Title: Base 2
I Unit: Other based number systems
II Goals:
1) TLW understand the concept of base 10 and base 2 number systems.
2) TLW be able to go from base 10 to base 2 and v/v.
3) TLW be able to add and subtract in base 2.
III Instructional Objectives:
1) TLW list the characters used in base 2.
2) TLW change from base 10 to base 2 18 of 20 times.
3) TLW change from base 2 to base 10 18 of 20 times.
4) TLW add and subtract successfully 18 of 20 times.
IV Student Entry Level: Assume no knowledge of other-based number systems.
V Desired Mastery Level: 85%
VI Set:
As far as we're concerned, there are 10 different digits. 0,1, 2, 3, 4, 5, 6, 7, 8, 9. We make all the different numbers out of combinations of these digits, like 4,820.
But computers don't think like we do. The number of digits, 10, is actually fairly arbitrary. If we had 12 fingers, we would probably have two more digits that we'd use. But we don't, so the human world tends to understand base ten the best. Computers don't have any fingers, so it's a little tricky to teach them base ten. Before the programming is put in a computer, all it knows is ON and OFF. Think of on and off as the computer's fingers. Thus, the computer thinks of numbers with only two digits instead of 10.
This kind of number system is called "base two", because it only has two digits. We use 10 digits, so our number system is called what?
I am going to teach you to think like a computer. So forget that you have ten fingers and remember that you have two hands.
VII Instructional Procedures:
- count base ten numbers on fingers
- start with 0
- when the last finger goes up, a 1 goes in the next slot, the tens place
- in base 2,
- start with 0
- when your last hand goes up you put a 1 in the next slot, the two's place
- similar example for hundreds and thousands place and 4's, 8's, 16's, & 32's place.
- show the different slots as powers of 2 versus powers of 10
- examples (10=>2 & 2=>10) **work with manipulatives (coins, etc.)
- work for the class
- work with class
- class work examples
- demonstrate adding base 2 (with manipulatives)
- work for the class
- work with class
- class work examples
VIII Checking for Understanding: During lesson where it says "class work examples".
IX Supervised Practice: Begin assignment in class so questions can be asked and answered. Walk amongst the class observing work.
X Closure:
- Have class recap lesson by answering questions.
- What base do people usually use?
- What base do computers use?
- Why? (on & off)
- What digit means "on"? "Off"?
- What digit do you start with at the very beginning regardless of the base?
- Turn 10110 into base ten.
- Turn 27 into base 2.
- 101+11= (base 2)
XI Independent Practice:
Odd numbered exercises in chapter (select such that there are no more than 12 problems for any one objective.) Adapt directions as needed.
XII Lesson Evaluation: Complete after giving lesson.
XIII Materials and their Use:
- Text book - homework problems
- plastic chips, coins, or other manipulative - demonstrate only 2 digits
- fingers and hands - comparison
- overhead - demonstrate how written