Author: Wayne Smith
We have an inter-school collaboration group, sponsored by Math for America. This has given five of us the opportunity to meet together, discuss teaching strategies and more importantly find better ways to use our textbook. We all use the Glencoe Math course 2 math book for our 7th grade math classes.
Our group includes:
Geoff Busby- Timberline Middle
Nita Wood- Timberline Middle
Erin Barlow- Lehi Jr.
Melissa Cossey- American Fork Jr.
Wayne Smith- American Fork Jr
As a group we want to use our textbook and not feel like we need to recreate every lesson in order for it to be of high quality. We assessed the strengths and weaknesses of our textbook and picked a few areas where we saw a need for improvement.
The first area we picked was in chapter 2, the percent chapter—specifically we picked percent change problems. We built the entire unit around an introduction using bar models and a visual concept of 10%. Much of our discussion has been around the proper uses of bar models in helping students understand integers, percent’s, equations and ratios. Bar models are not a one and done concept. We are trying to find ways to use them throughout the year to aid in a visual understanding of many of the 7th grade concepts, such as understanding positive and negative value, including absolute value. Also, the bar models are excellent for helping to understand ratios and proportions. There is real power in learning using the Bar Models. We first heard about their use from the Singapore Math concepts found in the Singapore elementary books. Now we are using those ideas on a middle school level.
Our unit was built around this first lesson that starts with this question:
Visually, this problem creates bar models to show 10% units.
Everything we taught in the unit was linked back to the idea of visual, mental and 10%
Next we used the ideas to start doing routine percent problems like:
This was followed up with problems that required more thought, for example:
This was all in preparation for teaching our original purpose: Percent Change. With the bar model approach, students could now logically, pictorially and algebraically do many kinds of percent change problems.
In chapter one, students learned about ratios and used cross products to solve them, relating it to equal fractions. In chapter two students used the visual model to relate the visual to the proportion. It is hard to convey the power of the bar models until you see it in action and see how students can visualize and do problems that were inaccessible before. Even simple things like, “Why do you do 9 lines in a box when you want 10 spaces?” That simple concept alone helps students understand parts of a fraction, ratios and proportions.
About the author: Wayne Smith teaches math at American Fork Junior High School in the Alpine School District. He is the team leader for the 7th grade math teachers, firstname.lastname@example.org