Topic: Algebra / Arithmetic

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 their own challenges. Next, they try to predict which arrangements will make the seesaw balance and which ones won’t (and why!).

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.

Developed as part of the Math Circles of Inquiry project, this session is aimed at grades 7 or 8, but may be useful for high school algebra. It consists of worksheets and series of videos meant to get students to develop an understanding of solving linear equations, using the real world example of distributing M&Ms into jars.

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.

Developed as part of the Math Circles of Inquiry project, this short module explores a graphical solution to a system of equations. Students answer questions about lemonade sales and physically stand on the coordinates of a giant grid in order to see that plotting two equations on the same set of axes can give useful information. They will also gain experience in linear equation formats other than slope-intercept form and explore what the intersection points of the lines in a system of equations means.

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.

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.

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.

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 fun warm-up activity for fifth graders and deep questions investigated by research mathematicians!