Solving Fractions Division in Mathematics

 
 
 
Lesson
Divide Fractions
[
OBJECTIVE
]
 
The student will interpret and compute
quotients of fractions in mathematical and
real-world situations.
[
MY
 
SKILLS
]
 
Division of whole numbers
Fraction operations
Multiplication
[
ESSENTIAL
 
QUESTIONS
]
 
1. 
Why is it important to know how to build a
model for division of fractions?
2. 
What does a division sentence mean?
3. 
What are the steps for dividing a fraction by a
fraction?
 
[Warm-Up]
 
Begin by completing the warm-up for this
lesson.
 
DIVIDE FRACTIONS
 
SOLVE Problem – Introduction
 
[
LESSON
]
[
LESSON
]
 
SOLVE
 
S
 
Study the Problem
 
Underline the question.
[
LESSON
]
[
LESSON
]
 
SOLVE
 
S
 
Study the Problem
 
Underline the question.
 
This problem is asking me to find
 
the number of jars he can fill.
 
DIVIDING WHOLE NUMBERS BY
FRACTIONS
 
Concrete
Dividing Whole Numbers by Fractions –
Concrete
Dividing Whole Numbers by Fractions –
Concrete
Let’s build the problem with our fraction kits.
 
Let’s start with two whole units.
Dividing Whole Numbers by Fractions –
Concrete
Identify the
divisor.
Dividing Whole Numbers by Fractions –
Concrete
What is the
meaning of the
divisor?
 
It tells us the
size of the
items.
Dividing Whole Numbers by Fractions –
Concrete
Dividing Whole Numbers by Fractions –
Concrete
 
8
Dividing Whole Numbers by Fractions –
Concrete
Dividing Whole Numbers by Fractions –
Concrete
Let’s build the problem with our fractions kits.
 
What do we start with for our model?
 
2 whole units
Dividing Whole Numbers by Fractions –
Concrete
Identify the
divisor.
Dividing Whole Numbers by Fractions –
Concrete
What does the
divisor mean?
 
The divisor
tells us how
many sections
to divide the
whole number
into
Dividing Whole Numbers by Fractions –
Concrete
 
No
Dividing Whole Numbers by Fractions –
Concrete
Dividing Whole Numbers by Fractions –
Concrete
Dividing Whole Numbers by Fractions –
Concrete
 
3
Dividing Whole Numbers by Fractions –
Concrete
 
3
 
DIVIDING FRACTIONS BY
FRACTIONS
 
Concrete to Pictorial
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the meaning of the division fact?
Dividing Fractions by Fractions –
Concrete to Pictorial
Let’s build the problem with our fractions kits.
 
What fraction do we represent?
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the
divisor?
Dividing Fractions by Fractions –
Concrete to Pictorial
What does the
divisor mean?
 
The divisor tells us
how many sections to
divide the dividend
into
Dividing Fractions by Fractions –
Concrete to Pictorial
Dividing Fractions by Fractions –
Concrete to Pictorial
 
2
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the meaning of the division fact?
Dividing Fractions by Fractions –
Concrete to Pictorial
Let’s build the problem with our fraction kits.
 
What fraction do we represent?
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the
divisor?
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the
meaning of the
divisor?
 
The divisor tells us
how many sections to
divide the dividend
into.
Dividing Fractions by Fractions –
Concrete to Pictorial
Dividing Fractions by Fractions –
Concrete to Pictorial
 
6
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the meaning of the division fact?
Dividing Fractions by Fractions –
Concrete to Pictorial
Let’s build the problem with our fraction kits.
 
What fraction do we represent?
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the
divisor?
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the
meaning of the
divisor?
 
The divisor tells us
how many sections to
divide the dividend
into.
Dividing Fractions by Fractions –
Concrete to Pictorial
 
Dividing Fractions by Fractions –
Concrete to Pictorial
 
You can see that
two of the green
strips show more
than one half.
Dividing Fractions by Fractions –
Concrete to Pictorial
 
Dividing Fractions by Fractions –
Concrete to Pictorial
Dividing Fractions by Fractions –
Concrete to Pictorial
How many of the
one third units cover
the one half unit?
Dividing Fractions by Fractions –
Concrete to Pictorial
How many groups of
one third are in one
half?
Dividing Fractions by Fractions –
Concrete to Pictorial
What is the division
fact?
 
