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Fractions

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Dani Lutke

on 4 June 2014

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Transcript of Fractions

Fractions
What is a fraction?
* A fraction is part of a whole.

Part of a fraction:
Numerator
Fraction bar
Denominator
Websites:
• http://www.brainpop.com/educators/community/bp-jr-topic/basic-parts-of-a-whole/
• http://www.atozteacherstuff.com/Lesson_Plans/Mathematics/_Grades_3-5/Fractions/index.shtml
• http://www.teacherspayteachers.com/Browse/Search:fractions


The student will be able to:
Define fraction, numerator, denominator, fraction bar, unit fraction, and multiple.
Identify the number of shaded parts and the number of equals parts in a shape (circle, rectangle).
Identify a fraction by comparing the number of shaded parts to the number of equal parts.
Write a fraction using mathematical notation and using words.
Explain what a fraction is.

The student will be able to:
• Define simplifying a fraction, lowest terms, greatest common factor.
• Determine the common factors of the numerator and denominator of a given fraction.
• Simplify a fraction by dividing its numerator and its denominator by a common factor.
• Determine the greatest common factor of the numerator and denominator of a given fraction.
• Simplify a fraction by dividing its numerator and its denominator by their greatest common factor.
• Recognize that a fraction is in lowest terms when the greatest common factor of its numerator and denominator is one.
• Describe the procedure for simplifying fractions.
Fractions
Simplifying Fractions:

To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.

There are two methods to simply fractions:
Method 1
Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc).

Example: Simplify the fraction 8/24 :

Method 2
Divide both the top and bottom of the fraction by the Greatest Common Factor, (you have to work it out first!).

Example: Simplify the fraction 8/12 :

1. The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.

2. Divide both top and bottom by 4:


Adding Fractions With Like Denominators:

* Remember: what you do to the top you do to the bottom.
Subtracting Fractions:
Has the same steps as adding except you
subtract instead.
Make the denominators the same by
multiplying by each other, and then multiply
with the same number as the numerator.
Remember: what you do to the bottom you do the top.
Multiplying Fractions:
There are 3 simple steps to multiply fractions:
1. Multiply the top numbers (numerator).
2. Multiply the bottom numbers (denominator).
3. Simplify the fraction if needed.

Dividing Fractions:
You need to make a reciprocal fraction then
multiply the fractions to find your answer.
A reciprocal fraction is a fraction that gets
flipped so it turns into an improper fraction.
1. Turn the 2nd fraction upside down making it
a reciprocal.
2. Multiply the fraction with the reciprocal.
3. Simplify.
There are 3 Simple Steps to add fractions:

Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add the top numbers (the numerators), put the answer over the denominator
Step 3: Simplify the fraction (if needed)
Example 1:
1 + 1
4 4
Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.
Step 2. Add the top numbers and put the answer over the same denominator:
1 + 1 = 1 + 1 = 2
4 4 4 4
Step 3. Simplify the fraction: Ex:

2 = 1
4 2

1/2 + 1/3
The main rule of this game is that we can't do anything until the denominators are the same!

We need to find something called the least common denominator (LCD)... It's really just the LCM of our denominators, 2 and 3.

The LCM of 2 and 3 is 6. So, our LCD 6.

We need to make this our new denominator...

Change the 1/2:


Change the 1/3:




Now we can do it!


Adding Fractions With unlike denominators:
The student will be able to:
• Define equivalent fractions, whole number.
• Explain why two given fractions are or are not equivalent.
• Recognize that multiplying a fraction by one does not change its value.
• Recognize that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.
• Recognize that equivalent fractions are equal in value.
• Describe the procedure for finding equivalent fractions.
• Convert a fraction to an equivalent fraction with a specified numerator.
• Convert a fraction to an equivalent fraction with a specified denominator.
• Restate the definition of equivalent fractions.

