Fractions Nancy Hughes Olathe District Schools. Standards Seventh Grade N M7.1.4.K2d The student...
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Transcript of Fractions Nancy Hughes Olathe District Schools. Standards Seventh Grade N M7.1.4.K2d The student...
FractionsNancy Hughes
Olathe District Schools
Standards
Seventh GradeN M7.1.4.K2d The student adds,
subtracts, multiplies, and divides fractions and expresses answers in simplest form.
Eighth GradeM8.1.4.A1bThe student models, performs,
and explains computation with rational numbers, the irrational number pi, and algebraic expressions in a variety of situations.
VocabularyAddendCommon denominatorsDenominatorDividendDivisionEquivalent fractionFractionImproper fractionLeast common denominatorLowest termsMinuendMixed numberNumeratorProper fractionQuotientSimplifySubtrahendUnit fraction
Objectives
Develop concepts of fractions and mixed numbers
Use models to add, subtract, multiply and divide fractions
Add, subtract, multiply, divide fractions and mixed numbers
Adding Fractions – Using Fraction Circles
Pull out your fraction circles and sort them by colors. The clear circle is the number 1 or 1 whole.
Do the same with the fraction tiles. Sort them by color.
1
2
1
4
1
2
1
4
1
4
1
4
1
5
1
5
1
5
1
5
1
5
1
6
1
6
1
6
1
6
1
6
1
6
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
3
1
3
1
3
1
Adding Fractions – Using Fraction Circles or Fraction Tiles
4
2
4
1Let’s add
Which colored circle or tile will you need to add these fractions? Explain.
•Because the fraction has a denominator of 4, find the fraction piece that has been divided into fourths.
•Take the ¼ piece and add to it the piece.
+4
34
1
4
14
1=
+ =4
3
4
2
Adding Fractions – Using Fraction Circles or Tiles
5
2
5
1
5
3
Use either fraction circles or tiles to model
Again, look at the denominator and choose your tiles accordingly.
5
1+
5
1
5
1=
+5
3=
Adding Fractions – Using Fraction Circles or Tiles
3
1
2
1Use either fraction circles or tiles to model
•Notice we do not have like denominators. This makes it more of a challenge. Begin by taking the ½ and the 1/3 and find tiles or circles that are exactly the same size.
•Did you find like tiles? Explain.
•If you found tiles or parts of a circle that have a denominator of 6, you were correct.
•Notice the ½ matches up with 3/6 and the 1/3 matches up with 2/6.
½ ½6
1
6
1
6
1
6
1
6
16
1
3
1
3
1
3
1
6
1
6
1
6
1
6
1
6
1
6
1
Now we can add!
Adding Fractions – Using fraction circles or tiles
3
1
2
1Use either fraction circles or tiles to model
6
1
6
1
6
1
6
1
6
1
6
16
1
6
1
6
1
6
1
6
1
6
1
+ =6
5
+ =6
5
6
3
6
2
You Try
Use your fraction circles or fraction tiles to find 10
3
5
1
+ =
2
1
10
5
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1+ 10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1 =
2
1
10
5
Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions, and then add.
Roll 1st Fraction
2nd Fraction
Sum
#1
#2
#3
#4
#5
Quick Review
How to use your calculator to check!
Fraction bar
Change to a decimal
Change to a fraction
Simplify Mixed Number and Improper Fraction
Subtracting Fractions
Visual approach using fraction tiles or fraction circles
Subtracting Fractions using fraction circles or fraction tiles
What is ? Again we will have to find like denominators. Which sets of tiles or circles will work? Explain.
If you guessed the 10th’s you were right, 6/10 = 3/5
5
3
10
7
5
1
10
1
10
1
5
1
5
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
5
1
5
1
5
1
10
1
-
Subtracting Fractions using fraction circles or fraction tiles
What is ? If you used fraction circles, your work should be identical to the fraction tiles.
5
3
10
7
5
3
10
6
10
1
10
6
10
7
=
-
You Try – Use fraction tiles or fraction circles to show your answer.
What is ? 2
1
12
9
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
2
1
-12
1
12
1
12
1or ¼
4
1
- =
Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then subtract.
Roll 1st Fraction
2nd Fraction
Difference
#1
#2
#3
#4
#5
Quick Review
Multiplying fractions
Multiplying fractions is like finding what one fraction is of another.
Multiplying fractions
For example, to find , we begin with an area model.
4
303
2f
12
6
4
3
3
2x
3/4
2/31 2 3
4 5 6
7
8
1211109
Multiplying Fractions
To simplify ,find the prime factorization of 6 and 12.
