# Audience: 3rd - 5th

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Audience
• 1st - 2nd (12)
• 3rd - 5th (30)
• 6th - 8th (83)
• 9th - 12th (85)
• College Level (72)
• For Teachers (81)
Topics
Topics
• Algebra / Arithmetic (33)
• Combinatorics (31)
• Geometry (36)
• Mathematical Games (26)
• Mathematical Modeling (15)
• Number Theory (25)
• Parity / Invariants (2)
• Probability and Statistics (3)
• Problem Solving / General (39)
• Social Justice Mathematics (5)
Supporting Materials
Supporting Materials
• Facilitator Guides (88)
• Featured in MCircular (25)
• Handouts (38)
• Lesson Plan (10)
• Photos & Videos (28)
• References (36)
• Virtual Tools (17)
Session Styles
Session Styles
• Integrates Technology (17)
• Kinesthetic Element (11)
• Manipulatives (33)
• Multiple Representations (33)
• Problem Posing (45)
• Problem Sets (51)
• Try a Smaller Problem (40)
• Work Backwards (21)
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)

### 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?

### 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...

### Locked Out: A Breakout Box Session for Your Circle

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Escape Rooms and “Bomb Disposal” activities are growing in popularity as a form of team building and entertainment. This session blends the two ideas to create a cooperative math activity where the challenge is to solve math problems whose solutions generate combinations to open a locked box. The math problems...

### 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...

### Piece of Cake; Delectable Fractions and Decimals

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While exploring the relationship between fractions and decimals, participants will have the opportunity to practice operations with fractions, notice and explain patterns, review understandings of place value and number sense, and justify their reasoning. You can get a taste of math research by repeating these two steps: Think about an...

### 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...

### Primes, Divisibility, and Modular Arithmetic

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Number theory is all about adding and multiplying integers: pretty simple stuff, good for elementary school or for PhD mathematicians. Dr. Arnold Ross says of number theory, that the purpose is “to think deeply of simple things.” So let’s do that together. This session includes multiple problem sets beginning with...

### Recruiting Change for a Dollar

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How many different ways are there to make change for a dollar? As mathematicians we often search for patterns in a problem. However, for this problem, there is no simple, predictable pattern to build to an answer, encouraging participants to reach outside their comfort zones and ponder alternative strategies in...