In my capstone class for future secondary math teachers, I ask my students to come up with ideas for *engaging* their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Jason Trejo. His topic, from Algebra: solving one-step algebra problems.

A2) How could you as a teacher create an activity or project that involves this topic?

How can I engage my students with solving for a variable? Off the top of my head, I came up with 3 tried and true surefire ways that would not only further my students understanding but also be a ton of fun for them: Algeblocks with accompanying interactive whiteboard, using a balance and counters, and possibly using snacks (e.g. cookies, chips, candies, etc.)

First things first, the Algeblocks:

Essentially, Algeblocks are made of a variety of cubes and rectangles that represent ones, tens hundreds, thousands, and even the variables x and x^{2}. Although obscured in the picture, the Algeblocks mat in the back represents a balance where the fulcrum is “=” and each end of the balance represent both sides of the equation. There is even a place that represents negative numbers! Using the problem “x+4=8”, students would have 8 green blocks to the left of the fulcrum and 4 green blocks with an x block. Students would then add or take away tiles to solve the equation. As for problems such as “4x=16”, the students would display the problem using the blocks and then group the green blocks with the x’s to find there answer. Now that I think of it, I would essentially do the same thing but use either a real balance with any type of manipulative.

B1) How can this topic be used in you students’ future courses in mathematics or science?

Being able to solve single step algebraic problems is a foundation to algebra in general, correct? This means that this will continue to pop up regardless of what math class (and even science classes like chemistry). There will always be problems given to students where they will need to solve for a variable and the final step of even the most excruciatingly, horrific looking algebra problems is usually adding, subtracting, multiplying, dividing, etc. to get the “x” all alone. In reality, solving an initial value problem (like I currently do in my Differential Equations class) boils down to one step algebraic solutions.

E1) How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

Interestingly enough, I have the perfect example that ties both Khan Academy and the “use of a balance” activity I mentioned earlier. A quick Google search for “one-step equations” gives a link to Khan Academy that allows for a digital balance and you are to solve the equation given with the balance. This would be an amazing tool for teachers to use when they don’t have actual balances for their class or even have their students create a profile on Khan Academy and use it to be able to track extra problems the students can do. Besides Khan Academy, there are even some cheesy yet fun games (like “Equations Pong” off the XP Math website) that would give the students more practice with these equations while feeling like a reward since they are playing a game. Plus, students can go head-to-head in “Equations Pong” and a vast majority of students like to best their friends in anything and everything.

__References__:

Information on Algeblocks: http://www.hand2mind.com/brands/algeblocks

Image of Algeblock Mats: https://cdn.hand2mind.com/productimages/76986_Algeblocks_Mats_BQS-web.jpg

Khan Academy use for subject: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/e/one_step_equation_intuition

Equations Pong Game: http://www.xpmath.com/forums/arcade.php?do=play&gameid=105

“Being able to solve single step algebraic problems is a foundation to algebra in general, correct?”

I would disagree with this. Algebra is about relationships, the simplest being “the second number is one more than the first number”, or symbolically y = x + 1. And so on.

Algebraic manipulation is the business of finding out what can be done to algebraic statements while preserving their original meaning. This is what leads to “solving equations in one unknown”