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This is the worksheet to go along with the activity.

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This activity would be used for 6th grade students.
MS College and Career Readiness Standard-
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

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Students will first be divided into groups. Students will use a spoon to "catch" goldfish out of Styrofoam bowls. After the goldfish are captured, they will be replaced by the second type of goldfish (pretzel). The students will continue to catch fish and record the ratios on the worksheet provided. Then, students will use the formula given to compare their ratios, aka setting up a proportion.

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Bullins, //  by Lesa M.K. “20 Fun Ratio and Proportion Activities for Middle School.” Teaching Expertise, 27 June 2022, www.teachingexpertise.com/classroom-ideas/ratio-and-proportion-activities-for-middle-school/.

TodayShow. “A Definitive Ranking of Goldfish Crackers - Including the New Old Bay Flavor.” TODAY.com, 20 May 2022, www.today.com/food/snacks/best-goldfish-flavors-rcna29853.

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Manipulative of Choice-The Snack That Smiles Back!

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Manipulative of Choice-The Snack That Smiles Back!

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The manipulative I chose to go with is food, so I found an activity that uses two different types of goldfish. Not only does this serve as a manipulative, but a snack for a reward if all of the problems are completed.

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https://cognitivecardiomath.com/cognitive-cardio-blog/ratios-and-proportions-and-goldfish/

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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 capture-recapture method. Using a sample ratio, we talked about how we could create a proportion to figure out an estimate of the population.

Ratios and Proportions Lesson Materials

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.

Ratios and Proportions Lesson Procedure:

Teacher Demo
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 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 (if they don't have allergies)!

To see the PBS Mathline lesson, click HERE.

What ratio and proportions lessons are your favorites?

For some engaging ratios and proportions notes, check out the Ratios Fold it Up post!

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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?"