Group items tagged

Short list of questions for teachers to use while problem solving

There are a lot of great problems here that could be used in math class. Starting class with one of these problems could be a great way to hook students into the lesson and have the students start generating their own questions and problem solving methods. Then, the math can be brought in appropriately. A lot of these problems seem to lend themselves to the "3 Act Task" model. A video/image representing the problem could go a long way in getting kids hooked.

I saw this Dan Meyer TED Talk on re imagining Math through problem solving. I like how he takes a problem from the textbook and makes it more rigorous. "Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. In his talk, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think. (Filmed at TEDxNYED.)"

I've never been a huge baseball fan, but I do like data. This interactive display shows the total expenditure of every Major League Baseball team (from 1998 out until a few years in the future). Clicking on a team in the top chart will break that expenditure down per player and show what each player makes per year. Just looking at this chart for a few minutes, I've come up with the following questions that could be used in a math class for a problem solving lesson. Some of these questions would also require the students to locate some additional data as well. * Is there a correlation between team expenditure and winning the Championship/making the playoffs/number of wins in a season? * What percent of a team's total expenses do "star players" take up? * Are star player's "worth it" for a baseball team? * How have team expenses changed over the past 15 years? * Are baseball players being paid more today than in the past or are their salaries just keeping up with inflation? * How much do today's baseball stars make in comparison to the stars of the late 90's and early 00's? Is this difference warranted? I'm sure there are plenty of better questions here that I'm missing.

"To solve engineering problems, you use your brain. Solving classroom problems uses your whole being." Nice article to share with teachers when everyone needs a bit of a boost. May share once we return from break.

"Too often kids have trouble with word problems. Too often they don't know what to do with two numbers let alone a bunch of numbers. They guess at division when one number is big and one is small. They add when they see two fractions. They multiply because that was how they solved the last word problem. I will also do this with my 8th graders because I suspect they will have trouble too. And this is exactly the kind of trouble we need to get into. Now rather than later. This task gets them thinking about ratios - which is like the most important math thing in all of the math things." This is a short description of how to get your students developing questions for mathematical scenarios. This would be a great activity to work on if you feel like your students are having difficulty deciphering word problems or are stumped when presented with unfamiliar mathematical scenarios.

"Add "Would You Rather?" to your bookmarks. Phrasing math problems in terms of "Would You Rather" is simple and brilliant. I love this framework for three reasons:" Interesting framework for solving math problems. This post links to a resource of "Would you rather" problems that could be useful in a variety of different math courses.

How can a game help students develop mathematical habits of mind? "Then we talked about the game for a bit, and discussed the "habits of mind" they had employed to figure out the game - noticing and wondering, guessing and checking, persevering, struggling productively, learning from mistakes without worrying about making mistakes (since they knew the only way they were going to make progress was to make mistakes and learn from them), and working together. We talked about how these skills are as important as any content they learn in their school classes, and how they can use those skills to make progress on math problems they're not sure how to solve. In fact, much of the math programming we did the rest of the year employed huge doses of Noticing and Wondering and generating ideas about math situations, or scenarios (a math problem with no stated question). Anecdotal reports suggest that by the end of the year, most of the students felt pretty confident that they could generate ideas about most math situations we handed them. Big win!"

"The root cause of the American Civil War is perhaps the most controversial topic in American history. Even before the war was over, scholars in the North and South began to analyze and interpret the reasons behind the bloodshed." Another interesting problem that Voyant (and other data viz/textual analysis tools) could help us solve. Provide students with a little background and then give them the Articles of Secession for a variety of states. Have them analyze/interpret the overall reasons for Secession based on what they uncover.

"Solving a math problem means unfolding a mystery, enjoying the pleasure of discovery. But in every geometry lesson that year, I blundered along and blurted out the secret. With a few sentences, I'd manage to ruin the puzzle, ending the feast before it began, as definitively as if I'd spat in my students' soup. Math is a story, and I was giving my kids spoilers." This post speaks directly to math, but can be applied to any content. When we provide students with the answers rather than developing lessons that let the students ask (and answer questions), we take the fun out of learning.

"A puzzle by Sam Loyd. The red strips are twice as long as the yellow strips. The eight can be assembled to form two squares of different sizes. How can they be rearranged (in the plane) to form three squares of equal size?" Interesting brainteaser or problem that could act as a warmup. You could make these strips into manipulatives in Inspire or give the students physical strips to help with the visualization process. I'm sure there's math here, I just don't know what it is...

Variety of Three Act lessons Timon Piccin.

This is the Newest webtool developed by Dan Meyer and Dave Major. Dan Meyer discusses the tool and task in a post on his blog here - http://blog.mrmeyer.com/?p=17503 I think this tool would be very engaging for students. Give them the task of finding the quickest route, and they will go nuts with it. I see two main applications for this particular tool/task: You could use this tool as an introduction to angles. Put it on the board, give the kids the task, and have them discuss how they would tell the ship captain to navigate around the buoys. When non-mathematical language and vocabulary bogs down the ship's progress, overlay a grid/protractor and introduce the idea of angles. Have the kids play around with the tool to come up with the quickest route. Discuss the result of small differences in angle measurement on the ship's progress (each degree above the necessary increases the amount of time lost). This could lead into a discussion on the importance of precision… This would be an easy task to make over if you wanted to talk about slope and writing equations of lines (Algebra I). You could overlay a grid on the board, The kids could draw the lines in to get the ships around the buoys, write the equations, then you could talk about how cumbersome the equations are and how ships are actually piloted and bring in the idea of degrees/vectors (direction and angle). Not only does this tool help to teach angles/vectors, but it's also a tool to get students estimating (angles AND distance).

""What's the sine of π/2?" I asked my first-ever trigonometry class. "One!" they replied in unison. "We learned that last year." So I skipped ahead, later to realize that they didn't really know what "sine" even meant. They'd simply memorized that fact. To them, math wasn't a process of logical discovery and thoughtful exploration. It was a call-and-response game. Trigonometry was just a collection of non-rhyming lyrics to the lamest sing-along ever. Some things are worth memorizing--addresses, PINs, your parents' birthdays. The sine of π/2 is not among them. It's a fact that matters only insofar as it connects to other ideas. To learn it in isolation is like learning the sentence "Hamlet kills Claudius" without the faintest idea of who either gentleman is--or, for what matter, of what "kill" means. Memorization is a frontage road: It runs parallel to the best parts of learning, never intersecting. It's a detour around all the action, a way of knowing without learning, of answering without understanding."

"Since demolishing 78 traffic signals and installing 80 roundabouts, the northern Indiana city of Carmel has reduced the number of accidents by 40 percent and the number of accidents with injuries by 78 percent." There's a great lesson in here somewhere. I'm not sure of the exact structure for it, but here are some of my random thoughts. Let me know if you have others: Use Googlemaps and GoogleEarth in order to determine how many traffic lights are in a specific location in a county/city. Using the calculations in this article/video, how much could the county/city that you researched in Google maps have saved if they installed traffic circles rather than traffic lights. Extension - Research the number of accidents and injury/fatality stats for the area that you've researched. Using the calculations in this video/article, how many lives would traffic circles save in this area?

"Empower your students to think critically about data, ask meaningful questions, and communicate their conclusions."