## Active, Engaging, Effective Learning

## Each activity in FogStone Isle is centered around a math topic and its concepts. The program adapts to each student’s level, adjusting the difficulty of the problems and the concept being learned as they progress through the game. Below is a sample of some of the activities in FogStone Isle, all focused on aiding late elementary through middle school students in mastering the most difficult math concepts.

## Fraction Addition

Learn more about how Cignition deeply integrates neuroscience to improve math learning: cignition.com/neuroscience

## Fraction Multiplication

Common Sense Education reviewer stated, “*with an exciting sense of urgency, kids compare fractions to decimals to determine if they have enough water left to take out the weeds. The ever-changing grid on the farm plot lights up to give an additional visual representation. This is incredibly powerful in helping kids truly understand what it means to multiply fractions.*”

Learn more about how Cignition deeply integrates neuroscience to improve math learning: cignition.com/neuroscience

## Fraction Division

This approach is encapsulated in the action of a fun and engaging game: the Gruffins raise Rollerdillos, a feisty creature that tends to run amok if not kept corralled. In this exciting game, students use fraction division to create a pen around the rolling Rollerdillos before they escape. Each time a piece of fence is built, the student is solving a fraction division problem. Fraction division is taught conceptually using the panels of the fence as the divisor and the fence length as the dividend. The activity goes through a series of fraction division problems to illustrate why you invert and multiply when solving a fraction division problem.

Learn more about how Cignition deeply integrates neuroscience to improve math learning: cignition.com/neuroscience

## Fraction Equivalence

To keep the Gruffins warm on cold winter nights, students add chimneys to their houses. To build the chimney, tiles appear that represent different fraction sizes (visual representations and/or numbers). By alternating the representation of fractions as numbers and visuals this activity deepens students conceptual understanding of equivalent fractions, a common stumbling block for many students. A scaffolding tool is available to help students find the equivalent fractions (numbers and visual representations) by multiplying or dividing the numerator and denominator by the same amount.

## Ratio and Proportion

In the example shown in this video, the student has discovered how to use equivalent ratios to simplify manufacturing – creating products requiring a final parts ratio of 6:4 by running through two phases of stamping out parts in a 3:2 ratio – thereby cutting in half the number of machines needed to manufacture their product.

## Adding and Subtracting Decimals

This game gives children practice adding and subtracting decimals to the thousandths. By choosing from a variety of wallpaper colors and styles, students decorate the inside walls of their houses. Students are given tools to add wallpaper (adding decimals) and cut wallpaper (subtracting decimals) to obtain the right fit for each inside wall. Scaffolding tools and inquiry based lessons are included to deepen conceptual understanding and address misconceptions.