Introduction to Fractions, Equivalent and Simplifying
Introduction to Fractions, Equivalent and Simplifying
(1-2 days)
Vocabulary:
1. Fraction
2. Numerator
3. Denominator
4. Equivalent
5. Simplest form
Real World Examples:
1. Fractions in general, why and where we use them
2. What are some application to using fractions
Conceptual:
1. During lesson use fraction circles or have them draw rectangles . Have
them mimic what the
teacher is doing on the board or overhead. They need to be able to visualize why
two fractions are
the same and recognize it is the area of the objects they are comparing.
2. Include examples of what fractions are NOT equivalent and ask them if they
understand why.
3. Write examples on the board of just pictures and just fractions and have them
figure out which are
equivalent and which are not.
4. Lead them into a discussion on how mathematics isn 't only conceptual but you
will need some
type of algorithm or procedure to show two fractions are equivalent.
Computational:
1. After the conceptual part is done and there has been some discussion
start drilling them with practice
questions. Have them look at two fractions and computationally see if they are
the same.
2. I have seen different ways but I like these two specifically:
a. Have them write the prime factorization of the numbers and see how they can
cancel the
“ones”
b. Have then find common multiples and reduce.
3. Make a note that you are in fact simplifying and this is another thing they
must recognize.
4. Give them a real world problem like with a survey or something.
5. Finish with word problems.
Activities:
Vocabulary: |
Real World Example: |
1. Least common denominator
2. Review of <,>,= signs. |
Give this question: According to a survey done,
here is what people think
of the U.S. penny:
8/25 say we should get ride of it
3/100 are undecided
13/20 say keep the penny
How can we tell which opinion is the majority?
This is a good introduction because it shows the students why they might
want to order and compare fractions . |
Conceptual:
1. This really stems from what we did with equivalent
fractions. We will look at areas of fractions
circles or rectangles to see the difference in the sizes of fractions. The nice
part about this is you
do not need to find a common denominator (most of the time) to see why a
fraction would be bigger
then another.
2. They must realize that they will have to find the LCD
to actually compare them computationally.
Computational:
1. To compare two fractions the must be able to:
a. Find the least common denominator
b. Rewrite each fraction as an equivalent fraction using LCD
c. Compare numerators.
2. For practice and part of the lesson the teacher could:
a. Basic drills of comparing and order
b. List a group of fractions from greatest to smallest
c. Big fractions such as 100/150.
d. Surveys
3. For rounding: We will start with talking about 0, 1/2
and 1. Most people in general say thing like
oh its about a half because people can recognize 1/2 more often. Have practice a
bit with you and
see if they can understand the relationship between the numerators and
denominators to tell what
the fraction is closest to!
4. End with talking about estimating sums and differences .
Activities:
Vocabulary: |
Real world examples and the beginning
of the lesson: 1. Talk about estimating sums
and differences and how estimation
can really help you know if your answer is correct
and will also give you a sense of what the answer will be.
2. Find a real world problem. |
1. LCD
2. Like fractions |
Conceptual:
1. Start with the basics. Show them pictures of fractions
with the same equal parts or denominators
and show them how we can add them.
2. Have a few practice with the pictures then ask them
what they re present numerically . They now
should be able to see 1/4 +1/4 = 2/4 and actually write it down. Give them a
couple on their own
to see if they are getting it.
3. Now give them a picture where they are adding objects
with a different number of equal parts.
4. The idea will be to have them see what is needed
pictorially get them to transfer that numerically.
Computational:
1. Once they have this concept down they can start doing
examples and practice.
2. They will also need to do problems like 1 + 1/2 (this
will be a lead into mixed numbers which is
next). Same idea of finding a common denominator.
3. Of course we need to include story problems and open
ended questions.
Activities:
1. Fraction Rummy (pg 233 of Fayette’s book)
2. Pennies and Nickels (235 of Fayettes book)
3. Good problem for them to do (239)
Mixed Numbers and Improper Fractions (1 day)
Vocabulary: |
Real World and introduction to the lesson: |
1. Mixed Number
2. Improper Fraction |
1. Talk about what you found when you added
1+1/2.
