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### How Many Hits?

6-8

Students will continue their investigation of the Paper Pool game by exploring more tables and organizing the results. Using the data that they collect, they will attempt to find a relationship between the size of the table, the number of hits that occur, and the pocket in which the ball lands.### Wrapping It Up

6-8

In the first four lessons of this unit, students investigated the Paper Pool game, collected data, identified patterns, and made predictions about the number of hits, the pocket in which the ball lands, and the path of travel. In this lesson, students finalize their work and write a report that summarizes all of their findings.### Which Pocket?

6-8

In this lesson, students continue their investigation by discovering a rule to predict the pocket in which the ball will land. As an extension, students can also consider the number of squares that a ball crosses while traversing its path.### Graphical Representations for the Number of Hits

6-8

Finding a rule for the number of hits is only the first step in exploring the Paper Pool game. Students can gain a deeper understanding of the patterns by considering graphical representations of the results.### Exploring the Isometric Drawing Tool

6-8

Students explore using the isometric drawing tool and gain practice and experience in manipulating drawings.### Pinwheel

6-8, 9-12

Each student creates parallelograms from square sheets of paper and connects them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and students discover a surprising result.### Finding Surface Area and Volume

6-8

Using the isometric drawing tool, students build three-dimensional figures and find the surface area and volume of each figure.### Building Using the Front-Right-Top View

6-8

Students explore drawing the front-right-top view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the front-right-top view.### Do They Match?

6-8

Using three dimensional figures they have constructed, students determine when two isometric drawings can represent the same shape and explain their reasoning. Students will also determine what possible shapes might have the same isometric drawing and explain their reasoning.### Are They Possible?

6-8

Students examine some isometric drawings that seem to be impossible and
investigate one way Escher used to create these "impossible" figures.