# Catching Up

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## Objective

SWBAT solve systems of linear equations by substitution

#### Big Idea

When will one contender Catch Up to the other? Students answer questions like this one solving systems by substitution.

## Launch

10 minutes

To begin this lesson I ask that students open their notebooks and open the Launch Catching Up PowerPoint. The first of the 2-slide presentation instructs students to solve 3 simple equations. I ask students to answer these in their notebooks and I walk around making sure everyone is on task and assessing their work. As I walk around I check to see which students write "substitution" as one of the properties used for Question 4. I want to call on one of these students when going over the tasks.

After a few minutes I call on students to give me the answers to each of the equations, including question 4.  I address the class and ask if anyone else wrote "substitution" as the property they used. I usually get a good show of hands, and end by stating that "yes, besides the properties of equality used to solve these equations, substitution is used in all three."

## New Info

15 minutes

I now proceed to show Slide 2 from Launch Catching Up. The class may recognize this system of equations. I remind them that it's one we worked with in a previous lesson about CD Mail Order Clubs.

I will ask students to observe the graph of the system, its solution, and then I encourage the class to find another way of solving this system without graphing. Most of the class will make the connection with the equations solved in the first slide and substitute the value of y in the first equation and for y in the second equation.

I walk around monitoring and leading struggling students toward substituting to solve the system. Most students substitute and find the value of x, but some may stop there, forgetting that they need to find the y coordinate.  When this occurs, I question students and lead them into realizing that they must find y by substituting the value of x, back into the equation.

I like to ask, "which equation should you substitute x into?" I hope that my students will say, "Either of the two because the point is a solution to both equations." This is the direction where I plan to lead them today.

## Application

25 minutes

Completing the Application problems works best when the students work in pairs, each with their own sheet. I hand each student the "Catching Up" application problems worksheet: Solving by Substitution Catch Up problems.

The worksheet has two problems for which student must find the equations to and a third in which the system of equations is given and they must create a "catch up" problem for it. I always ask students to check their answers by substituting x and y back into the original equations. Before beginning, I remind the class that d = rt, and that speed in our problems is constant.

Students may struggle with problem 1 because the solution to the system is not the final answer to the problem. For those that cannot immediately see how to solve the entire problem, I tell them to think about what they can find. Then I ask them to try and connect that, with the original question. The value of x (time) in the problem is 10, which means that Bart's turtle catches up to his sister's in 10 minutes. Students must then substitute 10 back into either equation to get 40. So, because the race is 50 meters long, Bart's turtle wins.

I try and make time for discussion of the problems. If time runs short, I would skip the 3rd problem and include it in the homework.

I make sure to walk around assessing students working and giving some guidance, especially to those students having difficulty coming up with the equations. Since the goal of the class is being able to solve systems by substitution, I don't want these students to fall too far behind because of this. I may even give a set of equations to struggling students so they can go ahead and solve by substituting.

## Closure

10 minutes

To close the lesson, I ask student volunteers to go up to the board, write the system of equations and solve it. I ask if there are any questions. Students may ask if the equations in the systems will always be in slope-intercept form. I reply saying no, and that we will see this in the following lesson.

Finally, I ask the class to give me one advantage of solving systems by substitution has over the graphing method.

## Homework

Students should show ALL work on the homework assignment sheet. If there wasn't enough time to problem 3 in the Application section, I would include it here for homework:

Homework Catching Up