Lesson 1: What Floats Your Boat?

Student pairs will build boats from squares of aluminum foil with the goal of floating at least 15 pennies. After several design iterations, they will display their boats and examine others’. Each pair will then use one of their boats to gather data about water-level change when adding pennies to a boat. [Commonly, pairs can get somewhere between 10 and 30 pennies to float.]

The challenge does not require (and should not be immediately preceded by) any explicit mathematical content beyond counting. The data gathering prompts the students to expect and look for a relationship between changing quantities, and prepares them for the follow-up lesson in which they model this relationship and use the data to predict.


Sinking and Floating

10 minutes


  • Teams of 2 (together throughout cycle)
  • 5 pitchers of water spread around room
  • Each team (on a lunch tray if using):
    • one beaker (some .5 liter, some 1 liter)
    • one 4” square of aluminum foil
    • 4 paper towels
    • small container of pennies (around 50).


[include purposes and a discussion of what students should be doing/thinking/discussing/struggling with]

In this warmup activity, students have a chance to predict and experience what happens when they place their pennies or  foil in the water, and generate a few ideas about what could be made with this set of materials

Launch (narrative could include comments on timing)


(5 minutes) Teams should put some water in their beaker and predict then experiment with the foil and pennies in the water. Each team should come up with a few ideas of things we might make with this set of materials

Task statement

  • Put water in the beaker. Predict what will happen when you put your pennies or foil in the water, then experiment
  • Come up with several ideas about things we make using this set of materials

Orchestrating & Monitoring (narrative could include comments on timing)

Watch for any teams that start trying to float their foil, or even float pennies using the foil, during their experimentation.

After a few minutes, remind teams to be thinking of things they could make

Discussion (could be synthesis; narrative could include comments on timing)

End with a brief discussion:

  • What happens when you put pennies in the water?
    • They sink
    • Anything else? (they get wet… See if anyone notices the water level goes up, but don’t raise the idea or highlight it)
  • How about the foil?
    • Some might get it to float
  • What are some things we could make?
    • Take ideas
  • Today we’re going to try to use these materials to make some pennies float.

Anticipated solutions

Pennies sink, foil can float or sink

Possible things to make: stacks of pennies to make buildings, use the foil to make a model, use pennies as wheels for something that rolls, make lemonade (requires other materials…), make a boat.

Anticipated misconceptions and challenges

The class may not generate a lot of ideas for what to make with these materials.

Building & Refining

30 min


Same as warmup


[include purposes and a discussion of what students should be doing/thinking/discussing/struggling with]

Teams of 2 will be tasked with figuring out a way to get as many pennies to float as possible, using only pennies and one 4” square of heavy-duty aluminum foil. First they will make some predictions, then building and testing time.

After one try, they save their construction and display it with the number of pennies it held, then get another two squares and can make two more efforts (but each attempt can only use one square of foil). Then they scout other groups’ attempts, and get two more squares to try some final creations.

            Students should be struggling with design ideas here. They may base their creations on boats they have seen, or have other ideas like a sealed ball with pennies inside. The availability of additional squares of foil is meant to encourage rapid prototyping, and preservation of earlier attempts for documentation and evidence of improvement.

Launch (narrative could include comments on timing)

We’re going to try to get some pennies to float. Do you think we can get some to float?

[hopefully most will think yes]

(5 minutes) Each team, write down a sticky note with your initials and three numbers on it

Have the teams bring up their sticky notes and put them on the board, arranged in order of best guess along a number line (constructing a line plot).

(20 minutes) each team can try three different pieces of foil (but each boat can only use one piece). Once they’ve tried a design, they should save it and put a sticky note with it that says the number of pennies it could float and the letter “A”. Then give them their next 2 foil square; label them sticky “B” and “C.”

After 20 minutes, each team should display up to 3 “boats” with sticky notes, and each pair should circulate to look at others, tasked with finding one idea that they would try the next time they build.

After the scouting, give each team 2 more 4” squares of foil for their final attempts; label them “D” and “E.”

Task statement

First, decide as a team and write down on a sticky note

  • A number you are sure you can get to float
  • Your best guess for how many pennies you can get to float
  • A number you are sure is too high (but not a huge number)

And bring your sticky notes up and put them on the board in order of your best guess.

Use 4” squares of foil to float as many pennies as you can. Preserve each attempt and label them with a letter (“A” for first attempt, etc.) and include the number of pennies each one could float. You’ll have a total of 5 attempts. After the first three attempts, I’ll ask you to look around at what other groups have tried.

Orchestrating & Monitoring (narrative could include comments on timing)

  • You may want to prompt teams that are using wet pennies with “what weighs more, a dry penny or a wet penny?”
  • Watch for and note teams with evolving design, and query them about reasons for changes.
  • Watch for and note teams that notice the water level goes up when they add pennies.
  • If any team has not reached 15 pennies with one of the first three constructions, give them some extra attention and make sure they have paid attention to what other teams have tried and are not stuck on non-working ideas.

Discussion (could be synthesis; narrative could include comments on timing)

Anticipated solutions

  • Some teams will try to build “boats” similar to boats they may have seen.
  • Others will try large flat-as-possible “boats” to maximize surface area of the bottom
  • Some will build very tall sides

Anticipated misconceptions and challenges

Teams that have the smaller beaker (500ml) may complain that their building options are more constrained than others with larger beakers (which they are). That’s OK--different teams have different constraints. The variation in beaker size is intentional, and helps gradually build the case that displacement is a function only of the mass of the floating (boat + pennies), not of the shape of the boat or beaker or…. This will not be explored directly, but experiences like this are important to build this understanding gradually.

Lesson synthesis

10 minutes

Whole-group discussion (use pair-share when appropriate). Try to bring out these points:

Maker ideas:

  • What helped your pair work well together? [?Teamwork, listening to and offering ideas?]
  • Rapid prototyping: Identify groups that showed evidence of changing design between iterations, and ask them to explain their changes.
  • Scouting: learning by observing others
  • What made this difficult?

Mathematical ideas:

  • [comparing to initial estimates] Who thinks their maximum was closest to their initial guess?
  • Did any pair float more pennies than their initial “too high number”? How many pairs’ actual maximum was outside of their initial range? Why might that be? [we don’t have much experience floating things, so our estimating ability might not be very good]
  • What do you think are characteristics of boats that help them hold a lot of pennies?
  • Do the boats that held lots of pennies have similarities in how they are constructed, or is there a big variety? Can you find anything they have in common? [The volume displaced before the water overflows the edge is the determining factor, so they might say “they all have tall sides” or “they all have a big bottom;” the actual maximum is some sort of “balance” between large surface area of the bottom and tall sides. Note this is not the focus of this learning cycle, but this context could be referenced in a unit on volume or optimization.]

Bridge to the next lesson:

  • [If anyone filled their beaker too full and had it overflow] [Josephina], what happened to your beaker when you added a lot of pennies?
  • [If not]: What did you notice about the water level when you added pennies? [It went up.]

Conclude by telling students that you would like to use the next lesson to try to understand the relationship between the number of pennies and the change in water level. Have teams save a boat that floated at least 15 pennies in a safe location. If you are using lunch trays, each team could save their whole setup (beaker, pennies, boat) on a tray, if you have a place to keep them.

Materials for this Lesson



Activity 1: Warmup:  Sinking and Floating: 10 minutes

Activity 2: Building and Refining: 30 minutes

Lesson wrapup: 10 minutes