Composite Prime Composite Prime
6 2 12 2 3 6 2 3
12
6
6 2 • 3 = 1
12 2 • 2 •3 2
Multiplying fractions
What is?
?4
1
5
4x
¼
5
4
5
1
20
4
4
1
5
4x
Multiplying FractionsTo find the answer to ½ x 3/5, we will use another model.
Show 3 out of 5
Show 1 out of 2
Shade the answer
10
3
5
3
2
1x
You try! To find the answer to . Model your answer.
Show 2 out of 3
Show 1 out of 5
Shade the answer
15
2
5
1
3
2x
5
1
3
2x
Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then multiply.
Roll 1st Fraction
2nd Fraction
Product
#1
#2
#3
#4
#5
Quick Review
Dividing Fractions – Fraction Tiles
Find 4
1
8
5
8
1
8
1
8
1
8
1
8
1
4
1
4
1
4
1
2
12
4
1
8
5
Visualize how many ¼’s will go into 5/8. Using fraction tiles, visualize how many ¼’s you can place upon 5/8.
Dividing Fractions – Fraction Tiles
Find 5
2
10
8
25
2
10
8
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
5
1
5
15
1
5
1
You try! Use your fraction circles or tiles.
Find 3
1
6
5
2
12
2
12
6
5
6
1
6
1
6
1
6
1
6
1
3
1
3
1
3
1
Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then divide.
Roll 1st Fraction
2nd Fraction
Quotient
#1
#2
#3
#4
#5
Quick Review
Adding Fractions – Using Arithmetic
Method 1 3 x5 15 4 x5 20 2 x4 8+5 x4 20 23 20
Method 2 3 x5 15 + 2 x4 8 = 23 4 x5 20 + 5 x4 20 20
Method 3
20
23
20
815
5
2
4
320
45
xx
You try!
Use one of the three methods to find
24
19
3
2
8
1
If you do not know the common denominator, find the LCM.
Composite
Prime
8 4
222
Composite
Prime
3
222
3
LCM = 2x2x2x3=24
Subtracting Fractions – Using Arithmetic
Method 1 3 x5 15 4 x5 20 2 x4 8-5 x4 20 7 20
Method 2 3 x5 15 - 2 x4 8 = 7 4 x5 20 5 x4 20 20
Method 3
20
7
20
815
5
2
4
320
45
xx
You try!
Use one of the three methods to find
04
3
12
9
If you do not know the common denominator, find the LCM.
Composite
Prime
12 6
223
Composite
Prime
4
22
223
LCM = 2x2x3=12
Multiplying Fractions – Using Arithmetic
Method 1
5222
52
40
10
5
2
8
5
Composite
Prime
10
25
Composite
Prime
40 20 20
2225
¼
Method 2
4
1
5
2
8
5
1
4
You Try!
Use one of the two methods to multiply fractions.
2
1
16
18
9
4
Dividing Fractions Using Arithmetic
Divide the following:
52
16
8
5
16
2
8
5
Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign.
Multiply the fractions.
You try!
Divide the following:
212
28
7
6
28
12
7
6
Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign.
Multiply the fractions.
JournalingAnswer two of the following questions in your journal:1. Explain how to add fractions using either fraction circles
or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
2. Explain how to subtract fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
3. Explain how to multiply fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
4. Explain how to divide fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
Practice Operations with Fractions
What is the value of….. ?
6
5
3
1
6
11:Answer
What is the value of….. ?
18
7
6
1
9
5:Answer
What is the value of….. ?
14
9
7
4
14
31:Answer
What is the value of….. ?
13
3
26
9
26
15:Answer
What is the value of….. ?
16
3
8
7
16
11:Answer
What is the value of….. ?
21
5
7
6
21
13:Answer
What is the value of….. ?
10
7
9
8
90
17:Answer
What is the value of….. ?
3
1
2
1
6
1:Answer
What is the value of….. ?
12
7
8
7
24
7:Answer
What is the value of….. ?
5
3
9
7
45
8:Answer
What is the value of….. ?
2
1
2
1
4
1:Answer
What is the value of….. ?
3
1
4
3
4
1:Answer
What is the value of….. ?
9
8
4
3
3
2:Answer
What is the value of….. ?
15
14
7
5
3
2:Answer
What is the value of….. ?
5
3
11
6
55
18:Answer
What is the value of….. ?
5
2
4
1
8
5:Answer
What is the value of….. ?
5
4
8
5
32
25:Answer
What is the value of….. ?
5
3
9
2
27
10:Answer
What is the value of….. ?
2
3
5
3
5
2:Answer
What is the value of….. ?
8
33
4
5
33
10:Answer
