Pct 13 Traditional Math: Bar Modeling (Tape Diagram) Approach for Solving Percent Problems Pt. II
Seventh Grade
Continued from Pt. I
More examples. Following below are examples of various types of problems, and how to represent them using bar models. I want the students to be comfortable with using the bar model and then will transition over to homework, which consists of problems that are more of the same. Occasionally I will have students who say they like the other approaches better than using the bar models. I’m fine with that and tell them so. But I like to show the bar modeling approach since it can help some students put all the pieces together—literally and mathematically.
1. A camera is discounted 20% and sells for $864. What was the original cost?
(We are given final sales price so we need to subtract 20% from 100%)
2. A watch is discounted 20% which results in a $90 reduction. What is the sales price
This problem is different from any others we have done, so will require more guidance. I will walk through it with them at the board.
The difference is that we are not looking for original cost but sales price, given the amount of the reduction. “We have a 20% reduction and we’re told the amount of the reduction. Do we use 20% or 80% to represent the discount amount?” This part is similar to what they have done before, so there should be a consensus of 20%.
“The 20% is associated with what amount?” $90.
“What are our other two values?” 80% and the unknown, x. Plotting it, we have:
This can now be written in two ways, as long as students maintain consistency of the order:
3. Mr. Grant sold a bicycle at a discount of 15%. If the selling price was $340, find the original amount prior to discount.
Homework. The problems should be kept fairly straightforward and limited to no more than ten. For those students who prefer the other methods, they should be encouraged to use them. Others may find the bar model easier to use.
There are a large variety of percentage problems which will be presented in warm-ups and subsequent lessons. Over time, students will be able to recognize how to solve the various problems, including those that involve increases or decreases other than price, such as number of students in class, questions answered correctly on a test, and so forth. It takes time and much practice and in my experience pays off in a subsequent course in algebra.