2. Show how you can write this as 1 1/2 and dicuss the definitions.
3. Give a real world example. |
Conceptual:
1. We once again return to a visualization of these numbers.
2. Ask how you can represent the numbers pictorially like 10/5.
3. Show the relationship between mixed numbers and improper fractions.
4. Use the number line example to talk about the 0, 1/2, 1, 1 1/2 and 2 points
using an example like:
0, 1/4, 2/4, 3/4, 4/4, 5/4, 6/4….
5. We have to try to get them to the point where they can numerically describe
what is happening to
go from improper to mixed.
Computational:
1. Hopefully they can see the conceptual part and move on to the procedure
of the conversion.
2. Again need real world problems and open questions.
NOTE: We should probably focus some on rounding,
estimating, adding and subtracting mixed numbers
which might extend the day?
Activities:
Vocabulary: |
Real World and introduction to the lesson: |
1. Decimal
2. Terminating decimal
3. Repeating decimal
4. Place value |
1. We can talk about how we can represent
fractions with
decimals.
2. Ask them why we would want to use decimals instead of
fractions.
3. Make sure they know that some times a decimal is an estimate
and that a fraction is the true representation. |
Conceptual:
1. This may not be conceptual but we will need to review and go over the
place values.
Computational:
1. Going from fractions to decimals
2. Going from decimals to fractions
3. I had this for two days because I think they will just need to practice it.
4. We can do an activity or game on the second day to close out what they have
learned up till now
and also maybe a quiz.
Activities:
Decimal war (pg 115)
Vocabulary: |
Real World and introduction to the lesson: |
1. Compatible numbers |
1. We will talk about estimating products using
compatable
numbers.
2. We can touch on mixed numbers.
3. Real world problem on why we would need to multiply
fractions. |
Conceptual:
1. We can use models as usual to see it visually.
2. Need to lead them into a discussion on how to see the multiplication
numerically.
Computational:
1. Multiplying fractions
2. Multiplying fractions and whole numbers
3. Simplifying before multiplying
4. Multiplying mixed numbers and improper fractions. The need to convert to
improper.
5. Open ended questions
6. Number sense questions: Natalie multiplied 2/3 and 22 and got 33.. does this
make sense, why or
why not. Give two numbers and ask whether their product will be a mixed number
or an improper
fraction or a regular fraction or not even a fraction??
7. Drills.
Activities:
Multiplication Chaos
Dividing Fractions (2 days)
Vocabulary: |
Real World and introduction to the lesson: |
1. Reciprocal |
1. There are 8 cookies and I want to give it to
16 people, how
do I do it? |
NOTE: I think this might take some time to rely due
to the definition of reciprocal and
the inversion technique for dividing fractions so I gave it two days. Again we
can have
some time to catch up or even play some games depending.
Conceptual:
1. We start with a basic example of 1 divided by 1/5. You make a model of 1
(dividend) and think
how many 1/5s go into 1? We will need to rename 1 as 5/5. This is an important
concept that
they must understand… why 5/5 = 1 that I know many people to not get.
2. We can do more practice with whole numbers then move to
both being fractions.
3. We have maybe 3/4 divided by 3/8. We can rename the
fractions to have a common denominator
so we can see the pictures better. But we can show both easily. here they will
have to see that you
do not need to have a common denominator to do this problem.
4. Talk about the relationship between the dividend and
the divisor and how the compare. This will
help with knowing what the answer should be.
5. We will need to practice more then move on to the
development of the reciprocal rule. I do not
think we should state this but have them work to finding it themselves.
Computational:
1. Using the reciprocal rule
2. Divide by whole numbers
3. Divide to solve problems.
4. Number sense questions
5. Open ended questions
6. Practice
7. Critically thinking and solving mentally.
8. Mixed numbers and improper fractions.
Activities: