I will being with the essential question: How can you find a percent of change?
I will present the example problem using the bar model. We'll read the problem, then I''ll ask if the amount increased or decreased to make sure they know those terms. I will point out that it would be a mistake (common error) to suggest a 7% increase. Next I will label the bar. The original or initial amount - 28 hours - will be written at the top of the bar over 100%. We will find the value of each unit - 7 hours - and then see that the new amount - 35 hours - is 7 more than 28. The bar shows clearly that this represent a 25% increase.
I will then show the formula that I will be using for Percent of Change. Where it says amount of change I will tell students to draw an arrow to this labeled subtract old and new values. I tend to encourage my students to first determine if there is an increase or decrease and then subtract the largest value minus the smallest value to find the change.
I'll let my students use calculators for this lesson so the reminder is given that they cal divide numerator by denominator and then multiply by 100. I'll have to be on the lookout for students who habitually divide the greater value by the lesser value!
Example 1 solves the same problem modeled using bars only this time only a formula is used.
In example 2, I will solve the decrease problem.
Each example is accompanied by an additional problem that can either be used as a check for understanding or an additional example depending on how quickly the students are grasping the lesson.
Before beginning the guided problem solving section, I have included 5 questions that students should be able to answer to be successful. We will discuss each of these and fill in the answer. The purpose is to get students to be as self reliant as possible. I will cold call students for each question. If a student is stuck, I will make a big show of turning back to the previous page of notes. I will do this in a manner of curiosity (hopefully) as opposed to being obnoxious! It is to serve as a reminder to students that these answers can all be found in the notes.
Students then may work with partners to solve the 5 problems. It may be worth discussing the term "original" to make sure students understand what this means.
Students now work independently. The first 7 problems are similar to the previous 5 problems. Students should be able to successfully solve these problems.
The last page brings in some "real-world" problems. Problem 6 uses real (yet rounded) population data for New Orleans showing how the population has grown in the last 8 years.
Problem 7 requires students to explain their reasoning (MP3). This will really show how well students understand the meaning of percent change.
Problem 8 involves area and perimeter and the results of doubling dimensions.
Before beginning the exit ticket, we will go over the questions posted at the top of the guided problem solving section as a final reminder of how to solve percent change problems.
Students have 5 problems. Success in the lesson will be measured as at least 4 correct answers.