You need your Journal open to the next clean page to glue in your Quiz ruler and a pencil Please copy your Agenda for the week Bar Models and Number Lines Using the problems for 12 3 4 ID: 684187
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Slide1
Dividing Fractions
CCSS.6.NS.1: Apply and extend previous understandings multiplication and division to divide fractions by fractions.
You need your Journal open to the next clean page to glue in your Quiz, ruler, and a pencil. Please copy your Agenda for the week.Slide2
Bar Models and Number Lines
Using the problems for 12
÷
3 = 4
to create bar models in your Journal.
Create a number line for
10
÷
5
=
2.
Check/correct
your work with the examples on
the board.Slide3
PART 1
Apply what you learned about dividing whole numbers to dividing whole numbers by fractions.
Use a bar diagram to help you understand what it means to divide.
This board is 1 yard (3 feet) long.
Sam wants to divide it equally into 1 foot pieces. What do you know? What do you need to find?
Draw a model that represents the length of the board. Draw lines to separate the board into thirds. Each third represent one foot.How many groups of 1 foot are in 3 feet?Slide4
Juan is building a set for the school musical. He has a 3-foot board that he needs to equally divide into ½ foot pieces. How many pieces will he have after he cuts the board?
What do you know?
What do you need to find?
1. Draw
a model that represents the length of the board. Draw lines to separate the board into thirds. Each third represent one foot
.2. Divide each foot into halves.3. Determine how many groups of ½ are in 3. Circle the groups that are the size of the divisor ½. ½ ½ ½ ½ ½ ½ Slide5
Juan is building a set for the school musical. He has a 3-foot board that he needs to equally divide into ½ foot pieces. How many pieces will he have after he cuts the board?
3. Determine how many groups of ½ are in 3. Circle the groups that are the size of the divisor ½.
½ ½ ½
½ ½ ½ Conclusion: There are 6 groups of ½ . So, 3 ÷ ½ = 6. (And 3 x 2 = 6.)Check by multiplying: 6 x ½ = 3.Slide6
Find 4 ÷
.
Draw a model to represent 4.
Divide each whole into thirds.
Circle
groups of
on the model. Think: How many
groups of
are in 4?
1
111Slide7
Find 4 ÷
.
Circle
groups of
on the model. Think: How many
groups of
are in 4?
There are 6
groups of
. So, 4 ÷
= 6.Check by multiplying: 6 x
= = 4.
Slide8
You try it. Find 3 ÷
.
Draw a model to represent 3.
Divide each whole into _____.
Determine how many groups of _____ are in _____. Circle groups of _____ on the model.
There are _____ groups of ___. So, 3 ÷
= _____.
Slide9
Work with a partner in your group. Draw a bar model or number line to find each quotient.
2 ÷
6
÷
4 ÷
3
÷
Sept 22
nd …Please be ready to check this first thing. Materials…the usual.Slide10
Check your answers
2 ÷
= 8
6
÷
= 94 ÷
= 8
3
÷
= 4
Slide11
How can a bar diagram or a number line help you understand what it means to divide fractions? Discuss this idea in your groups.
The diagrams show the relationship between the factors and the quotient. The model shows that a quotient can be greater than the dividend when the divisor is less than 1.Slide12
More Practice
Use the same process for the bar diagram to create number lines for the following problems.
2 ÷
=
3÷
=4 ÷
=
Slide13
Part 2
Developing the Algorithm.
Vocabulary
Reciprocal:
any two numbers with a product of 1.
Describe the relationship between the numerator and denominator of a number and its reciprocal.
NumberProductReciprocal
x 2 = 1
2
x
= 1
Number
Product
Reciprocal
2Slide14
Connect to the vocabulary.
Another name for reciprocal is
multiplicative inverse
.
What
are some words in everyday language that are similar to reciprocal or inverse?Pilots can fly in an inverted position, or upside down. How can you use the everyday meaning of invert to help you remember the mathematical meaning of multiplicative inverse, or reciprocal?Slide15
Find Reciprocals
Dividing 3 by
gives the same result as multiplying 3 by 2, which is the reciprocal of
. Any two numbers with a product of 1 are called reciprocals.
3 ÷
= 6 3 x 2
=
6
reciprocals
same resultSlide16
Practice finding the reciprocal.
Find the reciprocal of
.
Since
x
= 1, the reciprocal of is
.
Find the reciprocal of each number.
71
Slide17
Divide by a fraction:
Words:
To divide a whole number or a fraction by a fraction, multiply by its reciprocal (or multiplicative inverse)
of the divisor
.
EX.5 ÷ =
x
=
= 7
Five divided by two thirds means you need to find how many two thirds are in 5. (part of a whole)
÷ =
x
=
Three eighths divided by two thirds means you need to find how many two thirds are in three eighths. (part of a part)
Slide18
Practice – find the quotients.
When you are finished please check your answers.
5 ÷
4
÷
10
÷
12
÷
÷
÷
÷ 8
4 ÷1
2
÷
Slide19
Practice – find the quotients.
When you are finished please check your answers.
5 ÷
= 10
4 ÷
= 5
10
÷
= 12
12
÷ = 32
÷
=
÷
= 1
÷ 8
=
4
÷1
= 2
2
÷
= 4
Slide20
Homework Practice
Complete the practice worksheet applying what you have learned about finding quotients to the contextual problems.
You will have a quiz tomorrow over dividing fractions. Also, you will have an opportunity to improve your first quiz score by completing an optional section on the quiz over adding, subtracting, and multiplying fractions.