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### Analyzing Numeric and Geometric Patterns of Paper Pool

6-8

This mathematics excursion is based on the Paper Pool Project from the *Comparing and Scaling*unit of the Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications, (1998), Paper Pool Project, pp.106-111.

### Deep Sea Duel

3-5, 6-8

Using the online game Deep Sea Duel, students play a card game against Okta. The objective is to choose cards so that some subset of three cards within their hand has a particular sum. Students will play several variations of the game, attempt to identify a winning strategy, and compare the game to other games that they know. ### Do You Notice Sum-Thing?

6-8, 9-12

This lesson invites students to investigate the patterns when a "plus sign" (a cross-shaped arrangement of five squares) is placed on the board in various locations. Students will conjecture about the pattern of the five displayed numbers, the sum of the five numbers, and any other patterns that they notice. Students may also explore similar patterns when other shapes, such as a 2 × 1 rectangle, are placed on the hundreds board.### Elevator Arithmetic

6-8, 9-12

Students will use vertical movement of an elevator to evaluate signed number expressions.

The idea behind the method of adding and subtracting signed integers offered in this lesson and the next is that the number of rules that students have to *memorize* and the amount of *understanding* are minimal, while the underlying concepts are not trivialized.

### Explore More Tables

6-8

The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple.### Exploring Diagonals and the Pythagorean Theorem

6-8

Students further explore square roots using the diagonals of rectangles. Using measurement, students will discover a method for finding the diagonal of any rectangle when the length and width are known, which leads to the Pythagorean Theorem.### Flipping for Integers

6-8, 9-12

In this lesson, students will adapt expressions that add or subtract two signed integers.### Puzzling Pentominoes

6-8

In this lesson, students construct the 12 pentomino figures then utilize them to explore area and perimeter. By the end of the lesson students will be able to identify those constructions that are pentominoes and those that aren't. Students will also be able to calculate area and perimeter of pentomino combinations.### Walk to the Movies

6-8, 9-12

In this lesson students measure their speed walking in a hallway and predicting how long it takes them to get to the local movie theater 3 miles away. This is an open-ended problem in which students must develop a strategy on how to collect the data, how to convert the data to MPH, and finally make a prediction. In addition to reasoning skills, students will practice unit conversion, prediction, proportions, and graphing.### Factor Game

3-5, 6-8

Exercise your factoring ability against a human or the computer in this Calculation Nation game.