Lesson 5: Representing Information

Overview

In this lesson students will represent information using a deck of cards. They will first use playing cards to store yes or no answers to a series of questions. Next, they will create a set of rules to represent the letters of their initials with a card or sequence of cards, then allow another group to retrieve the text using those rules. Last, students will modify their rules so that they can store any short piece of text using only two states (face up and face down), in a reflection of the computer’s use of binary. They will have the opportunity as before to test their rules by allowing another group to retrieve the text stored in the cards. By the end of this lesson, students should understand that there are many ways to represent information and that information in a computer is represented using binary states.

Purpose

This lesson is designed to give students a sense of how information can be represented in a computer using binary states. The key insight is that with properly designed rules it is possible to represent even complex information like text using sequences of these binary signals. The lesson is not designed to teach how a base-2 or binary number system works.

In subsequent lessons students will learn a little bit about how computers process information, including the next lesson which demonstrates how a computer might process information at this lowest level. This lesson sets the stage by showing how information is represented in a computer throughout that process.

Agenda

Warm Up (5 min)

Activity (30 - 60 min)

Wrap Up (10 min)

Assessment

Objectives

Students will be able to:

  • Create and use a representation system to store and retrieve information.
  • Use a binary system to represent information.

Preparation

For each student

For each group

  • Playing Cards
  • Construction Paper
  • Markers and/or Colored Pencils

Links

For the Teacher

For the Students

Support

Report a Bug

  • Do students need an intermediate challenge between representing a yes/no and representing the letters of alphabet?
  • If you have students who already know binary did you need to do any kind of differentiation for the Face Up / Face Down challenge?

Teaching Guide

Warm Up (5 min)

Goal: Students will begin to think about how the same information can be represented in different ways.

Yes/No Questions

Prompt: Tell the class that you’re going to ask some questions of them, and each person should answer truthfully, but in a different way. They can use a different word, a gesture, or whatever they want, but they need to answer the questions truthfully and in a different way than anyone who came before them.

Proceed to ask a series of questions to different students that all have “yes” or “no” answers (e.g. “Are you a student?” “Do you go to _____ school?” “Are you wearing a red shirt?”)

Discussion Goal

The students should understand that there are many different ways to represent the same information. They should also realize that it’s important that everyone agree on the rules for representation.

Discuss

How many different ways were you able to say “yes” to my question? Can you think of any other ways you might be able to represent “yes” or “no”? Would everyone know that that meant “yes” or “no”?

Remarks

There are many different ways to represent information. The most important thing is that we have a clear rules for what your words or gestures mean. Computers also need to have clear rules for representing information.

Activity (30 - 60 min)

Representing Simple Information with Cards

Goal: Students will explore different ways of storing information and create rules to interpret information.

Review: Quickly review the definition of the computer as a machine that can input, store, output, and process information, and tell students that they will be looking more closely at how computers are able to store information.

Remarks

What if I wanted to store your “yes” or “no” answers so I could look at them again later? But instead of using paper and pencil or a computer, I’m going to store them in a deck of cards. How could you use a the cards to represent your “yes” and “no” answers?

Group: Put students in groups of 3-4.

Distribute: One deck of cards per group, and one activity guide per student, and review the instructions for the activity as listed in the activity guide.

Discussion Goal

Students should be able to conclude that there are endless ways to represent the words yes and no using cards. These ways could fall into the following categories: colors, suits, numbers, arrangement, etc.

Circulate: Support students as they generate ideas for representing and storing their answers, and store and retrieve the information using the cards.

Share: Allow students to share out a few of the ways they came up with to represent yes and no.

Representing the Alphabet

Prompt: What if we wanted to store information that wasn’t just “yes” or “no” inside the deck of cards? What if we wanted to be able to store, for example, the letters of our names?

Share: Allow students to share out some ideas for representing text using a deck of cards.

Remarks

You and your group will be coming up with a set of rules that will allow you to use a stack of cards to represent the initials of everyone in your group. To communicate, the only thing you’ll be allowed to do is leave a single stack of cards on the table and rules for interpreting them. You can use any of the ideas we just generated for representing information, or you may choose to come up with new strategies of your own.

Direct students to the second page of the activity guide, where they will be instructed to come up with a way to represent and store the letters of their initials in the deck of cards.

