Lesson 2Binary Number 1Preparation: 5-10 minutesLesson: 90 minutes

In this lesson, students will understand and use the concept of number in base two and ten. _________________________Vocabulary Binary Decimal Base 10 Base 2 Expanded notation Convert

Students learn that the numbers we see every day are all in base ten. We can represent numbers in different bases, and particularly in base 2. all information in a computer is stored and transmitted as binary digits (base 2). A single piece of data which can be thought of as either zero or one.

ObjectiveStudents will be able to identify binary numbers and what they represent. write out and decode binary numbers. convert numbers from base two (binary) to base ten (decimal).

Tie-In Knowledge Mathematics Form 5 Chapter 1: Number bases

Student LearningLook for the following misconception: Numbers without written base notation has no base. Numbers in base two are not binary numbers.Look for the following insights: Numbers in base two are also known as binary numbers. Every number can be represented in binary form. Students read numbers in base two as: 1012 is read as one zero one base two.

MaterialsFor the Class A set of cards like the following:161248

Copy for Each Student Secret Message 1 Worksheet Secret Message 2 Worksheet

~MinActivitiesAssessment

15Introduction1. Show a set of cards with numbers to the students. The set should look something like this example: 168421

2. Have students sort the cards in descending order so that the largest is on the left and the smallest is on the right.3. Guide students to find the pattern in the numbers. Ask: What do you notice about the numbers on the cards? For the aspiring kids it is enough for them to notice that 1+1=2, 2+2=4, etc. Middle kids should recognize 1 x 2 = 2, 2 x 2 = 4, etc. Higher achieving kids should say something like "powers of 2." If I had given you another card, what would it have been? 32 How many cards would I have given you if the maximum card were 128? 8

20Activity 11. Explain to students converting between binary and decimal numbers is fairly simple, as long as you remember that each digit in the binary number represents a power of two.

Convert1011001012to the corresponding base-ten number.I will list the digits in order, and count them off from the RIGHT, starting with zero:digits: 1 0 1 1 0 0 1 0 1

numbering: 8 7 6 5 4 3 2 1 0

The first row above (labelled "digits") contains the digits from the binary number; the second row (labelled " numbering") contains the power of2(the base) corresponding to each digits. I will use this listing to convert each digit to the power of two that it represents:Expanded notation:128+ 027+ 126+ 125+ 024+ 023+ 122+ 021+ 12 = 1256 + 0128 + 164 + 132+ 016 + 08 + 14 + 02 + 11= 256 + 64 + 32 + 4 + 1= 357Then1011001012converts to35710.Binary Worksheet 1

35Activity 21. Divided students into groups.2. Distribute Secret Message 1 worksheet to each group.3. Each group have to decipher the secret message by changing binary number to decimal.4. Allow the groups 20 minutes to complete the task.5. Have every group present their respective secret message to reveal the entire message as a class.

Secret Message 1 worksheet

15Activity 31. Distribute Secret Message 2 worksheet to each student. Have student complete Secret Message 2 worksheet individually. Provide assistance to students having trouble completing the worksheet give.

Secret Message 2 worksheet

5Reflection1. Have students review the following questions:

Are binary numbers important? yes Why do you think it is important? It is much easier to work with because big numbers can simply be written with ones and zeros.