Overview

In this lesson, students will practice representing numbers in binary (base 2), transitioning from the circle-square representations they made in the last lesson. Students will create and use a "Flippy Do", a manipulative which helps students convert between binary (base 2) and decimal (base 10) numbers. They will practice converting numbers and explore the concept of place value in the context of binary numbers.

Goals

Students will be able to:

Purpose

This lesson is designed to give students as much time as possible using the Flippy Do to get comfortable with the relationship between binary and decimal numbers and the concept of place value.

Resources

Getting Started

Prompt: Yesterday, you created your own number system using circles and squares. What can we communicate using only two symbols? Is there a limit?

Discuss: Students should quietly write an answer, then share with a partner, then discuss with the whole class.


Discussion Goal

In previous lessons, students represented information using two options. This is a quick thinking question to tap into students' prior knowledge and experiences. Once students have mentioned a few of the points below, they can move on.

Activity

Lecture: Today's activity is introducing students to the binary number system. As a visual aid, you can use Code.org's presentation slides for Unit 1, Lesson 4: Binary Numbers. These slides use a lot of animations. The lecture notes below describe when to move to the next slide or click through an animation -- if you aren't using the slides, you can ignore these prompts.

Lecture

Slide: Binary Numbers

Say: Today we are going to explore how Binary Numbers work.


Slide: 1 place value - 2 possible patterns

Say: With only one place value, we only have two possible patterns: circle or square.

Click through animation.

Say: For this example I'm starting with circle, but we could easily start with square instead.


Slide: 2 place values = 4 possible patterns

Click through animation.

Say: With two place values, we can make two sets of the previous patterns. Then, insert circles in front of the first set and squares in front of the second set. This makes four possible patterns.


Slide: 3 place values = 8 possible patterns

Click through animation.

Say: For three place value patterns, we can make two copies of the two place value patterns. Then, just like we did before, fill in the first set with circles in front and the second set with squares in front. This makes 8 arrangements.

Note: Computer scientists like to start counting at 0!


Slide: Instead of two shapes, what if we had 10 shapes?

Say: Instead of two shapes, what if we had 10 shapes?


Slide: 1 place value = Ten 1-shape patterns

Click through animation.

Say: We could use more geometric shapes, or we could use letters, but the shapes we are used to are the numbers 0 through 9.


Slide: 2 places = one hundred 2-shape patterns

Say: With two places, we have one hundred 2-shape patterns. These are the numbers 00 through 99.

Click through animation.


Slide: Quiz: What comes next?

Say: What happens when we count up to the last shape?

Say: Suppose we have three value places, and the digits 0-9-9.

Do This: Quick quiz! What comes after this number?


Slide: Quiz: What comes next? (with answer to quiz)

Say: 100! When we run up to the last shape, 9, we roll over back to 0 and add one in the next place to the left. This is the place value that we have used all our lives.


Slide: Where is this heading?

Say: Where is this heading?

Click through animation.


Slide: "Binary" is a number system with 2 shapes...

Say: Binary is a number system with two shapes.

Click through animation.


Slide: Making Organized Lists -> Counting in Binary

Click through animation.

Say: Instead of shapes, we use 0's and 1's. In this example, each pattern maps to a decimal number from 0 to 7.


Slide: Make Your Flippy Do!

Say: For today's activity, you will be creating your own Flippy Do. This is a tool that will allow you to quickly and easily translate between the decimal number base we are used to as humans and the binary number base that computers use.

Distribute: Hand out the Flippy Do templates - one per student.

Do This: Lead students through completing their Flippy Do's using the steps below, or following the slide as a guide. If you chose to give students already-completed Flippy Do's, explain the meaning of each row and how to use the Flippy Do.

  1. In the top-right cell of the Flippy Do, write the first power of 2, 20. In the cell to left, write the next power of 2, 21. Do this until you've finished the entire top row. The last value should be 27.
  2. In the second row, write the whole number equivalent of each power of two in the cell above. For example, the right-most cell in the second row should read "1", because that is the value of 20 in the cell just above it.
  3. In the third row, write a "0" in each cell.
  4. Write a "1" on the back of each flap on the bottom -- these will be flipped up over the zeroes in the third row. Make sure the ones aren't upside down when they're flipped!
  5. Cut on the dotted lines at the bottom.

Slide: Each place value represents one "bit"...

Say: Each place value represents one "bit" which is short for "binary digit". A binary digit can be a zero or a one. Your flippy do has eight "bits".

Click through animation.

Say: Together, eight place values, or "bits", makes up one "byte". Since computers represent information digitally, the lowest level components of information are bits.


Slide: Try Out Your Flippy Do!

Do This: Use your Flippy Do to try out these problems:

Represent these decimal numbers in binary:

Represent these binary numbers in decimal:

Note: It may be necessary to demonstrate how values can be calculated by flipping up a "1" for each value required to arrive at the sum of values equal to the decimal number.

For example, To convert the decimal number 10, I would flip up a one in the 8's position, because eight can fit in 10 (The next bit to the left is 16, which is too big). Then I have 2 left. I flip up a one in the 2's position. This gives me the binary number "1010", which means 10 in decimal.

If students are having a difficult time understanding the rules of the system, remind them of the concept of place value and relate to base 10.


Slide: Flippy Do Activity Guide

Say: Let's continue to practice with our own two number bases, decimal and binary. After you finish each of the four parts of the Activity Guide, I want you to check your work with your partner. Feel free to use your Flippy Do as you work.

Distribute: Activity Guide

Note: Encourage students to use their Flippy Do as a resource.

Note: As you circulate, take an opportunity to be a Lead Learner. Help students discover the items below using the suggested questions:

Wrap Up

Remarks


Teaching Tip

Number Bases: Number bases help us express data and reason about quantities. With ten digits on our hands and feet, the decimal (base 10) number base was natural for humans to develop. The ten symbols we use for this number base are the digits 0-9. For a computer, however, it makes more sense that data be represented in binary (base 2), as this can easily be interpreted with electrical switches set to two states: ON or OFF. The two symbols we use for this number base are the digits 0 and 1.

Both number bases take advantage of the concept of place value. In decimal, numbers are composed of powers of 10, increasing in value from right to left. Binary is similar, however we use powers of 2 (1, 2, 4, 8, 16, etc.). Expressed in binary, these values are 1, 10, 100, 1000, 10000, and so on. These make up the incremental place values in the binary number system.

Why Binary?: Students will see in a later lesson how computers use binary numbers as a representation of electrical signals on a wire. The wire is always set to one of two different options: on or off. Off can be reprsented with a 0 and on with a 1.

Prompt: Now that we've had a chance to practice, let's find out what we've learned and what we still have questions about. Write down:


Discussion Goal

Use this exercise to help assess what students learned and what needs to be clarified.

Assessment: Check for Understanding

Question: How many bits would be needed to count all of the students in class today?

Question: Each time we add another bit, what happens to the amount of numbers we can make?

Question: What are the similarities and differences between the binary and decimal systems?

Standards Alignment