RECIPROCALS
 
 
Reciprocals
 
It is not always possible to draw a model of
division.
Reciprocals
Explain how to write the value of 2 as a fraction.
Reciprocals
 
1
Reciprocals
What is the value of 3 as an improper fraction?
Reciprocals
 
1
Reciprocals
What pattern do you see with the fractions?
 
When you are multiplying two fractions and the
second has the numerator and the denominator
inverted, the product is 1.
Reciprocals
Remember that to find the reciprocal of a
fraction, we should simply invert the numerator
and denominator.
Reciprocals
 
THE RELATIONSHIP BETWEEN
DIVISION AND MULTIPLICATION
 
The Relationship Between Division and
Multiplication
Let’s rewrite the problem vertically.
The Relationship Between Division and
Multiplication
 
The Relationship Between Division and
Multiplication
 
What process did we use to find equivalent fractions?
 
We multiply the numerator and denominator by the
same value.
The Relationship Between Division and
Multiplication
What does this mean for Problem 1?
 
DIVIDE FRACTIONS
 
SOLVE Problem – Completion
 
[
LESSON
]
 
[
LESSON
]
 
SOLVE
 
S
 
Study the Problem
 
Underline the question.
 
This problem is asking me to find
 
the number of jars he can fill.
 
O
 
Organize the Facts
Identify the facts.
[
LESSON
]
 
O
 
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
 
[
LESSON
]
 
O
 
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
 
L
 
Line Up a Plan
 
Write in words what your plan of action will
be.
   Divide the total quantity of strawberries by
the amount in each jar.
 
Choose an operation or operations.
 
Division
 
E
 
Examine Your Results
Does your answer make sense?
(compare your answer to question.)
Yes, because we are looking for the number
of jars.
Is your answer reasonable?
(compare your answer to the estimate.)
Yes, because it is close to our estimate of
about 3 jars.
 
DIVIDE FRACTIONS
 
Closure
[
ESSENTIAL
 
QUESTIONS
]
 
1.
Why is it important to know how to
build a model for division of fractions?
 
So we will know what the problems
mean.
[
ESSENTIAL
 
QUESTIONS
]
 
 
2.
What does a division sentence mean?
 
How many groups of ___ are in ___?
[
ESSENTIAL
 
QUESTIONS
]
 
3.
What are the steps for dividing a fraction
by a fraction?
 
Create a reciprocal of the second
fraction and then multiply.
 
Quotient
Dividend
Divisor
Fraction
Numerator
Denominator
Model
Reciprocal
 
 
 
Lesson
 
Divide Fractions
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Explore the concepts of dividing fractions, interpreting mathematical sentences, and applying fraction operations through real-world scenarios. Engage in warm-up activities, study essential questions, and solve problems involving dividing whole numbers by fractions. Enhance skills in division, multiplication, and fractional calculations to compute quotients effectively.

  • Fractions Division
  • Mathematics
  • Real-World Applications
  • Interactive Learning
  • Problem-Solving

Uploaded on Sep 14, 2024 | 0 Views


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  1. Lesson Divide Fractions

  2. [OBJECTIVE] The student will interpret and compute quotients of fractions in mathematical and real-world situations.

  3. [MYSKILLS] Division of whole numbers Fraction operations Multiplication

  4. [ESSENTIALQUESTIONS] 1. Why is it important to know how to build a model for division of fractions? 2. What does a division sentence mean? 3. What are the steps for dividing a fraction by a fraction?

  5. [Warm-Up] Begin by completing the warm-up for this lesson.

  6. SOLVE Problem Introduction DIVIDE FRACTIONS

  7. [LESSON] SOLVE Mr. Bryce has 4 needs to fill 1 be able to fill? 5 of a quart of strawberries. He 4 quart jars. How many jars will he

  8. [LESSON] SOLVE S Study the Problem Underline the question.

  9. [LESSON] SOLVE Mr. Bryce has 4 needs to fill 1 be able to fill? 5 of a quart of strawberries. He 4 quart jars. How many jars will he

  10. [LESSON] SOLVE S Study the Problem Underline the question. This problem is asking me to find the number of jars he can fill.

  11. Concrete DIVIDING WHOLE NUMBERS BY FRACTIONS

  12. Dividing Whole Numbers by Fractions Concrete 2 ? ? What is the meaning of the division fact 2 ? ?? How many groups of ? ? are in 2 whole units?

  13. Dividing Whole Numbers by Fractions Concrete 2 ? ? Let s build the problem with our fraction kits. Let s start with two whole units.

