# Mathematical Practice: MP3 - Construct viable arguments and critique others' reasoning.

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Mathematical Practices
Mathematical Practices
• MP1 - Make sense of problems and persevere in solving them. (83)
• MP2 - Reason abstractly and quantitatively. (53)
• MP3 - Construct viable arguments and critique others' reasoning. (58)
• MP4 - Model with mathematics. (58)
• MP5 - Use appropriate tools strategically. (40)
• MP6 - Attend to precision. (40)
• MP7 - Look for and make use of structure. (72)
• MP8 - Look for and express regularity in repeated reasoning. (61)

### Racial Profiling

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To investigate situations in the real world, we sometimes create a mathematical model. A mathematical model is a simplified version of the real world that allows us to understand the real world a little better. Over time we can change this model so that it gets closer and closer to...

### Cup Stacking

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Begin with a row of cups and end with all of the cups in a single stack. Rules: 1. Count the number of cups in a stack. That stack must jump that number of spaces. For example, 1 cup can only move 1 space; 2 cups have to move 2...

### Balance Beans

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If you start with some beans on a seesaw and you’re given certain additional beans to place on the seesaw, can you do it so the seesaw balances? In this activity, students start by trying to solve various challenges involving different arrangements of beans on the seesaw and then design...

### Percents

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Developed as part of the Math Circles of Inquiry project, this module has students grapple with different representations of percents in various contexts in order to solve real life problems. Students need fluency in percentages for real world applications such as shopping, eating at restaurants, commission based careers, etc. Understanding...

### Rational Numbers

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Developed as part of the Math Circles of Inquiry project, this module is an introductory activity for rational numbers, likely aligned with Grade 7. Students will be given five points on a number line and will be asked to estimate the values of each in a 3-part task and explain...

### Liar’s Bingo

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From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in...

### Lockers: An Open-and-Shut Case

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A classic Math Circle problem! At a large high school, there are 10000 lockers. The lockers are numbered, in order, 1, 2, 3, . . . , 10000, and to start, each locker is closed. There are also 10000 students, also numbered 1, 2, 3, . . . , 10000....

### Mathemagical Card Tricks

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There are many card tricks based on simple mathematics as opposed to sleight of hand. In this session, participants will play with a number of such tricks, test them out and work on discovering the math underneath, with a goal to formalize the mathematics that makes the trick work.

### Mathematical Games

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This session includes 15 games using manipulatives or paper and pencil. The goal is to decide which one of the two players has a winning strategy. To solve a game means to find a winning, or a non-losing, strategy for one of the players. An answer must include a detailed...

### One, Two, Three, Four: Building Numbers with Four Operations

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What numbers can you make with 1, 2, 3, and 4, using the operations of addition, subtraction, and multiplication? Work on these problems builds arithmetic fluency and provides opportunities to identify patterns, develop and defend arguments, and create conjectures. This investigation also highlights how thin the boundary is between a...