Practice Solving Systems Algebraically
Lesson 10 of 13
Objective: Students will be able to fluently solve a system of equations algebraically. Students can determine an appropriate method for solving a system of equations based on the structure of the system of equations.
This is a really important part of this lesson so if it runs long go with it. It is fine to sacrifice some practice time in order for students to gain a more thorough understading of why solving a system of equation by elimination works.
Each pair of students gets one six-sided number cube. The can use this to determine the scalar that they will be multiplying the first equation by. They can then manipulate the equations and "prove" that the resultant equation has the same solution.
After students have had the opportunity to try several different scalar multiples both positive and negative it will be important to process out what they have just learned. Have students write for two minutes in their notebooks on what they have learned as a result of the activity. They can then share their writing with their partner to look for commonality and new ideas. While students are talking in pairs listen for particularly insightful ideas and call on those students to share with the group in order to bring some closure to the concept.
Environment: For this lesson students should be grouped in homogeneous pairs. The independent practice portion of this lesson requires students to solve a variety of systems of equations. It is important that while students are working with their partners they are not relying too heavily on them (as can sometimes happen in heterogeneous pairs). You want to have a realistic picture about what students understand and what they do not.
Students will work with their partners to solve the systems of equations on the accompanying practice sheet.
What to watch for: Students will make mistakes...I make it a point to never tell them what their mistake is. I will find the mistake and then say, "I see the mistake, see if you can find it." I ask my students to go back to the beginning of the question and "retrace" their steps to look for errors. If they can not find a mistake after this or if it is a student who might really struggle algebraically I will tell them the line where the mistake happened and then have them try to find it again. I find that this scaffolding approach really helps students to become better at finding their own errors as the year goes on.
Ask students to reflect on solving systems of equations by elimination and by substitution. Which method do they prefer and why? Make sure that students refer to both methods in their explanation refering to the pros and cons of both. This will give you some insight into how comfortable students are with each method and choosing the most efficient method for a given question.