## Friday, July 27, 2012

### Whiteboarding activities in the MS/Algebra 1 classroom: Part 1

In my most recent post, I discussed how to get cheap whiteboards for student use in the classroom. I made large whiteboards (24" by 32") so that I could use them for group activities and investigations. The logical next question is what would be some activities and investigations that would make good use of this resource? Since my most recent experience is with MS Math classes, specifically Algebra 1, I'm digging through my files and seeing what would work well as a whiteboarding activity.

There are some awesome ideas at http://bowmandickson.com/2011/11/05/experiments-with-math-whiteboarding/If you know of others, please link to them in the comments or ping me on twitter (@Borschtwithanna).

So, from my files from last year, here are some activities that I think can be adapted to whiteboarding in groups.

1. "1, 2, 3, 4 competition": Groups compete to see how many different ways they can generate the integers -24 through 24 using the numbers 1, 2, 3, and 4 exactly once each and any of the standard operations (addition, subtraction, multiplication, division), as well as parentheses. Sometimes, I let groups use square roots and exponents, as an extra challenge. So for example, doing 1 + 3 • (2 – 4) generates the integer -5. Each different expression is worth one point, even if it generates the same integer. Bonus points if they can generate all of the integers in the set. After time is up, all of the whiteboards will be revealed and groups have a chance to challenge an expression they think is incorrect, getting a point for each error they find. (Adapted from an IMP, Year 1 task)
2. "Number tricks with expressions": students can work on the following problem in their groups:

A magician said to a volunteer from the audience, "Pick a number, but don't tell me what it is. Add 15 to it. Multiply your answer by 3. Subtract 9. Divide by 3. Subtract 8. Now tell me your answer."

"Thirty-two," replied the volunteer.

Then the magician immediately guessed the number that the volunteer had originally chosen.

a. What was the volunteer's number?
b. How did the magician know so quickly? (The magician couldn't possibly have worked backwards that fast.)
c. Create your own impressive number trick. Write down the directions that you would give an audience member and explain what you would do to figure out the number that was picked. (Adapted from Discovering Algebra)
3. "Mystery Bags" investigation, which builds towards formal equation solving using the balance scale model. (Adapted from IMP, Year 2)
4. "Pauline's Run": fractions, rates, and equation solving. Students could use whiteboards to compare and contrast different methods. (Adapted from IMP, Year 1)

One day, Pauline was walking through a train tunnel on her way to town. Suddenly, she heard the whistle of a train approaching from behind her! Pauline knew that the train always traveled at an even 60 miles per hour. She also knew that she was exactly three-eighths of the way through the tunnel, and she could tell from the train whistle how far the train was from the tunnel. Pauline wasn't sure if she should run forward as fast as she could, or run back to the near end of the tunnel.

Well, she did some lightning-fast calculations, based on how fast she could run and the length of the tunnel. She figured out that whichever way she ran, she would just barely make it out of the tunnel before the train reached her. Whew!!

How fast could Pauline run? Carefully explain how you found your answer.
5. Groups could use whiteboards to solve different versions of one problem so that the class can then discuss how they are related to one another. For example, one group could solve and graph the solution set for each of the following:
a. 2x – 3 = 13
b. 2x – 3 > 13
c. 2x – 3 < 13
d. |2x – 3| = 13
e. |2x – 3| > 13
f. |2x – 3| < 13
6. Sketching graphs to model situations and vice versa. For example, having students sketch a variety of graphs representing motion (walking away at a constant speed, standing still, walking away at an accelerating speed, walking toward at various speeds, etc) or having students create stories from a series of graphs representing different people's walks (there are lots of these types of activities in the book A Visual Approach to Functions). Here is a similar set of questions from the Exeter Math 1 packet:
Graphing Functions
7. Introducing slope-intercept form of a line through changing patterns (adapted from The Pattern and Function Connection).
8. Intro to Slope-Intercept Form
9. Group investigations that can be presented and summarized. One idea is that groups can use graphing calculators and sketch a variety of functions and what happens when you take their absolute value in order to reach a conclusion about the nature of the absolute value function and how it operates on other functions. For example, one group would graph $y=x^2-3$ and $y=\left | x^2-3 \right |$, another group would graph $y=x^3$ and $y=\left | x^3 \right |$, a third group would graph $y=x+2$ and $y=\left |x+2 \right |$, and so on. Many types of graphic transformations can be examined by having each group present an example to the class and then synthesizing the investigation into a cohesive conclusion.
Since this blog entry is getting a bit long, I'll put the activities from the second half of Algebra 1 into a new post.