I'll begin by telling students that today we will practice drawing bar models to represent percent increase and decrease problems. (Note: this lesson is about finding the new value not the percent of change.) As a quick check, I'll call on students to share the meanings of increase and decrease. I'll draw an up arrow by increase and a down arrow by decrease as a visual aid.
Before jumping into the models I'll provide a more concrete example. Each student will have about 15 color tiles (squares) of the same color. I will ask them to arrange one row of 10 and set the others aside. I'll ask them to tell me what percent is represented by 1 out of the 10 tiles. If a student simply says 10%, I'll ask them how they know. Next I'll write down the number 20. All ten tiles represent the value 20, so what does one tile represent? What is 10% of 20?
Next, if we increase the value by 30% how many tiles should we add? What is our new value? Students should now have 13 tiles and a value of 26. Then I'll write a 30% increase of 20 results in 26. I'll ask: our new value (26) is what percent of the original value (20)?
I will go through a similar problem for a decrease. Of course, this time tiles will be removed.
In small group interventions, I will sometimes spend the entire time doing problems with color tiles.
Next, we will go through the step by step instructions. I'll call on students to read through each step as we work on the examples. I want to make sure all students can use the instructions to solve the problems as opposed to relying on the teacher to get through the problems. It is worth asking as a check for understanding, why did you choose the 10% or 25% bar model?
Examples 3 and 4 require students to draw the bar models from scratch. I first have students draw a fairly long rectangle similar to examples 1 and 2. I then have students split the rectangle in half. If we are doing a 10% bar model, I'll have them draw 4 vertical lines to the left of the halfway point and 4 vertical lines to the right of the halfway point. This will make 10 boxes. It sometimes takes a little practice and patience! The 25% model is much easier.
For each model student provide the new value and the percent of the original value. This is presented here so that students are familiar with this idea when we find sales prices and totals including tax. For example, a 20% discount is simply a 20% decrease so the sales price is 80% of the original value. Or a 10% sales tax is simply a 10% increase so the total with sales tax would be 110% of the original value.
Students now have 10 problems to work on - 5 increase problems and 5 decrease problems. I have provided a partially drawn bar model for the first 2 problems in each group.
Students may want to take short cuts on drawing the models but there are a few non-negotiable things:
1) The bar models must have the percents labeled below. It is okay if students label every other increment. Like 0%, 20%, 40%, 60% as opposed 10%, 20%, 30%, etc.
2) The original value must be above 100% and each unit should have its value in the box.
3) Students should clearly show the units (boxes) that are added for an increase or removed for a decrease.
4) The new value and new percent must clearly be labeled on the model.
Before we begin the exit ticket it will be helpful to summarize. I'll ask:
1) How do you decide which bar model (10% or 25%) is most appropriate?
2) How do you determine the value of each unit (box)?
2) The original value goes with what percent?
3) When do we add boxes (units)? When do we remove boxes?
I'll tell students that each problem is worth 1 point for a total of 6 points. To earn the point for the bar model itself, students need to include the basic parts mentioned in the previous section as non-negotiable.
Question #5 is included to see if students can think beyond the bar model. I will probably not count this towards the exit ticket points.