The student will be able to:
• Define units, common denominator, simplify, and lowest terms
• Describe the procedure for adding fractions with like denominators.
• Determine the sum of two or more fractions with like denominators by applying the procedure above.
• Simplify the result when necessary.
• Recognize that only the numerators should be added, not the denominators.

The student will be able to:
• Find the Least Common Denominator (LCD) of the fractions
• Rename the fractions to have the LCD
• Add the numerators of the fractions
• Simplify the Fraction

The student will be able to:
• Find the Lowest Common Denominator (LCD) of the fractions
• Rename the fractions to have the LCD
• Subtract the numerators of the fractions
• The difference will be the numerator and the LCD will be the denominator of the answer.
• Simplify the Fraction

4th Grade GLCEs:
Understand fractions:
N.ME.04.20 Understand fractions as parts of a set of objects.
N.MR.04.21 Explain why equivalent fractions are equal, using models such as fraction strips or the number line for fractions with denominators of 12 or less, or equal to 100.
N.MR.04.22 Locate fractions with denominators of 12 or less on the number line; include mixed numbers.
N.MR.04.23 Understand the relationships among halves, fourths, and eighths and among thirds, sixths, and twelfths.
N.ME.04.24 Know that fractions of the form m/n where m is greater than n, are greater than 1 and are called improper fractions; locate improper fractions on the number line.
N.MR.04.25 Write improper fractions as mixed numbers, and understand that a mixed number represents the number of “wholes” and the part of a whole remaining.
N.MR.04.26 Compare and order up to three fractions with denominators 2, 4, and 8, and 3, 6, and 12, including improper fractions and mixed numbers.
Add and subtract fractions:
N.MR.04.27 Add and subtract fractions less than 1 with denominators through 12 and/or 100, in cases where the denominators are equal or when one denominator is a multiple of the other
N.MR.04.28 Solve contextual problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100).*
N.MR.04.29 Find the value of an unknown in equations
Multiply fractions by whole numbers:
N.MR.04.30 Multiply fractions by whole numbers, using repeated addition and area or array models.

Fraction Games:

http://www.hoodamath.com/games/papaspizzeria.html

http://www.primarygames.com/fractions/start.htm

http://www.softschools.com/math/fractions/games/
The student will be able to:

Define greatest common denominator (GCF), simplify, and lowest terms.
Recognize that the word OF means multiply.
Describe the procedure for multiplying fractions.
Determine the product of two or more fractions by applying the procedure above.
Determine the product of a whole number and a fraction by applying the above procedure.
Recognize that the result can be simplified by dividing the numerator and the denominator by their GCF, or by cancelling common factors.
Simplify the result of each problem when necessary by using the GCF method.
Apply the procedure above to solve word problems, and simplify the result
The student will be able to:

Define divisor, and invert.
Recognize that division indicates how many times one quantity is contained in another quantity.
Recognize that dividing a first fraction by a second, nonzero fraction, is the same as multiplying the first fraction by the reciprocal of the second fraction.
Describe the procedure for dividing one fraction by another.
Recognize that the second fraction must be a nonzero number.
Describe the process of inverting and multiplying.
Apply reciprocal relationships to convert division of fractions into a multiplication problem.
Apply procedures to divide fractions and simplify the result when necessary.
Apply procedures to cancel common divisors.
Connect real-world problems to dividing fractions.
Equivalent Fractions:
By: Dani Lutke
Oh No Fractions!
Fraction Pizza
Equivalent Fractions
Fraction Circles
Fraction Wall
Chicken Coop Fraction Game
Fractions for Kids
Versamate
Slice Fractions
Squeebles Fractions
Freddy Fractions
Jungle Fractions

Apps on Fractions:
3-4 weeks depending on how well the students understand the material
Using technology with fractions will allow the students to better understand and grasp the idea of how to solve fractions. Having the different options such as youtube videos, ipad apps, and other presentations will assist them if they are struggling with a part of the fraction unit.
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