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
  • Sopris Textbooks
  • Understanding Algebraic Expressions (2005)

Understanding Algebraic Expressions (2005)

1: Place Value: Expanded Addition and Subtraction

Screenshot of Cargo Captain (Multi-digit Subtraction)

Cargo Captain (Multi-digit Subtraction)

You are the captain of an interplanetary cargo ship, delivering important supplies to the outer planets. The cargo can be stored in barrels, crates, and holds. (There are 10 barrels in a crate, and 10 crates in a hold.) Model multi-digit subtraction by unloading cargo on each planet. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Target Sum Card Game (Multi-digit Addition)

Target Sum Card Game (Multi-digit Addition)

Play an addition card game! The goal is to create a sum that is as close as possible to the target sum. Students will deepen their understanding of place value as they get better at playing the game. Many game options allow students to vary the game for more practice. The game can be played with one or two players. 5 Minute Preview


Lesson Info
Launch Gizmo

6: Working Horizontally

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo
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

8: Rules About Order

Screenshot of Order of Operations

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview


Lesson Info
Launch Gizmo

11: Fractions

Screenshot of Modeling Fractions (Area Models)

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Toy Factory (Set Models of Fractions)

Toy Factory (Set Models of Fractions)

Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys into groups to simplify the fractions. 5 Minute Preview


Lesson Info
Launch Gizmo

12: Adding and Subtracting Fraction

Screenshot of Adding Fractions (Fraction Tiles)

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Fractions with Unlike Denominators

Fractions with Unlike Denominators

Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview


Lesson Info
Launch Gizmo

13: Multiplication of Fractions

Screenshot of Multiplying Fractions

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview


Lesson Info
Launch Gizmo

14: Equivalent Fractions

Screenshot of Equivalent Fractions (Fraction Tiles)

Equivalent Fractions (Fraction Tiles)

Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers. 5 Minute Preview


Lesson Info
Launch Gizmo

16: Division of Fractions

Screenshot of Dividing Fractions

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview


Lesson Info
Launch Gizmo

18: Decimal Numbers

Screenshot of Modeling Whole Numbers and Decimals (Base-10 Blocks)

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Treasure Hunter (Decimals on the Number Line)

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview


Lesson Info
Launch Gizmo

22: Percents

Screenshot of Percents and Proportions

Percents and Proportions

Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview


Lesson Info
Launch Gizmo

24: Putting it All Together

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview


Lesson Info
Launch Gizmo

26: Understanding Variables

Screenshot of Using Algebraic Expressions

Using Algebraic Expressions

Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview


Lesson Info
Launch Gizmo

28: Ratios

Screenshot of Part-to-part and Part-to-whole Ratios

Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo

30: Proportions

Screenshot of Beam to Moon (Ratios and Proportions)

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Proportions and Common Multipliers

Proportions and Common Multipliers

Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview


Lesson Info
Launch Gizmo

31: Translating Statements Into Equations

Screenshot of Using Algebraic Equations

Using Algebraic Equations

Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview


Lesson Info
Launch Gizmo

33: Proportions and Geometry

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

37: Another Kind of Percent Problem

Screenshot of Percent of Change

Percent of Change

Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview


Lesson Info
Launch Gizmo

38: Another Kind of Percent Problem

Screenshot of Compound Interest

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview


Lesson Info
Launch Gizmo

41: Rate

Screenshot of Beam to Moon (Ratios and Proportions)

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Estimating Population Size

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Measuring Motion

Measuring Motion

Go on an African safari and observe a variety of animals walking and running across the savanna. Videotape the animals, and then play back the videotape to estimate animal speeds. Which animals run fastest? 5 Minute Preview


Lesson Info
Launch Gizmo

47: Double Inequalities

Screenshot of Compound Inequalities

Compound Inequalities

Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview


Lesson Info
Launch Gizmo

50: Negative Numbers

Screenshot of Integers, Opposites, and Absolute Values

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview


Lesson Info
Launch Gizmo

53: Adding Positive and Negative Numbers

Screenshot of Adding and Subtracting Integers

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Adding and Subtracting Integers with Chips

Adding and Subtracting Integers with Chips

Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview


Lesson Info
Launch Gizmo

56: Subtracting Positive and Negative Numbers

Screenshot of Adding and Subtracting Integers

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Adding and Subtracting Integers with Chips

Adding and Subtracting Integers with Chips

Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview


Lesson Info
Launch Gizmo

58: Coordinate Graphs

Screenshot of City Tour (Coordinates)

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Points in the Coordinate Plane

Points in the Coordinate Plane

Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview


Lesson Info
Launch Gizmo

61: Lines of Symmetry

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

62: Slides

Screenshot of Rock Art (Transformations)

Rock Art (Transformations)

Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview


Lesson Info
Launch Gizmo

63: Reflections

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
Screenshot of Rock Art (Transformations)

Rock Art (Transformations)

Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview


Lesson Info
Launch Gizmo

64: Similarity

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

68: X/Y Tables

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

72: Investigating Slopes of Lines and Intersecting Lines

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

81: The Associative Property

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

89: Cubic Volume

Screenshot of Balancing Blocks (Volume)

Balancing Blocks (Volume)

This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview


Lesson Info
Launch Gizmo

91: Volume of Cylinders, Prisms, and Cubes

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

92: Volume of Cones and Pyramids

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

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