Lesson plan at a glance...

In this lesson plan…

• Lesson Overview
• Materials and Equipment
• Preparation Tasks
• The Lesson
• Learning Objectives and Standards
• Additional Information and Resources

Confirm that your computer is on and logged-in, if used

1 to 3 minutes

Confirm that your projector is turned on and is projecting properly, if used

1 to 4 minutes

Confirm that all students’ computers are turned on and logged-in

15 to 25 minutes

Draw picture or project picture of the flasks

5 minutes

Warm-up Activity: The challenge

15 minutes

Activity 1: Pour the water

20 minutes

Wrap-up Activity: Assessment

10 to 20 minutes

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 exactly one of these containers to hold exactly 5 millilitres?

Notes to the teacher:

Tell the students the containers are blacked out and oddly shaped, so you can’t tell by weight or watermark how much is in the container - you can only accurately tell if it is empty or if it is full. You can’t look at the container to ascertain any other quantities.

You may notice that some students need help to get started. Stop their work and ask, “What do you know about the final desired volume?” “How can you express that value other than ‘5’?” “How do you think you can break this big problem into smaller problems?”

Assessment:

Ask students how they came up with the process for determining the correct solution. After the discussion, continue to Activity 1 in which you will suggest decomposition as a starting point.

Activity:

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:

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:

Assessment:

Assess students on their ability to reach the correct answer. Assess higher-level students on finding the most efficient/optimal method (the fewest number of steps).

Activity:

Give students the task of optimizing the algorithm in Activity 1 (if not done already).

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?

Assessment:

Instructors should assess student answers to a new problem or assess optimization strategies.

A1: You know that you do not have a 5 mL container, so the only way you can get 5 is by adding two smaller components like 4 and 1 or 2 and 3, for instance. The only way you can get 1 mL, 2 mL, or 3 mL of water is to mix and pour water from one container into another.

A2: Generally speaking pouring the smaller container (4) into the larger container (7) gets you to the amount of 1 mL much faster which is helpful if you want to add it to 4 mL in order to get 5 mL, the goal.

Learning Objectives

Standards

LO1: Students will be able to use decomposition to break the water measurement problem into smaller more manageable problems.

Common Core

CCSS MATH.PRACTICE.MP7: Look for and make use of structure.

NGSS HS-ETS1-2: Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

Computer Science

CSTA L2.CT.12: Use abstraction to decompose a problem into subproblems.

LO2: Students will be able to develop an algorithm to solve similar measurement problems.

Common Core

CCSS MATH.PRACTICE.MP2: Reason abstractly and quantitatively.

CCSS MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.

Computer Science

AUSTRALIA 6.4 (Creating digital solutions by: defining): Define problems in terms of data and functional requirements, and identify features similar to previously solved problems.

CSTA L2.CT.1: Use the basic steps in algorithmic problem-solving to design solutions (e.g., problem statement and exploration, examination of sample instances, design, implementing a solution, testing and evaluation).

UK 3.2: Understand several key algorithms that reflect computational thinking [for example, ones for sorting and searching]; use logical reasoning to compare the utility of alternative algorithms for the same problem.

LO3: Students will be able to record the data from the simulation for efficiency assessment.

Common Core

CCSS MATH.PRACTICE.MP5:Use appropriate tools strategically.

Computer Science

AUSTRALIA 6.4 (Creating digital solutions by: defining)

CSTA L2.CT.1

UK 3.2

LO4: Students will be able to analyze and evaluate the algorithm to determine its efficiency.

Common Core

NGSS HS-ETS1-3: Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.

NGSS MS-ETS1-2: Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

CCSS MATH.PRACTICE.MP2: Reason abstractly and quantitatively.

Computer Science

AUSTRALIA 6.4 (Creating digital solutions by: defining)

CSTA L2.CT.1

UK 3.2

Term

Definition

For Additional Information

Optimization

The process of modifying a software system to make some aspect of it work more efficiently or use fewer resources.

http://en.wikipedia.org/wiki/Program_optimization]

http://en.wikipedia.org/wiki/Mathematical_optimization

Complexity

Characterization of something with many parts where those parts interact with each other in multiple ways, or the degree to which something can be characterized in this way.

http://en.wikipedia.org/wiki/Complexity

Concept

Definition

Decomposition

Breaking down tasks into smaller, manageable parts

Algorithm Design

Creating an ordered series of instructions for solving similar problems

Simulation

Representing or modeling a process

Contact info

For more info about Exploring Computational Thinking (ECT), visit the ECT website (g.co/exploringCT)

Credits

Developed by the Exploring Computational Thinking team at Google and reviewed by K-12 educators from around the world.

Last updated on

07/02/2015

Copyright info

Except as otherwise noted, the content of this document is licensed under the Creative Commons Attribution 4.0 International License, and code samples are licensed under the Apache 2.0 License.