Middle and Upper School Math, Morning Course Block Instructor: Ron Lancaster, Univ of Toronto, Toronto, Canada
In this workshop we will begin by examining problems that all students in grades 7 - 12 can enter into by making use of the floor space in classrooms, gymnasiums and hallways. We will create physical representations of the solutions to these problems that can be displayed on a wall or hung from a ceiling. We will examine other low-floor, high-ceiling and multi-grade problems that don't make use of the floor space and discuss how all students can access all of these problems according to their own competency and background knowledge, and learn alongside their peers with different strengths.
Middle School Math, Morning Course Block Instructor: Ira Nirenberg, Ben Franklin HS (ret)
Fraction mathematics is one of the most challenging topics for middle school students. In fact, there is a substantial body of research that asserts that a poor understanding of fraction mathematics is the best indicator of a poor understanding of algebraic concepts. In this day long workshop we will address strategies in teaching fractions from the Fraction ThinkBook: Bridging the Fraction-Algebra Gap. The methods used are visual and conceptual and seek to build student comprehension and mathematical intuition rather than techniques that focus on memorization or rote learning. We’ll also take a look at a few challenging problems involving ratio, proportion, decimals and percentages, and, explore the rules governing fraction mathematics. A free digital copy of the Fraction ThinkBook is available for all participants on Amazon.com. Please contact me at firstname.lastname@example.org for information on claiming your free copy. This workshop addresses CORE concepts!
In this six-hour course, designed for upper elementary and middle school teachers, we will address strategies in teaching fractions from the Fraction ThinkBook: Bridging the Fraction-Algebra Gap. The methods used are visual and conceptual and seek to build student comprehension and mathematical intuition rather than techniques that focus on memorization or rote learning. We’ll also take a look at a few challenging problems involving ratio, proportion, decimals and percentages.
Upper School Math, Morning Course Block Instructor: Karen Bryant, St. Marks School in Southborough, MA
Math Modeling is a six hour course suitable for upper school mathematics teachers who want to help their students see how mathematics can be applied to real world problems. You will learn how to engage your students to solve such problems as:
How can you determine if a particular flight you want to book is going to be safe?
A young entrepreneur is going to set up a coffee cart on his college campus, where should he locate it?
Finding an efficient way to get all employees to their respective floors on time with only three elevators.
Mathematical modeling is a “Standard for Mathematical Practice” of the Common Core, and is the answer to: When am I going to use this? Learn how to integrate modeling exercises into existing courses or create a course on mathematical modeling. During the course, participants will solve problems using the mathematical modeling cycle, examine models, and create their own modeling problem. In addition, we will discuss successful problems and grading rubrics for modeling exercises.
Middle and Upper School Math, Morning Course Block Instructor: Dan Butler, Moundsview High Schools, Moundsview, MN
Algebra is solving equations, graphing functions, and studying the mysterious X. But it is so much more. Algebra is thinking about the world around us and figuring out how to use mathematics to better understand this world. In this course we will use our Algebra skills to help us solve some real, and interesting problems. We will also try to look at some of our regular Algebra topics and find some ways to get a better understanding of how our algorithms work. We will explore Algebra using Geogebra, spreadsheets, calculators and anything else we can think of that might help. Come and join the fun!
These are fascinating examples of how a single algebraic definition may be used to graph an intricate design (as opposed to the more common project of using many independent curves to construct a design).
In this course we explore a process that will allow the secondary student and teacher to create a "complicated" design with just a single algebraic definition. This process (different from that used for the Batman Equation and Person Curves) will reinforce deeper understandings of secondary Math topics such as: domain and range, graphical transformations, function addition/subtraction, function composition, parametric equations.
We will use Desmos or Geogebra, both free, or other graphing software of your choice.
Here are some examples of student work from the course instructor's classroom:
Upper School Math & Science, Afternoon Course Block Instructor: Karen Bryant, St. Marks School, Southborough, MA
Have you seen or heard about the marshmallow challenge? Want to engage your students in other fun STEM/STEAM challenges? Do you want to incorporate good problem solving using the engineering design cycle into a course? Over the six hours, participants will engage in some challenges that I have used that require students to brainstorm, prototype and refine. Most of the challenges require very inexpensive materials and are suitable for all ages of students.
Upper School Math, Afternoon Course Block Instructor: Ron Lancaster, Univ of Toronto, Toronto, Canada
We will begin by examining a number of surprising appearances of the powers of 2 such as in shuffles performed by magicians, the making of candy in South Korea and the poems of an award-winning Canadian poet. Then we will examine applications of logarithms, particularly ones that are not very well known. These applications will engage students in Algebra 1 & 2 and Precalculus classes. The materials developed in this course will arouse students' curiosity about mathematics; deepen their understanding of mathematics and strengthen their appreciation of the subject.
Middle and Upper School Math, Afternoon Course Block Instructor: Ira Nirenberg, Ben Franklin HS (ret), New Orleans, LA
It’s been said that the definition of insanity is to keep doing the same thing over and over again but expecting different results—ready to try something different? In this workshop, rather thanbeginning with definitions, formulas, and equations, we begin with hands-on activities that inspire those definitions, formulas, and equations. Let’s stop putting the cart before the horse. Most middle and high school mathematics begins with an abstraction—we write down a ratio, and then go through some kind of mathematical manipulation (perhaps we cross multiply) to arrive at an answer. We draw lines and begin talking about slope and intercept. We show students how to “solve” word problems. We give students formulas that appear out of the blue. How well have these approaches worked for you? If they haven’t been as effective as you’ve wished, and you’d like to bring back some classroom ready activities, join us for something a bit different. Please bring a calculator!
Upper School Math, Afternoon Course Block Instructor: Dan Butler, Moundsview High School, Moundsview, MN
Let's spice up our precalculus curriculum with some amazing labs. We will use Excel, The Geometer's Sketchpad, GeoGebra, the TI-84, hands-on materials and anything else we decide to use to explore some of the concepts of precalculus through great problems and interesting constructions. We will also take some time to discuss what needs to be in a precalculus course in light of the current state mathematics education.