Segment Addition Exploration with Cuisenaire Rods

This weekend, I was working on a special project, and I was pushing myself to develop a conceptually rigorous activity for the segment addition postulate. When you search for segment addition postulate activities, you find a lot of problem sets, a lab or two on paper and Geogebra, and a few other odds and ends. Don't get me wrong - some of these are great. However, I really like for kids to build conceptual understanding through hands-on exploration. So, I wrote the following activity:

First, students are given a set of Cuisenaire Rods. They will need 2 lime rods, 2 orange rods, 2 red rods, 2 fuchsia rods, and 1 of every other color. This exploration will likely work best in groups, so you could easily give one group of students a set of rods, rather than each student a set. Note: If you don't have Cuisenaire Rods, You could probably cut down some popsicle stick or something. It'll just be a lot of cutting.

First, explain to students that this is a complete set of Cuisenaire Rods:

It is their job to find the length of each rod without using a ruler. Instead, they will have the actual rods to manipulate at their desks as well as corresponding algebraic expressions for the length of many rods.

Next, students will need access to the problems. I have the problems in a PowerPoint file, but I'm thinking each group probably needs a handout at their seat so they can work at their own pace. Regardless, here are the questions as a converted PDF file. If you want the PowerPoint, click HERE.

Ask the kids to work through the problems and solve. You will need to circulate around the room and prompt students when they are stuck. This activity will likely come easily to some and less easily to others.

After students have successfully solved for the lengths of these bars, the should check their solutions against the whole set to see if their solutions make sense. They could also double check themselves with a ruler( Note: measurements are all in cm).

Then, the last four slides of the PowerPoint is hopefully where the geometric representations and algebraic thinking gels. What similarities did students notice? Differences?

The last three slides takes you through the three different types of problems encountered in the activity and asks students to discuss how they viewed and solve that particular type of problem.

I am excited about trying this lesson in a classroom soon. Special thanks to @pamjwilson and @mrdardy for their help in developing this activity.

Teaching Segment Addition with Types and Socrative Task Cards

If you are interested in this post have haven't read Teaching Segment Addition with Types, I strongly recommend you skim that first before reading this post.

Now, moving on to the fourth day of segment addition and betweeness postulates, the students just needed to practice.To do this, students completed some Socrative Practice problems using the three types. Basically, each problem becomes two questions. In the first question, students must classify the type of Segment Addition problem. Then, in the second accompanying question, students must apply the strategy needed to correctly solve that particular type of segment addition problem.  Here is an example:

If you would like to use this Socrative practice assignment, just use the following code: SOC-17443219

Teaching kids to first identify the type, recall the strategy, and then solve in this very systematic way proved so beneficial for my kids and for further applications later on in the year.

Teaching Segment Addition with Types

In the past, as I had planned for segment and angle addition topics, I would almost always expect a bumpy ride. I always started the unit off with a lab/discovery activity but found my students could not transfer what they had learned in the lab to different types of segment addition problems. Therefore, I chose to give them additional guidance so as to smooth the seemingly difficult transition for them between algebraic reasoning alone and the marriage of algebraic and geometric reasoning.

I came up with three primary types of Betweeness problems. While not every problems fits nearly into one of these three categories, most do. And, by teaching my students and classifying the different kinds of geometric relationships that could exist helped them to build a firmer geometric reasoning foundation almost immediately. The difference between this lesson and lessons in prior years was quite large.

The three primary types were differentiated in the slides I gave in class. A PDF of those slides is included below:

I introduced these types over the course of two days. On the first day, we only did Type I and then quite a bit of practice. On the second day, we did Type II and III problems and practice. Then, on day three, the types were combined. Students had to classify the problems by type and then solve them. The practice sheet for their notebooks was the following:


I will definitely continue to teach the Betweeness postulates like this, simply because it helps kids catch onto the geometric reasoning layer so quickly.