Engaging students: Solving one-step linear equations

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 Jessica Trevizo. Her topic, from Pre-Algebra: solving one-step linear equations.

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

            Many students have played “Around the World” at one point in their elementary childhood, or have at least heard of the game. Around the World is an activity that is commonly used by elementary school teachers when they are teaching multiplication. Students are supposed to sit in the form of a circle. One person is chosen to attempt to go around the world. He/she will stand behind a student and will compete against the student that is sitting down. Once both students are ready the teacher holds up a multiplication card. The student who responds with the correct answer first gets the chance to move on to the next person. If the student who is standing up loses then he/she gets to sit down while the other student who obtained the correct answer advances. Every person has to attempt the problem on a sheet of paper, but they are not allowed to call out the answer. The student who “goes around the world” first is the winner. If a student is not able to complete the entire circle then the student who advanced the farthest is the winner. The same idea will be used after the students have learned how to solve one step linear equations.  After having a deep conceptual understanding of the topic it is very important for the students to keep practicing problems.  Around the World allows the students to keep practicing in an entertaining way. The students should be able to solve the equations within 30 seconds since it only requires one step to solve. The ability to use calculators with this activity will vary depending on the level of difficulty of the problems as well as the teacher.

 

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

            Being able to solve one step linear equations is an important skill that every student should acquire. After the students learn how to solve one step linear equations they are expected to be able to solve multi-step equations, solve absolute value equations, solve inequalities, finding the side lengths of a shape given a certain area in geometry, etc. If the students are not able to master solving one step linear equations then they will have a very difficult time in other math courses.

In geometry the Pythagorean Theorem requires the skill to solve one step equations. Students are expected to solve for the missing variable in order to find the missing side length of a right triangle. In Algebra II the students are required to manipulate equations in order to solve systems of linear equations through substitution. Also this basic skill is necessary when finding the inverse of a function. This topic is also used in physics. For example, if the student is asked to find the acceleration of an object given only the force and the mass, then it involves using Newton’s second law which states Force=mass*acceleration.

 

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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?

This website is an amazing tool that allows the students to visualize how to solve linear equations using algebra tiles. If the teacher decides to teach this lesson using algebra tiles in the classroom, then this website will allow the students to continue to practice at home. Also, the website automatically lets the student know if he/she responded correctly. Obtaining quick results allows the student to know whether or not they truly understand how to solve the equations as opposed to having a worksheet with 50 problems for homework and not knowing if the same mistake was repeated.  Also, by using the online algebra tiles the students are able to understand the zero pair concept and see how it is being applied. This website can also be used for other algebra topics such as factoring, the distributive property, and substitution.

http://illuminations.nctm.org/Activity.aspx?id=3482

 

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