## Activity Database

Search
Activity Authors
Activity Circles
Click To Sort By
Audience
• 1st - 2nd (12)
• 3rd - 5th (30)
• 6th - 8th (83)
• 9th - 12th (85)
• College Level (72)
• For Teachers (81)
Topics
Topics
• Problem Solving / General (39)
• Probability and Statistics (3)
• Social Justice Mathematics (5)
• Algebra / Arithmetic (33)
• Combinatorics (31)
• Geometry (36)
• Mathematical Games (26)
• Mathematical Modeling (15)
• Number Theory (25)
• Parity / Invariants (2)
Supporting Materials
Supporting Materials
• Facilitator Guides (88)
• 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)

### Pick’s Theorem

By:

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 pegs, and the number of interior pegs.

This session is also suitable for student circles or the classroom.

### Visualization in Algebra

By:

Many topics in mathematics can be made much clearer when symmetric aspects are made clear or when nice alternative visualizations are possible. When this occurs, it helps both the student and the teacher. We will examine visualization and symmetry in a very general way by means of a set of problems.

There is a large amount of potential classroom material here, and almost any small part of it could be used for an entire class session.

### Introduction to Diophantine Equations

By:

Diophantine equation – an equation whose roots are required to be integers. In this article we will only touch on a few tiny parts of the field of linear Diophantine equations. Some of the tools introduced, however, will be useful in many other parts of the subject. Suppose that dolls sell for \$7 each, and toy train sets sell for \$18. A store sells 25 total dolls and train sets, and the total amount received is \$208. How many of each were sold? Easy, two equations and two unknowns. However what if the problem was changed to: Suppose a store...

### KenKen

By:

Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic skills. The puzzles range in difficulty from very simple to incredibly difficult. Students who get hooked on the puzzle will be forced to drill their simple addition, subtraction, multiplication and division facts.

### Big Numbers

By:

Using the standard arithmetic operations (addition, subtraction, multiplication, division and exponentiation), what is the largest number you can make using three copies of the digit “9”? While this would be a pretty large number, with a little cleverness you can do far better. This session explores VERY large numbers!

### Catalan Numbers

By:

Suppose you have n pairs of parentheses and you would like to form valid groupings of them, how many groupings are there for each value of n? How many “mountain ranges” can you form with n upstrokes and n downstrokes that all stay above the original line? What about counting the number of ways to triangulate a regular polygon with n + 2 sides? We begin with a set of problems that will be shown to be completely equivalent. The solution to each problem is the same sequence of numbers called the Catalan numbers.

### Coloring

By:

Consider a 9 × 9 chessboard, and you wish to cover as much of it as possible using figures shaped like the one to the right, where each of the four squares is the same size as the squares on a chessboard. The pieces can be rotated or flipped over. What is the maximum number of non-overlapping pieces that you can fit? Here are nine problems exploring coloring, or covering, grids and other shapes.

This collection of problems can be used in a single problem solving session, or as individual teaser questions.

### Conway’s Rational Tangles

By:

What do adding positive and negative fractions have to do with tying knots? In this entertaining lesson, students will use ropes to explore and identify mathematical operations that untangle knots and lead to new thinking. Simple operations of twists and rotations circle back to practicing the addition of positive and negative fractions.

### Practical Probability: Casino Odds and Sucker Bets

By:

Gambling casinos are there to make money, so in almost every instance, the games you can bet on will, in the long run, make money for the casino. However, to make people gamble, it is to the casino’s advantage to make the bets appear to be “fair bets,” or even advantageous to the gambler. Similarly, “sucker bets” are propositions that look advantageous to one person but are really biased in favor of the other. We’ll examine what is meant by a fair or biased bet and look in detail at some casino games and sucker bets. Various problems can be...