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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.

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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.

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Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections.

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Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line.

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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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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.

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Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find fractions that are equivalent to one-half.

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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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Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators.

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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.

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

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

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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.

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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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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.

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

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

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

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

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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.

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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.

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Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions.

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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.

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The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This is a nice illustration of division with remainders.

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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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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 humans with bees. Students collect data from the farm and elephants to hypothesize and test solutions that will protect the crops without hurting the elephants.

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5 Minute Preview

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.

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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 humans with bees. Students collect data from the farm and elephants to hypothesize and test solutions that will protect the crops without hurting the elephants.