Water Water everywhere!

In this activity, students will be faced with the complex problem of measuring 5 mL of water with only a 4 mL container and a 7 mL container. Students must use decomposition to break the problem into smaller problems and then to design an algorithm to solve it.

Activity:

Ask students to solve the following problem:

You’ve run into a predicament. You want to do a science experiment. Given two containers, one that can hold 4 millilitres and one that can hold 7 millilitres, how can you get one of these containers to hold exactly 5 millilitres?

In this activity, students will use decomposition to break down the problem into discrete steps and use the set of steps to design a method, or algorithm, to measure 5 mL of water.

Encourage students to describe the solution in discrete steps and to record the amount of water in each container (A and B) contains at each step.

We can do this by first noting that at any point there are only three actions we can do: completely fill a container, completely empty a container, or move the contents of one container to another (for this, we can use the shorthand A -> B to mean pouring the contents of A into B).

So an instruction to fill up the first container (A), pour it into the second (B) and then empty container B would look like:

In this activity, students will use decomposition to break down the problem into discrete steps and use the set of steps to design a method, or algorithm, to measure 5 mL of water. Finally, they will execute a simulation to test their algorithm for optimization and efficiency.

Once students are comfortable with the notation, allow them to create their own table to describe the solution by interacting collaboratively in small groups.

An example solution might look like:

If students find a valid solution, encourage them to find other solutions to the same problem. Ask them to count the number of ‘instructions’ used by their solution (for example, the number of instructions for the above would be 12). Explain that the number of instructions used can be taken as a measure of the optimization or efficiency of their solution - the lower the number, the more efficient the solution because it takes fewer operations to achieve the goal.

A more efficient solution (because it only uses 9 instructions) would be:

In this activity, students analyze their method for measuring 5 mL to determine: a) how they figured out how to start - decomposition, b) how they worked out the solution - algorithm - to solve the problem, and c) if their method is efficient based upon testing a simulation. Finally, they solve a similar problem and their solution is assessed.

Activity:

Give students the task of optimizing the algorithm they designed.

Assign a similar problem with different sized flasks of water and a different goal. If they have learned a process for solving this type of problem, they can apply the process to a different scenario.

Q1: How do you know how to start?

Q2: How do you know if you should use the method that pours A into B or the method that pours B into A?

Lesson Vocabulary

Computational Thinking concepts