Browse by Grade & Topic: Number and Operations

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

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.

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.

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

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

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.

Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid.

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

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.

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

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.

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

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

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.

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

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

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

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

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

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...

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...

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.

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

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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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.

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...

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...

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...

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...

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

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

Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps.

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

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

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...

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.

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...

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...

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.

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