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 comes from my former student Chi Lin. Her topic, from Pre-Algebra: solving two-step algebra problems.

How could you as a teacher create an activity or project that involves your topic?

There is an interesting activity that I found online. It is called mini task cards. However, I want to rename this activity as “Find your partners” as an engage activity in this topic. I am going to create some two-step equations on the cards and give those cards randomly to the students at the beginning of the class. Each student has one mini card. The students will have 5 minutes to solve the equations and they will find the partners who have the same answers as them (there is 2-3 person in each group). The person who has the same answer with them will be the partner that they are working together with in the class. I will set up the answer as their group name (for example, if the answer is 1, then it means the group name is “Group One”). Here is an example that how the card will look like.

How can this topic be used in your students’ future courses in mathematics or science?

Solving two-step equations is the foundation of solving multi-step equations. Solving two-step equations looks easy but it can become very hard. This topic can be applied in lots of areas such as high-level math classes, computer science, chemistry, physics, engineer, and so on. Most definitely, the students will see lots of problems about solving multi-step equations in different high-level mathematics courses in college, such as pre-calculus, calculus 1-3, differential equations, and so on. Also, the students will use the knowledge when they write the code in computer science class. For example, when they write down the code of two-step or multi-step algebra problems, they need to know which step goes first. If they do the step wrong, then the computer program will compute the wrong result. Moreover, the students will use solving two-step equations in chemistry class. For example, the students will apply this knowledge, when they write down the chemical equations and try to balance the equations.

How does this topic extend what your students should have learned in previous courses?

First, students should know what linear equations are and how to write down the linear equations. Second, students should know how to solve one-step algebra problems, such as or . Students should have learned that when they solve for the one-step equations (addition and subtract), whatever they do to one side of the equation, they need to make sure they add the same thing to the other side. For example, when they solve the equation , they can subtract 8 for both sides, which is . Therefore, x=8. Also, student should know that when they solve for the one-step equations (multiplication and division), they need to multiply both side by the reciprocal of the coefficient of the variable. For example, when they solve the equation , they need to multiply the reciprocal of for both sides, which is . Therefore, . Thus, when they learn to solve two-step equations, they need to combine these rules.

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