Math 87 - Lesson 27
I Title: Multiples / LCM’s / Equivalent Division Problems
II Goals:
- TLW be able to find multiples of any positive number.
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TLW be able to find the least common multiple of any pair of positive numbers.
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TLW be able to convert appropriate division problems into simpler division problems
III. Objectives:
- TLW be able to find the first ten multiples of 8 of 10 positive number.
- TLW be able to find the least common multiple of 9 of 10 pairs of positive numbers.
- TLW be able to convert 4 of 5 appropriate division problems into simpler division problems.
IV Student Entry Level: limited background with multiples, but know factors; sound background in division
V Desired Mastery Level: 85%
VI. Set:
Does anyone in here ever read comic books or watch super hero television shows? I love shows like that. A few weeks ago, I saw a Batman cartoon where Batman and Robin were in a big maze and they only had a little time to get to the end. They started out trying to solve the maze, but they ran out of time. So instead, they found a way to go over the maze and get to the end quickly.
Did Batman solve the maze? He found the end. That was the goal he set out to achieve. He did get the bad guy, the Riddler I believe, and justice was served. So tell me, was there anything wrong with Batman’s shortcut?
No there is nothing wrong with taking a shortcut, as long as the shortcut works. We’ve all seen sit-coms where the dad "knows a short cut" and they end up in the middle of no where.
In math the same thing can happen. If you try a short cut that doesn’t really work, you can end up in Albuquerque instead of at your answer. I’m going to teach you one simple shortcut for division that really does work.
VII. Instruction:
- Multiples
- Start with any whole number, like 3.
- Multiply that by any other whole number, like 7.
- The result (21) is what we call a multiple of 3.
- The multiples of a number are that number times 1, 2, 3, 4, etc.
- Examples: multiples of 2, 3, 4, 9, 10, and 12.
- Common multiples
- Demonstrate common multiples of 2 & 3 (from above).
- Common multiples
of two numbers are the multiples shared by both numbers.
- Examples with 4 & 9 and 10 & 12.
- Least Common Multiples
- Simply the smallest of the common multiples of the two numbers.
- Examples with pairs as above.
- Equivalent Division Problems
- This is the shortcut part
- 16 lollipops for $4.00 how much is 1 lollipop? The problem is $4 / 16.
- Look at 16 and $4. They’re both multiples of what?
- They’re even, so easily they are multiples of 2.
- So take half of each: half 16 is 8 and half 4 is 2.
- Both even, so divide them both in half again
- ½ of 8 is 2 and ½ of 2 is 1.
- I know that you can solve that: If 4 lollipops are $1, how much is 1 lollipop?
- $1 / 4 = $0.25
- Examples: 210 / 30 , 108 / 27 , 1024 / 128 , 279 / 81.
- Observed Practice: Practice problems a.-h. in class
- Review and Practice: Problem set 27, # 1-29 for homework.
VIII Checking for Understanding: During lesson where it says "Examples".
IX Supervised Practice: Begin assignment in class so questions can be asked and answered. Walk amongst the class observing work.
X Closure: Give a quick quiz with 2 questions per objective ten minutes before class lets out. Review answers orally.
XI Independent Practice: All practice and problem set exercises in. Adapt directions as needed.
XII Lesson Evaluation: Complete after giving lesson.
Lesson went very well. It was a lot of content to cover in one class session. Did not have a chance to get to closure. Maybe shorten set for next time, it was distracting to discus cartoons and took longer than anticipated.
XIII Materials and their Use:
- Text book - homework problems
- Dry erase board – notes and examples