  14. Dividing Whole Numbers by Fractions Concrete 2 ? ? Identify the divisor. 1 ? ? 1

  15. Dividing Whole Numbers by Fractions Concrete 2 ? ? What is the meaning of the divisor? 1 It tells us the size of the items. 1

  16. Dividing Whole Numbers by Fractions Concrete 2 ? ? Place ? side facing down, under the whole units so that we completely cover both whole units. ? units, label 1 1

  17. Dividing Whole Numbers by Fractions Concrete 2 ? ? How many yellow strips, or groups of ? ? units, are equal to 2 whole units? 1 8 1

  18. Dividing Whole Numbers by Fractions Concrete 2 ? ? What is the meaning of the division fact 2 ? ?? How many groups of ? ? are in 2 whole units?

  19. Dividing Whole Numbers by Fractions Concrete 2 ? ? Let s build the problem with our fractions kits. What do we start with for our model? 2 whole units

  20. Dividing Whole Numbers by Fractions Concrete 2 ? ? Identify the divisor. 1 ? ? 1

  21. Dividing Whole Numbers by Fractions Concrete 2 ? What does the divisor mean? The divisor tells us how many sections to divide the whole number into ? 1 1

  22. Dividing Whole Numbers by Fractions Concrete 2 ? ? Do we have a fraction strip that is ? ?? 1 No 1

  23. Dividing Whole Numbers by Fractions Concrete 2 ? ? How can we represent ? 1 ?? Combine 2 of the ? ? fractions strips. 1

  24. Dividing Whole Numbers by Fractions Concrete 2 ? ? 1 1 Place groups of two ? facing down, under the whole units so that we completely cover both whole units. ? units, label side

  25. Dividing Whole Numbers by Fractions Concrete 2 ? ? 1 1 How many groups of two ? equal to 2 whole units? ? units are 3

  26. Dividing Whole Numbers by Fractions Concrete 2 ? ? 1 1 How many groups of ? ? are in 2 whole units? 3

  27. Concrete to Pictorial DIVIDING FRACTIONS BY FRACTIONS

  28. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the meaning of the division fact? How many groups of ? ? are in ? ??

  29. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Let s build the problem with our fractions kits. What fraction do we represent? ? ?

  30. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the divisor? 1 ___ 4 ? ?

  31. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What does the divisor mean? 1 ___ 4 The divisor tells us how many sections to divide the dividend into

  32. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Place ? side facing down, under the ? 1 ___ 4 ? units, label ? units.

  33. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? How many groups of ? units does it take to equal a ? ? unit. ? 1 ___ 4 2

  34. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the meaning of the division fact? How many groups of ? ? are in ? ??

  35. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Let s build the problem with our fraction kits. What fraction do we represent? ? ? with two ? ? units

  36. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the divisor? 1 1 ___ 3 ___ 3 ? ?

  37. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the meaning of the divisor? The divisor tells us how many sections to divide the dividend into. 1 1 ___ 3 ___ 3

  38. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Place ? side facing down, under the ? so that they completely cover these units. ? units, label 1 1 ___ 3 ___ 3 ? units

  39. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? How many groups of ? ? units does it take to equal a ? unit. 1 1 ___ 3 ___ 3 ? 6

  40. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the meaning of the division fact? How many groups of ? ? are in ? ??

  41. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Let s build the problem with our fraction kits. What fraction do we represent? Lay a ? ? unit on your desk.

  42. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the divisor? 1 ___ 2 ? ?

  43. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the meaning of the divisor? The divisor tells us how many sections to divide the dividend into. 1 ___ 2

  44. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Place ? side facing down, under the ? that they completely cover these units. ? units, label 1 ___ 2 ? unit so

  45. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? You can see that two of the green strips show more than one half. 1 ___ 2

  46. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? Place two ? label side down, under the ? ? units, 1 ___ 2 ? unit.

  47. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? ? ? is half of the green ? strip, so we need one green strip and another half of a green strip to equal the one half strip. 1 ___ 2 ?

  48. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? How many of the one third units cover the one half unit? 1 and ? ? green units completely cover the ? ? unit. 1 ___ 2

  49. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? How many groups of one third are in one half? There are 1? thirds in ? 1 ___ 2 ? groups of ?.

  50. Dividing Fractions by Fractions Concrete to Pictorial ? ? ? ? What is the division fact? 1 ___ 2 ? ? ? ? = 1? ?

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