### Loved That Lesson

Today I'm linking up with The Teacher Studio for Loved that Lesson!

This is a lesson that I wrote about a while back, but I'm at the point in the year when I'll be using it again, so I thought I'd share it for this link up.
"Something Fishy" is a great hands-on activity to help students understand a real-life application of ratios and proportions, AND it 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 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 capture-recapture 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 70-90 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 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 40-min 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.
7. Allow students to eat the goldfish!

What ratio and proportions lessons are your favorites?

1. How much fun is THIS! Thanks so much for sharing...PBS has some great teaching tools! Thanks for linking up this month--hope to see you in April!

2. This is such a fun lesson!! I'm sure the goldfish motivated your students; I know anything with food gets my kids excited! Thanks!!

### Memory Wheels - First Day, Last Day, and Any Day in Between!

This post has been moved to:  http://www.cognitivecardiowithmsmm.com/blog/memory-wheels-first-day-last-day-and-any-day-in-between

### How Much Math Homework??

I am very curious about math homework in middle school, from a teacher perspective:     How much math homework do you give?     What kind of homework do you give?     How do you go over it in class? Let me explain why I ask these questions. I have taught 6th grade math for eight years, and every year, my goal is to "perfect" the homework issue. My basic issue is that I feel that I spend too much time going over it (not necessarily every day, but often). In the past, we have reviewed homework in the following ways:    1. going over answers as a class    2. self-checking answers that are on the board and sharing any questions    3. partner-checking and then verifying    4. choosing only a few problems to check When I taught elementary school (for 12 years), I never seemed to have this problem....we had 60 minutes for class and I never struggled to fit everything in. But at middle school, we have 44 minutes (minus time to switch for classes), and I just haven't fo

### Math Class - First Day Activity

Rectangle of pentominoes Many 6th graders seem to have a pretty negative attitude about math, so I try to do something interesting to "grab" them during our first class. Last year, during the first math class, we spent part of the period working with pentominoes. Before working with the pentominoes, however, we played a name game so we could learn each others' names (I find it impossible to start anything else if I don't know some names, and fortunately, I learn them fairly quickly). rectangle outline For the activity, I divided the students into groups of 3 or 4. The directions for the activity were not complicated - the task was to make a rectangle, using all of the pentominoes. I gave students an outline of the rectangle, as pictured to the left, so they would know the correct size of the rectangle. The squares in the grid are each one inch. The rectangle is 5 squares (inches) wide and 13 inches long (13 inches includes the row that has the "Pent