What are your favorite end of the year activities? One of my favorites for the end of the school year is to have the students create "Memory Wheels." I laminate them and save them to put up at the beginning of the new school year. Creating these wheels gives students a chance to reminisce about the school year, and the wheels give the incoming students a chance to see what the "old" students thought was fun about their 6th grade school year.
Students write "6th Grade" in the center, and then write a sentence or two in each section. They create illustrations to go with the sentences in each section. Students use a template to help them create their wheels, and I have them use either oak tag or large white construction paper.
Other Wheel Template Uses:
The wheels could also be used at the beginning of the year, as a "getting to know you" activity. The student's name would go in the center circle. The student would need to choose 8 things to share about him/herself, and then write a brief description of them and illustrate them. I haven't used the wheel in this way yet, but I like the idea:) The wheel templates can be used for any type of project, at any time during the school year. In the past, I have used the wheels as a book report project: students choose main events from the book to feature in each section, they write a brief description of each event, and then illustrate each one. The title and author are written in the center circle. Update: I've created quite a few wheels in different content areas!
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Have I mentioned that I love Jo Boaler’s books and site, Youcubed.org? Well, I do! She shares so much fantastic research and so many wonderful ideas.
So, I was reading her book Mathematical Mindsets this week, and read about the “array game” (called How Close to 100), which I’ve seen all over Pinterest and thought was very cool. I tried it with my classes last year during a little bit of down time, and they liked it. I hadn't really thought of using it this year, but last week I noticed the baggie of polyhedral dice that I've had for a looooong time and thought it would be cool to use the dodecahedron dice for the array game. With these dice, the students could use numbers up to 12, rather than 6.
To set up their game, students each outlined a 20 by 20 area on their own graph paper. They took turns rolling their dice and creating arrays to represent the multiplication problem they had rolled. It was very interesting to observe the way students arranged their arrays. Some started in the corner and worked their way out, while others started on one side and worked their way across. Some made the arrays touch, if possible, while others left a row between each one. Some just drew their first few arrays anywhere and then discovered that they didn't have a lot of room to fit additional ones. The "winner" was the student with the fewest number of boxes left (some did get to zero left). The students really had fun with this!
Of course, some finished their games earlier than others. In these cases, I asked students to create arrays that used different numbers than the numbers they rolled, but represented the same area. For example, if they rolled 12 and 5, their arrays could be 10 by 6, 15 by 4, or 20 by 3 (not 30 by 2, we discussed, because the grid is only 20 by 20). If they rolled a number that couldn't be represented by a wholenumber array, they could then use an irregular shape, or a triangle  anything they could find the area of. It was interesting to see how some students got stumped when they tried to draw an irregular shape to represent a number like 81.
Most students enjoyed this twist (we continued it the next day so they all got to play this version), but a few complained that it made their heads hurt! That's ok...I know they were really thinking and growing mathematically! The next extension for early finishers (only a few) was to use the icosahedron (20sided) dice, and have students create area models to cover their grids and find the answer to the multiplication problems. This required a larger grid, so I had them tape 2 pieces of graph paper together and create 20 by 40 grids. Using the icosahedron dice gave a mix of 1digit by 1digit, 1 by 2digit, and 2 by 2digit problems to model and solve. Most students didn't get very far with this before we ran out of time, but I think this is a great way to them to visualize what multiplying by a twodigit number means. I'd like to revisit this one! I'm so glad I thought about using those polyhedral dice! Have you used polyhedral dice in your math classroom? If so, please share how!
Ratios and Proportions Activity for the Middle School
Math Classroom
Food can make ratios and proportions more fun during a middle school math class, right? "Something Fishy" is a great handson activity to help students understand a reallife application of ratios and proportions. It also gives them the chance to munch on a few Goldfish :) This is a lesson I found through the Mathline Middle School Math Project, sponsored by PBS (I mentioned this program in the "Remove One" post).
This ratios and proportions lesson presents the students with an environmental problem: "scientists have determined that the number of fish in the Chesapeake Bay has decreased. Assuming this is true, scientists must have counted the number of fish and noted the change. How did they count the fish?" After introducing the problem, the students brainstorm ways that the scientists could count the fish. I have four math classes, and in each class, there was a student who said that scientists could tag the fish. So we discussed how tagging the fish would work, and talked about the capturerecapture method. Using a sample ratio, we talked about how we could create a proportion to figure out an estimate of the population. For this lesson, we used: * regular Goldfish crackers * pretzel Goldfish crackers * 2 paper bowls per group (any container that they can scoop from will work...we used the 2nd bowl to put the "captured" fish into) * a spoon to scoop with I didn't count the number of fish that I gave each group...I simply poured fish into the bowl...but they all ended up having 7090 fish.
I demonstrated all of the following steps for the students, so they understood what to do, and then I gave them a RECORDING SHEET (found below) that also included the directions.
Student steps for the lesson: 1. Students "capture" a sample of regular goldfish from the container. This sample should be tagged by replacing them with pretzel goldfish, and the "captured" goldfish should be set aside and no longer counted in the population. 2. Students put the tagged fish back into the container and mix up the fish so that the tagged fish are evenly distributed. Move on to the recapturing: 3. Capture a new sample and record both the total number of fish in the sample and the number of tagged fish in the sample. Return all fish to the container. 4. Recapture 6 times (or whatever you have time for...we were able to do 6 times, and we have a 40min math period). 5. Guide the students to create and solve the proportion for their "bay."
6. Have students count their fish and then compare their estimated total with the actual number of fish. Some of my groups got fairly close...I believe the closest was an estimate of 68 and an actual count of 74. It seemed that the groups with larger sample sizes ended up with closer estimates than those with smaller sample sizes, though I didn't analyze those relationships too carefully yet!
7. Allow students to eat the goldfish (if they don't have allergies)! To see the PBS Mathline lesson, click HERE. What ratio and proportions lessons are your favorites? 
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