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#### Right or Left: Adding and Subtracting Integers

Students add and subtract integers using animations on a number line, and understand that subtracting an integer is the same as adding its opposite.

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#### Making Means: Data Distribution and Averages

Students drag data points on a number line and observe how the mean of their values changes. Students can add, remove, and drag the data points to different locations to create examples of data sets with a given mean.

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#### Mean Meets the Median: Measures of Central Tendency

Students drag a fixed number of data points to different locations on a number line and observe the effects on the median and the mean. Students can explore the difference in the median that occurs between having an even and an odd number of data points. The emphasis of the activity is on understanding how the mean and median behave depending both on how the data is distributed and on the number of data points.

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#### Making a Kaleidoscope: Exploring Rotations

Students create virtual kaleidoscopes by rotating quadrilaterals and then animating them. Students learn that rotated figures keep their size and shape; only their orientation changes. Students make a variety of kaleidoscopes, each with a different number of quadrilaterals and amount of rotation.

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#### Mellow Yellow: Interpreting Graphs

Students interpret linear piecewise time-distance graphs that represent different stories about a character, Mellow Yellow. They decide whether a given graph corresponds to the motions (walking fast, walking slow, stopping, or going backward) described in the story. Students then create stories based on given graphs and create graphs based on given stories.

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#### Hikers: Solving Through Multiple Representations

Students use tables, graphs, and equations to represent and solve a real-world problem about two hikers walking at different speeds in opposite directions along the same trail.

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#### Quadrilateral Pretenders: Classifying Quadrilaterals

Students drag the edges and vertices of various *Sketchpad* quadrilaterals to discover which are constructed to have specific characteristics. As they make distinctions on the basis of these characteristics, they deepen their understanding of the definitions of various quadrilaterals, their properties, and the relationships among them.

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#### Parallel Pairs: Parallelogram and Triangle Area

Students explore the relationship between the areas of parallelograms and triangles using a process called shearing. Students discover that shearing does not affect the area, but changing the lengths of the height and base does. Based on their observations, students write formulas for the area of a parallelogram and the area of a triangle.

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#### Balancing with Balloons: Solving Equations with Negatives

Students use a *Sketchpad* pan balance model to solve a sequence of equations with positive numbers and variables (represented by weights), and negative numbers and variables (represented by balloons). As the problems increase in difficulty, students go from manipulating the pan balance to solving equations independent of the balance.

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