What we’re doing: We are starting a four-week project in our math and science lab school.
Goal: To use a real life example to frame the learning around a curriculum between mathematics and science. The learning goal is to introduce students to the scientific ideas of density, Archimedes’ Principle, buoyancy, surface area, volume, and the force of gravity. The mathematics is the language and the tool by which we are able to quantify each of these scientific ideas. For example, we will show that proportional reasoning and ratios help us to define and describe density, extending that description to explain concentration gradients and how that relates to buoyancy and Archimedes’ Principle. In addition, we would like to show that relationship between surface area and volume, how they relate, and how we use them in terms of density, buoyancy, and Archimedes’ Principle.
The project: The four-week project will have the students learning about the scientific principles as the students build miniature hot air balloons, which will culminate in the fourth week with a community event in which the students launch their balloons. The students will reinforce their learning and make predictions based upon their calculations as they build and design their balloons.
What we did: In the science part the students began their construction of their balloons immediately due to the short time spread between now and the launch date. The students were introduced to density through the idea of a density column and making predictions about what would happen when common household materials were mixed together. Then the students were given the materials and instructions to start making their hot air balloons.
I haven’t finished constructing the last three mathematics lessons, but I have a general idea for the next three weeks. What I did today was design a lesson that would cache a problem in terms of generating ideas with a general concept and getting specific as we refined our focus on the problem. The first iteration I am attempting to drum up interest in the problem, allowing students a gut level interaction with their imaginations and to fan the flame of their imagination. The next step with today’s lesson was to give them an idea of where we were going, and then have them come up with ideas that would be similar to the result we are aiming at. Today’s lesson involved essentially no direct mathematical concepts or computations, but was more trying to get their creative thinking going as we attempt to problem our situation.
The lesson started off with a quick slide show of cartoons drawing were two guys are sitting on a deserted island, then there is a helicopter and two people rescued. The next slide is a backpack with text that describes the two heroes are looking into their supplies to figure out the main problem situation we will spend the next lab period really digging into which is how to communicate with a helicopter at night, so the helicopter can find us upon its return from dropping off the first two rescued. After viewing the slide show students wrote their own ideas down, then shared out their ideas with the group. A few moments later I called on anyone who had idea in the first group to get more students to take part and have their voices heard (this class is a reluctant group of learners). The second group is famously into the lesson every time, so I followed the same format, but then had each group come up with a consensus of only two ideas – otherwise we would still be their listing ideas. The class results are recorded and displayed below:
7th Grade and 8th Grade
What are some ideas on how to effectively communicate with a helicopter at night?
- Break glow sticks and write SOS on island. 2
- Spell help with fire. 5
- Use flashlight in a strobe light fashion. 6
- Put a bomb in the water and make it explode. 4
- Rope and bright things and write the SOS sign. 2
- Throw rocks at the helicopter. 2
- Build a sling shot and shoot a fireball. 4
- Start a bonfire. 15
- Shoot a flare with the flare gun. 9
- Build a wood helicopter. 1
- Build a boat – times two. 6
- Bang thing to make loud noise. 9
- Make tree leave wings and fly away. 2
- Construct a statue of some sort and light on fire. 6
- Hug a tree. 5
- Make noise 4
- Swim away. 3
- Vocal communication either yelling or walki-talkie. 2
- Shake the tree. 3
- Perimeter of the island lined with torches and then climb to the top of the highest tree and light another torch. 2
What was in the video?
That science teacher was here?
He was about to fly. Using gravity (that was Jimmy’s idea)
Seeing which way the wind was blowing to see what direction the current was going.
Signal a helicopter with the big floating bag.
Boy was using force flow of air to make something float.
Signal a helicopter with the big floating bag. (idea too)
Get a leaf blower and act like it’s jet pack.
Current of ocean to sail somewhere.
What can we build with these materials?
Make a Chinese lantern and spell out SOS with the tape.
Construct a little hot air balloon.
Tape trash bags together and make a hot air balloon.
Burn shirts, light with candle, and then reflect fire light with foil.
Build a straw poker and poke the helicopter.
Make a straw and tree pole vault and jump to the nearest helicopter and yeah. No. no yeah. No what. OMG.
Light a candle, cover it and make a strobe light, and breakdance.
5th Grade and 6th Grade
What are some ideas on how to effectively communicate with a helicopter at night?
Group 1: 1. Flashlight pointed at sky, 2. Start a fire, boil water, and make beam (like Bat signal)
Shine light beam onto balloon to make a disco ball.
Group 2: 1. Break up into smaller teams with different ideas, 2. Reflect the fire with the ipad
Make a big balloon with coconut inside, light a little piece of wood on fire, and then let it fly.
