I like to use alternative ways of assessing students' understanding. A couple of years ago I used card houses as a way to teach algebraic expressions to my algebra and pre-algebra students. This year, I designed a lesson where students built card towers, gathered data, then created a poster describing the method of building, the dependent and independent variables, the linear equation resulting, and a graph of their results. Students used their equations to predict the height from the floor of a 10-story card tower, a 25-story card tower, and 131-story card tower, which is the height of the world record tower to date. Each pair of students presented their findings in poster format for their grade. Oh, and I added a prize for the tallest free standing tower. We began the lesson with a short video showing the record holder for the tallest card tower. Our efforts were hampered by the new decks of cards I had purchased which were slippery. However, that challenge spurred the students on to more innovative tower building strategies, as you can see from the photos here. I did not get a photo of an interesting strategy that involved a series of boxes made from cards, stacked on one another. The winning tower, shown above, was three stories tall, 27 cm. They won their choice of sports-themed hacky sacks, a popular prize. This year, I teach my eighth graders twice on Fridays so a longer plan such as this fits the bill. I gave the students 30 minutes to build their towers, and used an online timer. The lesson was successful, and produced great results.
And, we had a lot of comic relief as the timer ticked down and the slippery cards slipped. It was very interesting, and all were engaged.
My high school algebra class is working with linear equations. There is a lot of vocabulary. Much of the vocabulary sounds vaguely similar so it is easy for the students to feel "mushy" about the whole unit. In my book, "mushy" is not good, and leads to "mushier" as we move forward into inequalities, linear systems, and eventually quadratic equations. Ideally, students will have facility with equation solving tools, with which they can manipulate linear equations into various forms. And, they can see that certain forms of linear equations lend themselves to different applications. We aren't there yet, but closer. As I write this, I realize I need to design a lesson where they read problems and identify which form of the linear equation would be more applicable.
This Algebra I class is particularly fidgety after lunch, so I proposed "hall math" to them. The eight questions above were taped in the hall, within view of my room. I asked them how they should comport themselves in the hall, and we reviewed. Then I asked how many times I should have to prompt them to keep the noise down before I called them all back in. They suggested five! (not surprised) I told them that they would get one warning before I rounded them up, but I was sure they could handle it, and this was a trial run to see if we could have more hall math in the future... And, I asked them to pair up as follows: If you are comfortable with the material, find someone less comfortable, and vice versa. I gave them each clipboards with an eight-graph sheet attached and off they went. They were fantastic!
Last year, I attended the National Council of Teachers of Math conference which was held in Boston. May I say, what a treat to be among hundreds of people who are enthused about mathematics? I had sort of forgotten that many people continue to believe that Math is a mystery, or it became a mystery to them at some point in school and it moved forward without them. That's a topic for another day. But, one of the sessions I went to was about incorporating some social conscience into math class. It's easy to start; rather than having Roxanne contemplate which deal is better at the health club, you can formulate problems that involve giving, or that highlight some local or global concerns.
Here's an example of slope-intercept form in action:
Alex has set a goal of donating 76 books to the Boys and Girls club. He started by using part of his birthday money to buy 10 books. Each week he uses some of his allowance to choose 4 books from the sale rack at the local bookstore.
a. Write an equation representing Alex's progress toward his goal as a function of how many weeks have passed.
b. Graph the equation.
c. How many books will Alex have left to donate after 6 weeks have passed?
Thanks for reading along... I'm excited about hall math... "Get thee to a laminator".
I like to use alternative ways of assessing students' understanding. A couple of years ago I used card houses as a way to teach algebraic expressions to my algebra and pre-algebra students. This year, I designed a lesson where students built card towers, gathered data, then created a poster describing the method of building, the dependent and independent variables, the linear equation resulting, and a graph of their results. Students used their equations to predict the height from the floor of a 10-story card tower, a 25-story card tower, and 131-story card tower, which is the height of the world record tower to date. Each pair of students presented their findings in poster format for their grade. Oh, and I added a prize for the tallest free standing tower. We began the lesson with a short video showing the record holder for the tallest card tower. Our efforts were hampered by the new decks of cards I had purchased which were slippery. However, that challenge spurred the students on to more innovative tower building strategies, as you can see from the photos here. I did not get a photo of an interesting strategy that involved a series of boxes made from cards, stacked on one another. The winning tower, shown above, was three stories tall, 27 cm. They won their choice of sports-themed hacky sacks, a popular prize. This year, I teach my eighth graders twice on Fridays so a longer plan such as this fits the bill. I gave the students 30 minutes to build their towers, and used an online timer. The lesson was successful, and produced great results. 