Circulate: Ensure all students in the groups give input for the rules. During this time also encourage students to test their own rules, since they know they’re going to be used by other people.

Once students have finished storing their initials in the deck of cards, allow them to look at another group’s deck and use the given rules to figure out which initials have been stored inside it.

Circulate: Move around the room observing the different strategies each group is using. Ask them whether they are having success in interpreting the stacks of cards left for them or to reflect on why or why not that is the case. If there is time ask groups to try to use more than a single group’s rules and cards.

After all groups have had a chance to try a few of the other teams’ rules, ask students to return to their seats.

Prompt: Take a minute at your tables and talk about the following prompts. Be ready to share your thoughts.

Discussion Goal

This discussion is aimed to highlight the fact that there were many possible solutions to this problem. It may be the case that some groups found problems with their rules as a result of testing them. Use the second prompt as an opportunity to highlight the types of things they could think about as they move to make a new protocol in the second half of this class.

  • Were some rules easier to understand or use than others? Why was this the case?
  • Did you notice any patterns across the rules?
  • Are there some things that every group needed to account for to have good rules?

Discuss: After a couple minutes, invite students to share the results of their table discussions.

Face Up / Face Down Challenge

Remarks

I saw a lot of good ideas for this challenge, and even if there were a couple of “bugs” you identified in your rules, you probably are thinking about how you can improve them.

We’re going to run this challenge again, but now with more constraints. This first time you were allowed to use any piece of information about the card you liked to make your rules. This time you will only be able to use whether a card is face up, or face down. You also won’t know what your message is in advance, but I will tell you that it is only 10 letters long. That means that you can only use 5 cards to encode each letter.

Direct students to the third page of the activity guide, where students are instructed to come up with a way to represent any text using only patterns of face up and face down cards.

Teaching Tip

Extra Support for Students

If students seem to be having a hard time getting started, it might be helpful to have them think about a pattern that would allow them to start with simple pattern and just change one state of the pattern for the next letter. For example, if five cards face down is A, what could you change about the pattern to represent B, or C?

Circulate: Students should be discussing possible ways of represent letters with cards. You can also encourage them to use some space on the desk to lay the cards out to test for some patterns that could work. Once a group has completed its set of rules, give group members an 8-10 letter message to encode.

Once students have finished storing their message in the deck of cards, allow them to look at another group’s deck and use the given rules to figure out what message has been stored inside it.

Circulate: Move around the room observing the different strategies each group is using. Ask them whether they are having success in interpreting the stacks of cards left for them or to reflect on why or why not that is the case. If there is time ask groups to try to use more that a single group’s rules and cards.

After all groups have had a chance to try a few of the other teams’ rules, ask students to return to their seats.

Wrap Up (10 min)

Discussion and Journal

Discussion Goal

Students should understand that there were many different possible ways to store information in the cards. As long as the rules for representing the information are clear, the system will work. They may also note that when they had fewer options for using the cards (only face up and face down) they needed more cards to represent a single letter.

Discuss: Have students share out some of the different rules that they created to represent and store information in the deck of cards. How did changing the definition of the problem change the way that they approached it? Were their any similarities that all the approaches had? How did groups differ in the ways that they solved the problem?

Prompt: Ask students to reflect on the following questions in their journals

  • What is some good advice for people developing a system to represent information?
  • Do you think that any information could be represented using the face up/face down system? Why, or why not?
  • Could you use the same face up/face down patterns with a stack of coins? A list of up and down arrows? What other systems could use those patterns?

Remarks

There are lots of ways to represent information. The first step of getting a computer to help us solve a problem is to represent the problem in the way a computer can understand. Computers use a binary system to represent information, meaning that the system only has two options. You used a binary system today when you only used face up and face down to communicate your message.

Just as your groups came up with different ways to represent the same letters, computers have different ways of representing the same information. It’s important that we agree on the rules for representing information so that we can input, store, process, and output it effectively. This is the first major step in solving problems with computers.

Tomorrow we’re going to look at how computers can process information stored inside of them.

Assessment

Rules can be collected and displayed as a formative assessment

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Problem Solving - Computers and Logic: Lesson 5 - Representing Information

Background

In this lesson you’ll explore different ways of representing information as you design your own system for representing text using only a deck of cards.

Resources

Standards Alignment

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