Download Fraction

Chapter 2
Fractions
Part 2
Day…..
1.
Relating multiplication and division.
2.
Dividing fractions by fractions, whole numbers,
and mixed numbers
3.
Creating real world problems involving the
multiplication and division of fractions
4.
Using models to solve problems involving the
multiplication and division of fractions
5.
Mid-unit recap
Day 1
Bell Work
Hakeem’s front porch measures
9 3/4 feet by 4 feet.
Estimate the area of his front porch.
Justify and illustrate your solution path.
(Hint: Area = Length x Width)
Vocabulary
Denominator- the bottom number of a fraction (the whole)
Equivalent- equal or the same
Fraction- a number that represents part of a whole or part of a set
Greatest Common Factor- the greatest of the common factors of two or more
numbers
Improper Fraction- a fraction with a numerator that is greater than or equal to the
denominator
Mixed Number- a number that has a whole number part and a fraction part
Numerator- the top number of a fraction (the part)
Product- the answer to a multiplication equation
Quotient- the answer to a division equation
Reciprocal – two numbers with a product of 1 (flipped upside down)
Scaling- to increase or decrease a ratio
Simplest Form- a fraction in which the GCF of the numerator and denominator is 1
Test Critiques
Please your desk of everything except
for a blue ink pen and your test.
Today's Standard
Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions,
e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context
for (2/3) ÷ (3/4) and use a visual fraction model to show
the quotient; use the relationship between multiplication
and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup servings are in 2/3 of
a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?
Multiplying Fractions
(Review)
Essential Understanding:
• To multiply a fraction by a fraction, you simply
multiply the numerator by numerator, then the
denominator by denominator.
• To multiply a fraction by a whole number or a mixed
number, you must first change the number to an
improper fraction. Then, multiply numerator by
numerator and denominator by denominator.
• Write each product in simplest form.
Examples:
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Bell Work
Homework Critique
Vocabulary
Denominator- the bottom number of a fraction (the whole)
Equivalent- equal or the same
Fraction- a number that represents part of a whole or part of a set
Greatest Common Factor- the greatest of the common factors of two or more
numbers
Improper Fraction- a fraction with a numerator that is greater than or equal to the
denominator
Mixed Number- a number that has a whole number part and a fraction part
Numerator- the top number of a fraction (the part)
Product- the answer to a multiplication equation
Quotient- the answer to a division equation
Reciprocal – two numbers with a product of 1 (flipped upside down)
Scaling- to increase or decrease a ratio
Simplest Form- a fraction in which the GCF of the numerator and denominator is 1
Today's Standard
Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions,
e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context
for (2/3) ÷ (3/4) and use a visual fraction model to show
the quotient; use the relationship between multiplication
and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup servings are in 2/3 of
a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?
Dividing Fractions
Essential Understanding: There are two ways to divide fractions. One way is
to create common denominators and divide. The second way is to find the reciprocal
of the divisor, and multiply.
•To divide fractions using common denominators…
– You must first change all mixed numbers and/or whole numbers in to
improper fractions.
– Then, simply scale each fraction to the least common multiple to create
common denominators.
– Finally, divide the numerator of dividend (1st fraction) by the numerator of
the divisor (2nd fraction)
Examples:
Dividing Fractions
Essential Understanding: There are two ways to divide fractions. One way is
to create common denominators and divide. The second way is to find the reciprocal
of the divisor, and multiply.
•To divide fractions using the reciprocal…
–You must first change all mixed numbers and/or whole numbers in to improper
fractions.
– Next, find the reciprocal of the divisor. In other words, flip the second
fraction.
– Then, change the sign from division to multiplication.
– Finally, multiply numerator by numerator and denominator by denominator.
Examples:
Think: Keep Change Flip
Watch This
• http://learnzillion.com/lessons/1323-solvedivision-of-fractions-problems-usingreciprocals
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
Sandy wants to split one-half of a pan of
brownies between herself and three
friends. How much of the pan of brownies
will each person get?
