Topic: Algebra / Arithmetic

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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.

Rational Numbers


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.

Systems of Linear Equations


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.

One, Two, Three, Four: Building Numbers with Four Operations


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!

Optimal Locations of Firehouses (Taxi-cab Metric)


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 are a certain distance apart and at specific addresses. What firehouse should serve a given house with a specified address? What areas of town should each firehouse serve? What if there were three firehouses? The focus of the session is on a deeper understanding of the coordinate system and notions...

Piece of Cake; Delectable Fractions and Decimals


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 interesting unsolved problem, and Do Something to try solving it. Now Think about what you notice, and Do Something to explore your results. Repeat.