Double Number Lines and Round the World

Double Number Line

In my 7/8 Math class we're expected to cover 7th and 8th grade standards in 1 year. Last year I flew quickly through the 7th grade ratio and proportion strategies in order to allow more time for the 8th grade Linear Expressions unit. Unfortunately, this kind of back fired because the experiences they needed in understanding how ratios work would have made the 8th grade standards come much quicker.

This year, I'm trying to remedy that. We still need to move quickly, but I'm trying to incorporate lots of strategies at one time and how they relate to each other.

Today, we started with a ratio problem using a double number line. I wrote up my plan to implement it  here.

I used dry erase tents that I created by putting strips of packing tape on construction paper. They worked pretty well!

I used single strips of tape and trimmed off the edges. To the right are finished tents. The final picture is 2 pieces of tape together to make a larger tent.

I had students creating the number lines on whiteboards at their desks. I feel like I spent a little too much time on the activity and the students were getting a bit antsy. I think next time I wouldn't worry about getting all of the groups a chance at the number line or I'll switch to a different problem. It could also be that the problems wasn't challenging enough for these kids, but I'm still glad I did the activity because it's a good visual and they have a reference for how to solve ratio problems if they ever get stuck.

When I pointed to the ratio 35:1, I asked the question, "Does anyone know what this is?" The student I called on said, "The lowest it can go." I was SO EXCITED for his mistake! It allowed us to have a conversation about whether or not that was the lowest the ratio could go. Also, would it make sense to go in to the negatives? They had some fun trying to come up with situations that would result in the ratio being negative. (No...driving backwards is still positive miles! I need to show them the Ferris Beuller clip!)

Round the World

This is an activity I haven't done in a long time. I have 5 groups in the class so I put up 5 posters with problems. Each group had 1 color of marker and 3.5 minutes to start solving the problem on the poster. After the time is up, they switch posters. At the new poster they have 2 choices. They can either continue solving the problem using the method the other group used or they can start solving it their own method. We continue going around until every group has hit every poster.
Here are my thoughts...

• I honestly don't know if this is a good or bad strategy in math. I love the idea of students looking at other people's work, trying to decipher it and then continuing it...but I don't know if the time limit in this case is harmful. I don't feel like it is because they get to come back to the poster later and see what the results were.
• For this class, I think 3.5 minutes was too much time (at least for the problems that were presented...most were DOK 1 & 2.) . Almost all groups were able to solve the problems in the time allowed with time to spare.
• At the start of the activity, some groups spent very little time looking at the other strategies and just wanted to solve the problem their way...even if it meant duplicating a method that was already on the paper. Hopefully if we do this again, they'll have a better idea of what is expected.
• I think it's just because this is an "advanced level" class, but the posters were all very arithmetic heavy...it was the last session and a group was trying to come up with a new strategy and I heard someone say, "No one did any pictures." I was like, "No! They didn't! You should do that!" Unfortunately they didn't have time to finish, but at least we got to see that that method COULD solve that problem!
• I gave them time at the end to walk around to all the posters and see the methods others used to solve the problems. This allowed me to get an idea of what they know how to do as well as give the students some new ideas for how to solve these types of problems. Overall, I fell like it was a success.