# Topic: Geometry

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• 6th - 8th (1)
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• Geometry (2)
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Mathematical Practices
Mathematical Practices
• MP1 - Make sense of problems and persevere in solving them. (2)
• MP2 - Reason abstractly and quantitatively. (1)
• MP4 - Model with mathematics. (2)
• MP5 - Use appropriate tools strategically. (2)
• MP6 - Attend to precision. (1)
• MP7 - Look for and make use of structure. (1)
• MP8 - Look for and express regularity in repeated reasoning. (2)

### Mural Mathematics

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Students will explore existing equity themed murals to identify themes, and the mathematics necessary to plan/create a city mural. Students will utilize Google maps tools to begin connecting Mathematical representations to precisely interpret circle properties and apply them to the mural design.

### Fold & Cut

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What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?

### Making Connections Between Forms of Quadratic Equations

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Developed as part of the Math Circles of Inquiry project, the goal of this module is to help students in Algebra II become fluent in the various forms of a parabola equation based on the information that they are given. Students sometimes fail to understand that there are multiple ways...

### Trigonometric Ratios in Right Triangles

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Developed as part of the Math Circles of Inquiry project, this five to six day activity is designed to help students understand trigonometric ratios, by building on their understanding of similar triangles and ratios of corresponding sides. The purpose of this module is for students to spend time and energy...

### Systems of Linear Equations

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Developed as part of the Math Circles of Inquiry project, this short module explores a graphical solution to a system of equations. Students answer questions about lemonade sales and physically stand on the coordinates of a giant grid in order to see that plotting two equations on the same set...

### System of Inequalities: Math Dance

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You want this year’s dance to be LIT! The dance committee has a goal of fundraising \$3,500 through ticket sales. How many tickets do they need to sell? Developed as part of the Math Circles of Inquiry project, this module presents an engaging problem which will allow students to investigate...

### Optimal Locations of Firehouses (Taxi-cab Metric)

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This session asks participants to expand their notion of “distance,” using a nontraditional taxicab metric instead of the usual Pythagorean notion. Participants are guided to construct the equivalent of “circles” with this new metric and to look at the intersections of multiple such circles. In particular, two firehouses in Gridtown...

### Pigeonhole Principle and Parity Problems

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The pigeonhole principle states that if n pigeons are put into m cubbies, with n > m, then at least one cubby must contain more than one pigeon. Parity problems deal with odd and even integers. Here is a collection of problems that can be used in a single problem...

### Pick’s Theorem

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Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter...

### Probability

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Some probability problems can be solved by drawing a picture; this approach is sometimes called geometric probability. Other approaches can include experimentation, looking at smaller cases, looking at extreme cases, recursion, or carefully listing possibilities. This session includes ten problems that can be explored alone or in sets, providing material...