The following are inquiry or problem based course modules for middle and high school mathematics classrooms. These were developed as part of the Math Circles of Inquiry project unless otherwise indicated.
Contextualizing Mathematics: Fortnite - Surviving the Storm
Many activities involving putting math into context have been created. This one, like most of them, applies to high school geometry concepts.
We will explore the relationships between angles, arcs, and segments for intersecting lines in a circle through the context of the popular game Fortnite.
We are looking to build a larger library of activities that contextualize mathematics for your students, so feel free to contribute.
Efficiency with Linear Equations
for students familiar with linear equations, primarily late 8th grade, Algebra I/II and Geometry students
Student work starts with a very simple and concrete example of a linear relationship word problem which is then used to explore four forms of linear equations.
The purpose of the activity is to increase student familiarity and efficiency working with different forms of linear equations, particularly how an equation's structure can provide slope and point information without algebraic manipulation.
Designed or Middle School, probably 8th grade, but could be used in 7th grade or even in algebra
Activity which explores ideas surrounding exponents
Designed for Middle School, to be adapted for various grades as needed but likely grade 6 or 7
Focus is on developing algebraic expressions given visual situations
This module is an introduction to functions unit
This module allows students to investigate the definition of a function, function notation, key features of a function including increasing, decreasing (in both interval and inequality notation), maximum and minimum, average rate of change and domain and range.
This part of the unit (not including transforming functions) should take about 6 hour long classes.
Making Connections Between Different Forms of Quadratic Equations
High School algebra II
Examines different ways of expressing parabolas
Uses Desmos activities
Grade 7 (primarily), then pieces can be used at higher levels for review
Contains numerous activities that can be used at the discretion of the teacher for building an inquiry development of this topic or a review of this topic.
An introductory activity for rational numbers, likely aligned with Grade 7
Gets students to perform basic operations (addition, subtraction, multiplication, division) and absolute value of rational numbers
Emphasis on reasoning both abstractly and quantitatively
Ratios and Proportional Reasoning
Introduction and review activities for this topic, likely aligned with Grade 7
Introductory activity uses graphical and numerical thinking
Review activities give students choice about how to engage in their review session
Right Angle Trigonometry: Partner Heights
Applying right angle trigonometry in a double triangle problem
Provides students with an authentic mathematical experience by applying the trigonometric concepts they have learned in their geometry curriculum to solve the task of finding the heights of their group mates
Approximately one class period long
Aimed at grades 7 or 8, but also possibly useful for high school algebra
A series of videos meant to get students to develop an understanding of solving linear equations and in general what it means to be linear
Grades 7, 8, or high school algebra
Emphasizes counting, representations of mathematical objects
Students complete 3 tasks dealing with surface area and volume of rectangular and triangular prisms.
The tasks go from the concrete to the abstract as students gain understanding of what it really means to calculate surface area and volume.
A 3 act-type activity is included.
A review of area and perimeter is included.
To be used the first time students are introduced to a system of linear equations, or possibly as a refresher in high school after they are reintroduced to the subject after a period of "forgetting" it
This short module explores a graphical solution to a system of equations. From here, a teacher could explore algebraic solutions and/or different forms of linear equations.
This module will take approximately one class period and will allow students to investigate how to graph and solve a system of inequalities using a graph.
The prerequisites for this module are that students have written and graphed systems of equalities with two variables and understand the solution is where the graph lines intersect.
Trigonometric Ratios in Right Triangles
This five to six day activity is designed to help students understand trigonometric ratios, 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 extension includes introducing the Unit Circle and the Pythagorean and Quotient Identities.