Group 3: 1. Superman or 2: Or Mr. R’s ugly yellow shoes
(Missing their ideas here)
Group 4: 1. Flying rainbow pooping unicorns 2. Flashlight
Wanted to use leaves, giggle giggle,that’s her like glue bird poop glue. And tree bark that’s what she said. She said that out loud and make they could make the hot air balloon out of leaves and attached the leaves together. No that’s what shae said and then dear gonna gives up food and unicorns go woohoo?
Group 5: 1. Use glass (or smelter) when light shines on the glass and reflects it 2. Using ipad to signal with morse code or use c4 to blow up the island
Make a big balloon and get tree sap in the coconut, it’s a burnable material, and it floats. Draw SOS on balloon.
Group 6: 1. Something on fire to make a signal, 2. Yell really loud and crazy while jumping up and down
Turn balloon into hot air balloon and then fly after running really fast.
Group 7: 1. A bright banana, 2. Light their shirts on fire.
By getting air and filling it up with hot gas.
Group 8: 1. Get coconuts, light them on fire, and then throw them in the air, 2. Start a fire with leaves and glasses.
They make the hot air balloon with bright (giggle giggle) colors girl left in backpack and they need help with they are stranded in the island.
Next: The next part of the lesson had students watch a short 18 second clip showing a group of eighth graders holding a large balloon made of stitched together trash bags and a student walking around with the bag. I asked the students how we might use this idea with the ideas they had already generated in the same way as the first video (I mean that I ran through the same scenario where the kids wrote first, then shared in the group, and then shared whole class). We listed some of those ideas, and then I showed them my backpack with a slide that listed all the materials that were available. I pulled out all the goodies in the bag, and asked them to create an idea using the ideas they had generated but only using the materials that were in the backpack. We then had them share out as a group, and then whole class.
The lesson finished with having students write a few things they liked and a few things they wondered about. We will take their ideas and have them try to construct their ideas next week in class. We will then teach them the idea of density (described as a ratio) and proportional reasoning as it relates to the idea of hot air and get the kids to predict how that might make a difference in how the balloons will fly. As part of teaching them the idea of density, I am thinking about using hard-boiled eggs and a glass of water. Having students predict if the egg will sink in water, performing the experiment, and then asking them if there is a way we could make the egg float. I feel that the concrete demonstration is important for a better understanding for the kids, but I don’t know if they will become more confused as we are dealing with water and egg materials in one situation and air at different temperatures having different densities though it is the same material…I’ll have to ponder this over the week as I design the last concepts for that lesson.
How the kids did: The student samples from the day showed that a few of them picked up the more general ideas presented in the lesson. The general feedback had the students talking about the story created in the opening slide show. Many students liked the open-ended approach to the lesson, which I was afraid they might be hesitant to attempt, and they liked talking in the groups. One measure of success I feel is that several students made the comment verbally and in writing that they were not sure if this was really a math class. I take this as a compliment because we are trying to design a curriculum that approaches learning through problem solving and application. Another sign of success was several students wrote on their reflection they wondered what would happen next week, so they are already curious and want to come back for more. The last positive news was several students commented how much they enjoyed the class, how fast time goes by in lecture, and how they never get bored which are all great things to hear as a teacher – I’ll not mention the numerous students who wrote comments that I am funny and how much they like me, which is always fun to hear.
What I would like to see more of: I think the lesson is a good attempt at what I am thinking, but I don’t think it’s exactly right yet. I am also struggling with the usual problems of off topic chatter and unrealistic points of view from many of the eighth graders. The eighth graders are students attempting credit recovery, so they come with a lot of negative baggage toward school and are typically the lower performers which is part of the problem. What I am hoping to see is an increase in their engagement and a general increase in their attempts to problem solve. The students are starting to see that this is more gut level and with the absence of right and wrong, the students may come to realize that education is fun and interesting again. I will find it a huge success if I can just get these kids to ask questions and maybe, just maybe, determine some ways to answer their questions – that whole curiosity thing would be amazing. I would also like to increase the rigor and depth of the problems we attack and make them a little more relevant to the kids every day experiences.
Unity for now: What I am excited about is that we have a target for the next four weeks, with a definite outcome that the kids are constructing the product. I like that we have a framework to have some valuable learning go as an outcome and I like that there is a general buzz of good tidings from the students.
I wonder if I’ll be able to get the kids to understand the chain of relationships that different densities create a buoyant force as a result of Archimedes’ Principle which if great enough will overcome gravity. I want the students to understand the relationship between surface area and volume in relation to one another and how these relate to density and Archimedes’ Principle. I wonder if students will be able to compute these ideas as they are quite advanced for fifth to eighth graders, but I wonder if they will be able to scaffold through what they are building to these mathematical principles and their representation in the real world. I wonder if we can make that a reality for these kids.