What's My Solution?

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Objective

SWBAT determine the solution of an equation through substitution

Big Idea

Finding the solution through use of substitution helps student realize there is only one answer when solving equations.

DO NOW

20 minutes

I chose this problem for the do now because it has the students looking at a grid to determine the expression that represents a situation.  As students work through this problem they are asked to, first, use any method they like to determine the total distance.  Students should see that she travelled 5 blocks, one way, so her total distance was 10 blocks travelled.  If she travelled 20 miles, then the students would do 20 ÷ 10 = 2 miles.  So, the distance between her house and the tennis courts is two miles.  The visual representation is a plus for students that may struggle.  Since she can only travel gridlines, have the students map out her path by taking the problem one step at a time.  Continue to have them count straight gridlines to their destination.  Then ask,  how far to travel back?  Ask the students if they feel the blocks are the same distance or different?  They should say the same because the lines are equal.  Then ask, “if you have equal parts, what can you do to find one part”.  This should get them thinking about division. (SMP 1)

Next, the students are asked to write an equation with one variable to represent the situation.  Their equation should look something like this 10d = 20.  If students are struggling, ask them what part of the problem is unknown? (distance from home to tennis court).  What can we use to represent this? (variable). Now ask them what we know? (10 blocks and 20 miles)  Now have them write the equation knowing that 10 blocks x distance of each block has to equal 20 miles. (SMP 2)

Tools: Do now problem

What is an Equation?

10 minutes

During this part of the lesson, the students will be listening to me talk about what an equation is.  They will not be taking any notes, as this is already printed on the page.  They just need to follow along.  The first item I’m going to talk about is how equations are just two equivalent expressions. The equal sign says this side is the same as the other side.  Next, I will be showing the students that we can remove any of the values and replace it with a variable and the expressions are still the same.  This is a very important connection for students to make to help them when solving equations. Finally, I’m going to relate equations to a scale.  I always say, “what you do to one side, you have to do to the other?” “You have to keep the scale balanced”.  Again, this is another important connection to make with equations.

Tools: What is an equation slides

Determining the Solution

20 minutes

In order for students to determine the solution to an equation, they must substitute the value in for the variable to see if it makes the statement true.  Students should substitute in all values because we want them to see that there is only one solution to an equation (shhhh… let them figure this out on their own)

I will be going through two problems with them.  The first problem is a one-step equation.  I will be modeling for students how to substitute in and how to determine if the solution works.  The second problem is a 2-step equation.  I will be asking students what they think would be the first step when evaluating the expression.  Students should respond with multiply.  I will then ask them why?  Students should respond with the orders of operations say so. (SMP 3).  We will be working as a whole group to discover the solution to this equation too.

For the third example, I’m going to have students work independently.  Remind students to substitute in all values.  When students are done, have them share their solutions with a tablemate. 

Tools:  Determining the solution examples

Determining the Solution Roundtable Activity

25 minutes

The students will be working on a Roundtable activity.  As students are working on finding the solution, be sure to watch out for the inverse equations.  For example, 5 – m, is an inverse equation because the variable comes after the constant.  This usually trips kids up as they will substitute the variable in front and subtract 5 from it.  If you see students doing this have them read the expression out loud.  This usually helps students realize that they need to do 5 minus the number. (SMP 6)

Tools:  Determining the rule roundtable activity

Closure

10 minutes

The students will be reflecting on 3 questions:

  1.  How are equations like expressions?  I’m looking for students to say that equations are made up of two equal expressions.  The expressions are the same on both sides of the equal sign.
  2. How are equations different from expressions?  I’m looking for them to say that expressions don’t have an equal sign.  Equations give you the total whereas you have to find the value by knowing the quantity of the variable.
  3. What did you notice about the solution of an equation and what does it mean to you?  I want students to generalize their learning by saying that equations have only one solution and once you find the solution, you don’t have to look any farther. (SMP 8)

 

If time permits, have the students share their reflections with a tablemate.