Homework Critique
Vocabulary
Denominator- the bottom number of a fraction (the whole)
Equivalent- equal or the same
Fraction- a number that represents part of a whole or part of a set
Greatest Common Factor- the greatest of the common factors of two or more
numbers
Improper Fraction- a fraction with a numerator that is greater than or equal to the
denominator
Mixed Number- a number that has a whole number part and a fraction part
Numerator- the top number of a fraction (the part)
Product- the answer to a multiplication equation
Quotient- the answer to a division equation
Reciprocal – two numbers with a product of 1 (flipped upside down)
Scaling- to increase or decrease a ratio
Simplest Form- a fraction in which the GCF of the numerator and denominator is 1
Today's Standard
Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions,
e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context
for (2/3) ÷ (3/4) and use a visual fraction model to show
the quotient; use the relationship between multiplication
and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup servings are in 2/3 of
a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?
Story Problems
Group Work Activity
• Your group will be given a recipe.
• Your job is to create , model, and solve 2 story problems
using your recipe. (1 must be multiplication and 1 must
be division)
• You must work your problems out and include a
separate answer key.
• We will use these problems in class tomorrow, be ready
to share. 
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell Work
Create a story problem for
6÷¼=
Illustrate the solution
Homework Critique
Vocabulary
Denominator- the bottom number of a fraction (the whole)
Equivalent- equal or the same
Fraction- a number that represents part of a whole or part of a set
Greatest Common Factor- the greatest of the common factors of two or more
numbers
Improper Fraction- a fraction with a numerator that is greater than or equal to the
denominator
Mixed Number- a number that has a whole number part and a fraction part
Numerator- the top number of a fraction (the part)
Product- the answer to a multiplication equation
Quotient- the answer to a division equation
Reciprocal – two numbers with a product of 1 (flipped upside down)
Scaling- to increase or decrease a ratio
Simplest Form- a fraction in which the GCF of the numerator and denominator is 1
Today's Standard
Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions,
e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context
for (2/3) ÷ (3/4) and use a visual fraction model to show
the quotient; use the relationship between multiplication
and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup servings are in 2/3 of
a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?
Fraction Models
Essential Understandings: Fractions are numbers used to represent
part of a whole or part of a set.
•You can show/solve fraction equations using models.
Example: ¼ divided by ½
But first, you must know how to model different types of
fractions.
•You can model a part of a whole by using a single figure.
Example:
•You can model part of a set using multiple figures.
Example:
Modeling Fraction Equations
Essential Understandings:
Fractions equation models can be used to solve/prove…
•Addition Equations
Example:
•Subtraction Equations
Example:
•Multiplication Equations
Example:
•Division Equations
Example:
Watch This
• http://learnzillion.com/lessons/212-multiplyfractions-by-whole-numbers-using-bar-models
• http://learnzillion.com/lessons/199-dividewhole-numbers-by-unit-fractions-using-visualmodels
• http://learnzillion.com/lessons/1383-solveword-problems-involving-division-of-mixednumbers-and-fractions-using-picture-models
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Quick Quiz
Please clear your desk of
everything except for a
pencil and a piece of
scratch paper.
Homework Critique
Vocabulary
Denominator- the bottom number of a fraction (the whole)
Equivalent- equal or the same
Fraction- a number that represents part of a whole or part of a set
Greatest Common Factor- the greatest of the common factors of two or more
numbers
Improper Fraction- a fraction with a numerator that is greater than or equal to the
denominator
Mixed Number- a number that has a whole number part and a fraction part
Numerator- the top number of a fraction (the part)
Product- the answer to a multiplication equation
Quotient- the answer to a division equation
Reciprocal – two numbers with a product of 1 (flipped upside down)
Scaling- to increase or decrease a ratio
Simplest Form- a fraction in which the GCF of the numerator and denominator is 1
Today's Standard
Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions,
e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context
for (2/3) ÷ (3/4) and use a visual fraction model to show
the quotient; use the relationship between multiplication
and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup servings are in 2/3 of
a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?
Chapter Review
Math Time
Technology: PowerSchool Practice Items
Independent: Provided Page
My Choice: Try Something New!
Extension: Options have been posted.
Wrap it Up
• Review
• Questions
• Quiz