# Session Style: Problem Posing

Search
Activity Authors
Activity Circles
Click To Sort By
Audience
• 1st - 2nd (7)
• 3rd - 5th (16)
• 6th - 8th (45)
• 9th - 12th (44)
• College Level (38)
• For Teachers (44)
Topics
Topics
• Algebra / Arithmetic (17)
• Combinatorics (17)
• Geometry (18)
• Mathematical Games (12)
• Mathematical Modeling (10)
• Number Theory (16)
• Parity / Invariants (1)
• Probability and Statistics (3)
• Problem Solving / General (22)
• Social Justice Mathematics (5)
Supporting Materials
Supporting Materials
• Facilitator Guides (44)
• Featured in MCircular (9)
• Handouts (25)
• Lesson Plan (7)
• Photos & Videos (15)
• References (19)
• Virtual Tools (9)
Session Styles
Session Styles
• Manipulatives (17)
• Multiple Representations (22)
• Problem Posing (22)
• Problem Sets (35)
• Try a Smaller Problem (19)
• Work Backwards (12)
• Integrates Technology (12)
• Kinesthetic Element (5)
Mathematical Practices
Mathematical Practices
• MP1 - Make sense of problems and persevere in solving them. (43)
• MP2 - Reason abstractly and quantitatively. (53)
• MP3 - Construct viable arguments and critique others' reasoning. (38)
• MP4 - Model with mathematics. (36)
• MP5 - Use appropriate tools strategically. (21)
• MP6 - Attend to precision. (27)
• MP7 - Look for and make use of structure. (39)
• MP8 - Look for and express regularity in repeated reasoning. (33)

### Racial Profiling

By:

Topic(s):

Supporting Resources:

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...

### Liar’s Bingo

By:

Topic(s):

Supporting Resources:

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...

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

By:

Topic(s):

Supporting Resources:

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...

### Piece of Cake; Delectable Fractions and Decimals

By:

Topic(s):

Supporting Resources:

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

By:

Topic(s):

Supporting Resources:

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...

### Puzzles, Bands, and Knots

By:

Topic(s):

Supporting Resources:

This activity packed session starts with a fun Pythagorean Puzzle Proof. Then, Knot Theory is explored while experimenting with the Mobius Band, Knots and Links; Untangling Ropes and Rings, and acting out the Human Knot Experiment. These explorations are further connected to the coiling and knotting of DNA molecules. These...

### Quilt While You’re Ahead

By:

Topic(s):

Supporting Resources:

Quilts are a familiar set of cultural artifacts for many people. Quilts also happen to be beautifully mathematical. “What sorts of symmetries can a quilt block possess?” Participants will design and examine quilt blocks, and develop a taxonomy of symmetry in order to compare the blocks according to the symmetries,...

### Recruiting Change for a Dollar

By:

Topic(s):

Supporting Resources:

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...

### Semiregular Tilings

By:

Topic(s):

Supporting Resources:

Can you find all possible semiregular tilings of the plane? A tiling of the plane covers the (infinite) plane, without gaps or overlaps, using congruent copies of one or more shapes. A semiregular tiling is a tiling of the plane with certain constraints: two or more regular polygons are used,...

### Shifting Gears: Approximations in Cycling

By:

Topic(s):

Supporting Resources:

After studying James Tanton’s MTC session about bicycle tracks, avid bicyclist Michael Nakamaye started questioning the mathematics behind how a bike works.

How do gears work? How many teeth are there usually on the different gears? Why? How is a bike like a ratio machine?