Four Evil Math Wizard Spells That Change Basic Math Problems into Brain Bending Challenges

Yippee, more Common Core Math Strategies! I love this post from second-career teacher Deirdre Calhoun because it is not only well researched but also so very useful. Be sure to see her four “Evil Math Wizard” spells below…and check out her blog!

They don’t call me the Evil Math Wizard for nothing. For over 10 years, I’ve challenged my students to think and persevere when solving math problems. I don’t give them formulas; I start by posing real life dilemmas and encourage them to develop their own way of solving them using math. Teaching math this way takes time and can be frustrating for some students, but the learning is strong and the knowledge is deep. I have maintained this philosophy even with unwieldy amounts of math standards. Now the tide is changing.

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As teachers we are at a critical juncture. Most states have adopted the new Common Core State Standards, which gives us a chance to recalibrate, refocus, restructure, and, in some cases, restart. Resources are scarce, so we have to create our own materials. I relish the opportunity to teach Common Core standards that emphasize thinking. I also echo the sentiment of NCTM President Linda M. Gojak in her April address, “We have the opportunity to ensure that students will deeply understand the mathematics they are learning. Mathematics no longer needs to be experienced as a series of procedures and tricks by many students.” I understand this to mean that we need to teach students to think, and then our students will have the skills to be able to solve problems without necessarily knowing shortcuts. I have found that true with my experience. When I give my students enough time to think, recognize patterns, and share ideas, my students develop skills that let them handle other math questions without even knowing the formal procedure.

We need to help students be thinkers and creative problem-solvers, as well as be prepared for their futures. In March 2013 Thomas Friedman’s op-ed in the NY Times quoted Tony Wagner, author of the book Creating Innovators: The Making of Young People Who Will Change the World, Wagner observes that our K-12 and college tracks are not consistently “adding the value and teaching the skills that matter most in the marketplace.” Wagner also says, “Young people who are intrinsically motivated — curious, persistent, and willing to take risks — will learn new knowledge and skills continuously. They will be able to find new opportunities or create their own — a disposition that will be increasingly important as many traditional careers disappear.”

We have the responsibility to prepare our students for the challenges of the future, but how do we specifically do that? We run the risk of boring our students with meaningless questions that only require regurgitation, especially when the questions are primarily designed to enhance test performance. (Please read Rachel Lynette’s March 8, 2013 blog post on “Why I Have Stopped Creating Test Prep Task Cards.”) Instead, we can have more engaged, confident, and excited students. It does take some thinking on our part, so in a way Common Core is also making us become more creative thinkers.

Here are four of my “Evil Math Wizard” spells I cast to turn traditional math problems into deeper thinking, creative problem solving, brain-bending challenges.

1. Apply the problem to real life. Just simply changing a traditional problem to a story problem increases the complexity and makes students have to use clues to figure out how to set up the problem.
   1. Before: Find the mean of 4, 6, 3, 3.
   2. After: In four games Ben scored 4, 6, 3, and 3 goals. How many goals does he average per game?
2. Present the information in another way. Putting the information into a graph or a picture also challenges a student’s way of thinking and requires them to find the necessary information.
   1. Before: Find the mean of 4, 6, 3, 3.
   2. After: See graph.
   3. or…
   4. In the first four games with the soccer team the Strikers, Ben has started the season strong. In his first game he scored four goals, and in his last game he scored three. He has never scored less than three goals or more than six goals in his games, and he has averaged four goals so far. Identify the range, mean, median, and mode.

1. Reverse it. Instead of a student finding an answer, pose the answer, and have the student figure out the question.
   1. Before: Find the mean of 4, 6, 3, 3.
   2. After: Ben averaged four goals in the last four games. What are the possible goals he made in each of the four games? What are all the possibilities? How can you figure it out?
2. Hide something, aka: Algebra. Remove some information from the problem, and ask students to come up with possible replacements.
   1. Before: Find the mean of 4, 6, 3, 3.
   2. After: Ben averages four goals in the last four games. In the first game he scored 4, in the second game he scored 5, and in the third game he scored 3, but the coach lost the statistics for the last game. What did Ben score in that game?

I hope that the intent of Common Core succeeds and that test scores do not drive it and that we engage our students in meaningful learning activities.

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After a career as a product manager for a software company, I took a break to spend more time at home with my young daughter. When I began volunteering at her school, I saw a need for math lessons to have a more real-life, practical approach. I returned to school, became a certified teacher and just recently completed my master’s degree in Curriculum and Learning. I am passionate about math being practical and magical for my students; it should be fun! Please check out my blog, as well as my Teachers Pay Teachers store to see products that reflect this passion. (I do have some Mean, Median, and Mode Task Cards.)