MIXED NUMBERS AND IMPROPER FRACTIONS
Annah Kuriakose
7th Grade Math
Day 6
4th Period
June 16, 2009
Approximate Time:
50 minutes
OBJECTIVE:
TSW will learn how to convert mixed fractions to improper factors and vice versa. (DOK 1, 1c)
MATERIALS:
paper, pencil, dry erase markers, handouts, overhead projector, transparencies, wet erase markers
WARM UP: (4 min)
Add or subtract and reduce:
4/8 +2/4 =
1/5+3/5=
5/6-2/3=
4/7-7/7=
SET: (3 min)
How tall are you guys, do you know? I’m about…5’4”. How tall do you think the tallest person in the world is? How about the shortest? Here’s a picture of the tallest and the smallest people in the world standing next to each other. Pretty cool, right? So do you guys know how many inches are in a foot? 12 inches are in a foot. But when we talk about a 7 foot tall person, we don’t say he’s 84 inches tall, we say he’s 7 feet tall. So there’s two ways to say the same thing. In today’s class, we’re going to look at fractions, but of a slightly different kind, and we’re going to learn two different ways to write the same thing. In math, when we can write the same thing two different ways, we say we can convert between them. Convert just means change one into the other. So today, we’re going to be converting between what we call mixed numbers and improper fractions.
PROCEDURES:
A. Terminology (8 min)
Using overheard, define:
Proper fraction: A fraction whose denominator is greater than its numerator. This is the type of fraction we’ve worked with so far. Can someone give me an example?
Improper fraction: A fraction whose numerator is greater than its denominator. I’ll give you one example: 11/8. Can someone give me another?
Mixed number: The sum of a whole number and a fraction. For example, 1 ¼ means 1 +1/4. Can someone give me another example?
Remainder: The number left over from a long division problem. For example, divide 10/3. We get 3 and then 1 left over. 1 would be called the remainder.
Keep those definitions close by, but now I want to turn to how we would convert an improper fraction to a mixed number.
B. Converting improper fractions to mixed numbers. (9 min)
Remember that improper fractions are those that have greater numerators than denominators. In order to convert from improper fractions, all we have to do is a skill that we already know. Can someone tell me what the line means? [Expect to hear “division”]. Great. Let’s do 15/7. Go through the problem with a thinkaloud: Hmmm, 7 goes into 15 2 times and then I have 1 left over. If I look at my definition sheet,1 is the remainder for this problem. The way I would write this as a mixed number is, I would write the whole number and then I would write the remainder/denominator.
I want you guys to copy this into your notebooks with the heading Converting Improper Fractions into Mixed Numbers. Write 15/7 2 1/7, and include the work. I’m going to put two do-now problems on the board: 20/3; 99/8. I’m going to be walking around checking. Raise your hand if you have a question.
C. Ask students to come up to the board and complete the problems. (3 min)
Great, it looks like everyone has this concept down. Now before I hand out some independent work, let’s go over the rules again. Once I divide, if I’m left with a number, what is that number called? And how do I write a mixed number?
D. Independent work: converting improper fractions into mixed numbers. (5 min). Do as much as you can in the next five minutes and I’m going to ask that you do the rest for homework.
G. Converting mixed numbers into improper fractions. (9 min)
Now that we know what mixed numbers are and we know that we can convert from mixed numbers into improper fractions, let’s try the reverse, converting mixed numbers into improper fractions. This is actually very easy. All we have to do is follow this little diagram I’m going to draw for you. While I do this I want you to head a new page with Converting Mixed Numbers into Improper Fractions.
Draw [] multiply[]add [] to find the numerator. Denominator stays the same. Do a thinkaloud with 8 1/3 25/3. Assign do now with two more problems: 5 ¾, 18 1/7.
H. Ask students to come up to the board and complete the problems. (3 min)
Excellent, now as we know, the best way to learn math is to practice, so I want you guys to get started on this independent work as well, and complete the rest for homework.
I. Independent work: converting mixed numbers into improper fractions. (5 min). Do as much as you can in the next five minutes and I’m going to ask that you do the rest for homework.
CLOSURE:
So, today we learned what improper fractions are and what mixed numbers are. To convert an improper fraction into a mixed number, we divide, and then put the remainder over the denominator. To convert a mixed number into an improper fraction, we multiply the whole number by the denominator, add the numerator, and put our answer over the denominator. Tomorrow, we’re going to be continuing with fractions and learning how to multiply and divide them.
Objective:
The students will learn how to go convert mixed numbers to improper fractions and vice versa.
Assessment:
Informal:
The students will be observed as they work on their warm up and on the board(M) work over fractions (C).
Formal:
The independent work (C) will be picked up (M), graded for accuracy and entered into the grade book (D).