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  • Number and Operations

Browse by Grade & Topic: Number and Operations

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Adding and Subtracting Integers

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

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Adding on the Number Line

Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation.

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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.

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Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line.

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Multiplying with Decimals

Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region.

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Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line.

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Square Roots

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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.

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Sums and Differences with Decimals

Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line.

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Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.

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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.

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Dividing Mixed Numbers

Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps.

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Estimating Sums and Differences

Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences.

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Finding Factors with Area Models

Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree.

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Fractions with Unlike Denominators

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

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Multiplying Mixed Numbers

Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps.

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Percents, Fractions, and Decimals

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

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Improper Fractions and Mixed Numbers

Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently.

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Order of Operations

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

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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.

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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...

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Animal Group Behavior

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A farmer in Africa is having problems with elephants eating her corn and cotton crops. As a wildlife biologist, students learn about animal group behavior and relationships of elephants and...

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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...

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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.

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

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

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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...

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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.

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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...

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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...

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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...

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Beam to Moon (Ratios and Proportions) - Metric

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...

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Number Systems

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Explore number systems and convert numbers from one base to another using counter beads in place-value columns.

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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.

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Dividing Exponential Expressions

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

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Multiplying Exponential Expressions

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

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Permutations and Combinations

Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree...

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Square Roots

FREE with no time limit!

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.

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Number Systems

FREE with no time limit!

Explore number systems and convert numbers from one base to another using counter beads in place-value columns.

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How Free Gizmos Work

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

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

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

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

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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.
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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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© 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

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Find Gizmos
  • FREE Gizmos
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  • 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
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  • Success Stories
  • Insights
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© 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

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