning. STEM Cases, Handbooks and the associated Realtime Reporting System are protected by US Patent No. 10,410,534

  • Terms and Conditions
  • Privacy Policy
  • Accessibility
  • System Requirements
  • Sitemap