SWBAT apply the concept of solving equations to ratios and proportional reasoning.

Using part to part relationships create a homemade bubble solution while solving rational equations at the same time!

15 minutes

Warming up with fraction ladders is a great way to get your students’ thinking about ratios and equal parts for the lesson today.

Give students the handout Learning Ladders. If your students are unfamiliar with fraction ladders then take a few moments to discuss the first ladder. As a whole class. The idea of a fraction ladder is breaking a whole amount into different equivalent pieces. For example, the first ladder has a whole total of 100 and there are four total rungs on the ladder so you want to break 100 into four equal pieces (the rungs are evenly spaced). The finished ladder in questions one should have a 60 at the top and a 30 on the middle rung because 30 is half of 60 so each section in the ladder is 30 and 30. Just like the ladder with four rungs (four equal parts) will be numbered 15, 30, 45, 60 going up.

Allow students time to complete the rest of the ladders on the handout. As students work, move about the room assessing students and providing feedback that moves learning forward.

After students complete the ladders put the following questions on the board and ask students to write answers on a marker board (thick page protectors or slick notebooks work well also). Allow students about 20 seconds to record an answer to each question and then ask them to hold up the boards all at the same time so less looking and copying occurs.

Fraction ladder questions

- What amount is ¾ of 60?
- What amount is 33 1/3% of 60?
- 36 is what part of 60?
- What amount is 4/7of 60?
- 50 is what part of 60?

Again the activity today brings in ratios so this bellringer will prime your students’ brains for dealing with parts.

30 minutes

The title of this lesson was taken from the movie Willie Wonka and the Chocolate Factory when the group enters the room filled with Fizzy Lifting Drink. Willie Wonka says, “Bubbles Bubbles Everywhere but Not a Drop to Drink, yet.” I tried to find this on YouTube but couldn’t. If you have the movie, here would be a good time to show just about two minutes of it right when they enter the bubbles room after the lickable wallpaper.

Let your students know that we will be using bubble solution to talk about parts in a solution. You will immediately get the question about actually blowing bubbles, so you might as well tell them that if they work diligently to complete the activity on time and correctly with good detail, then yes they will be creating a very cool bubble solution to use outside. Pass out the activity “Bubbles Bubbles Everywhere But Not a Drop to Drink.” Allow students to work in collaborative groups to complete questions one through three. As student work, move about the room assessing student entry points into the work and providing feedback that moves their learning forward. As you notice multiple methods of answering the questions ask students to present one particular idea during the mini wrap-up session. If you have multiple approaches to the problems - great! Ask students from each approach to present and then have the class discuss the merit of each approach (only select correct approaches not incorrect thinking). Hold a mini-wrap up over the first three questions at the end of about 10 minutes. One question I particularly like is question two when students are asked why a solution described by parts is better than an exact measurement. Spend some time really discussing the usefulness of parts in a solution mixture.

Next, allow groups another 10 minutes to work collaboratively to complete questions four through six. Some of these questions are difficult but allowing students to work in groups to persevere in solving them demonstrates math practice standard one **MP1**. Question 4 is especially difficult because the corn syrup is on 3/4 of a part, not a whole part. The answers to question 4 are parts of parts and that gets very overhelming for some students with so many fractions. Again move about the room while students work and hold another mini wrap-up session at the end of 10 minutes. Then ask a student to read question seven out loud. Remind students you plan for them to really create bubble solution, however they must decide how much of each ingredient is needed for the solution to actually work. Allow collaborative groups the remainder of the class period to work together deciding how much detergent and glycerin the will need. Tell groups if they do not finish this work during class that they need to complete this question at home and be ready to mix their portions the next day into a correct bubble solution. Remind students incorrect mixtures might result in a mess instead of a fun bubble solution so be careful.

5 minutes

Prepare an exact measurement recipe for their group’s bubble solution by finishing question seven, all parts. Mixtures will be created during the next class period.

Glycerin can be purchased from most craft stores including Hobby Lobby and Michael’s. Be prepared with a quantity of Dawn, Glycerin, and distilled water appropriate for the number of groups you have in class. Also plan ahead for containers each group will need to store their solution. You can ask teachers to bring in containers or tell students to bring their own. Empty sour cream or yogurt containers would work well as they have large openings for student to dip into to blow bubbles. You will need several measuring devices as well for both cups and ounces (parts of ounces for the glycerin). Because measurement devices need to be accurate, you might want to check with your science teachers and ask about borrowing lab supplies. The solution works best when it sits for several days after mixing together. (If you choose to add paint to the mixture, add it on day one and let it sit for a few days as well for best results with paint rings).

**Suggested use for bubble solution:**

You can also purchase tempera paint and add paint to each bubble solution, add about 4-5 table spoons to each container. If you choose to add paint, then when students’ blow bubbles and they pop, a ring of paint will be left behind. If you gather sections of poster board paper and take students outside to blow bubbles at the paper, then you will create paper with circle designs all over it as the bubbles pop and leave the paint behind. You can use this paper as a bellringer activity and ask students to label important parts of a circle such as radius, diameter, circumference and area with a marker. Hang these designs labeled in marker and it is an instant connection to volume discussions in 8^{th} grade where the base is always a circle.