### Fold & Cut

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?

Skip to content # Mathematical Practice: MP5 - Use appropriate tools strategically.

### Fold & Cut

### Percents

### Making Connections Between Forms of Quadratic Equations

### Rational Numbers

### Trigonometric Ratios in Right Triangles

### System of Inequalities: Math Dance

### Magic, Latin, & Sudoku Squares

### Mathemagical Card Tricks

### Pigeonhole Principle and Parity Problems

### Place Value Problems

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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?

By:

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 percent expressions in seventh grade is necessary to be able to create exponential functions in Algebra 1.

This module contains twelve activities to address the various fine points associated with percent standards.

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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 to find an equation of a parabola. This module incorporates multiple activities both in the learning packet and using Desmos activities online to encourage students to discover and practice writing equations of parabolas in their various forms. At the end of this activity students will work more efficiently with equations...

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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 their reasoning. The activity is designed to have students then fluently add, subtract, multiply, and divide these rational numbers and justify the placement of their solutions on the number line.

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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 developing the reasons the sine, cosine and tangent ratios are effective tools for solving right triangles, by analyzing patterns that emerge when the trig table is compiled from class generated data, and to understand the numbers stored in their calculator before they start using it to problem solve. An optional...

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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 how to graph and solve a system of inequalities.

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Squares and numbers, numbers and squares. There is something very satisfying about arranging numbers in a square formation, following specific rules, whether it is a Magic Square, Latin Square or Sudoku. This is probably why Sudoku puzzles are so popular. This session touches on some of the deep mathematics behind these special squares.

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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.

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Algebra / Arithmetic, Combinatorics, Geometry, Number Theory, Parity / Invariants, Problem Solving / General

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 solving session, or as individual teaser questions.

Problems are suitable for a math circle or classroom.

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In this session, we’ll learn how to solve problems related to place value. This is one of the fundamental concepts in arithmetic, something every elementary and middle school mathematics teacher should understand profoundly. Several example puzzles are followed by a rich selection of over 30 additional problems to explore.

This collection of place value problems is suitable for student circles, teacher circles, or the classroom.