# Browse by Grade & Topic: Number and Operations

## Find Gizmos organized by grade level and topic.

See How FREE Gizmos WorkAdding and Subtracting Integers

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

Lesson Info Launch GizmoAdding 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.

Lesson Info Launch GizmoAdding 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.

Lesson Info Launch GizmoComparing and Ordering Decimals

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

Lesson Info Launch GizmoIntegers, 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.

Lesson Info Launch GizmoMultiplying 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.

Lesson Info Launch GizmoOrdering 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.

Lesson Info Launch GizmoSolving Equations on the Number Line

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

Lesson Info Launch GizmoSquare 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.

Lesson Info Launch GizmoSums 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.

Lesson Info Launch GizmoRational 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.

Lesson Info Launch GizmoDividing 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.

Lesson Info Launch GizmoDividing Mixed Numbers

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

Lesson Info Launch GizmoFinding 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.

Lesson Info Launch GizmoFractions with Unlike Denominators

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

Lesson Info Launch GizmoMultiplying Mixed Numbers

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

Lesson Info Launch GizmoPercents, Fractions, and Decimals

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

Lesson Info Launch GizmoImproper 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.

Lesson Info Launch GizmoOrdering 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.

Lesson Info Launch GizmoMultiplying 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...

Lesson Info Launch GizmoBeam 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...

Lesson Info Launch GizmoEstimating 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.

Lesson Info Launch GizmoPart-to-part and Part-to-whole Ratios

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

Lesson Info Launch GizmoPercent 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...

Lesson Info Launch GizmoPercents 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.

Lesson Info Launch GizmoProportions 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...

Lesson Info Launch GizmoDistance-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...

Lesson Info Launch GizmoDistance-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...

Lesson Info Launch GizmoBeam 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...

Lesson Info Launch GizmoOrder of Operations

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

Lesson Info Launch GizmoNumber Systems

FREE *with no time limit!*

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

Lesson Info Launch GizmoExponents 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.

Lesson Info Launch GizmoDividing Exponential Expressions

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

Lesson Info Launch GizmoMultiplying Exponential Expressions

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

Lesson Info Launch GizmoPermutations 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...

Lesson Info Launch GizmoPoints in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.

Lesson Info Launch GizmoRoots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and...

Lesson Info Launch GizmoSolving 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...

Lesson Info Launch GizmoDilations

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.

Lesson Info Launch GizmoTranslations

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

Lesson Info Launch GizmoSquare 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.

Lesson Info Launch GizmoNumber Systems

FREE *with no time limit!*

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

Lesson Info Launch GizmoHow 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 Jan 01, 2023.

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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