UNIT 4: Dividing Fractions

UNIT 4: Dividing Fractions

LET'S PLAY A GAME!

Ms. Kuqi is going to show you several types of objects. For each object, estimate how many are in a stack that is 5 feet high. Be prepared to explain your reasoning.

How did your estimates for the number of objects change as the object got thinner? Why might that be?

Why might that be?

IN FRACTION LANGUAGE

DIVIDEND = NUMBERATOR  → if this gets bigger the answer gets bigger, if this gets smaller the answer gets smaller.

DIVSOR = DENOMINATOR  → if this gets smaller the answer gets bigger, if this gets bigger the answer gets smaller

QUOTIENT = THE ANSWER

The size of the dividend and the size of the divisor both affect the quotient.

• Recall percentages 50% = 50/100 as we increase 50 we get closer and closer to 100 which means the percentage grow bigger! If we decrease the numerator the percentage gets smaller!

Multiple Choice

A stack of books is 72 inches tall. Each book is 2 inches thick. Which expression tells us how many books are in the stack? Even though the picture is super blurry!

• 72x2

• 72-2

• 2 ÷ 72

• 72 ÷ 2

Even though Ms. Kuqi loves to troll, the blurry picture is no match for our estimate and division powers!

HOORAYYY THE POWER OF MATH CAN BEAT EVEN WHAT WE CAN SEE. EMBRACE THE POWER OF ESTIMATES!

Open Ended

Here is an expression: 20 ÷ 4 What are some ways to think about this expression? Describe at least two meanings you think it could have.

Open Ended

A baker has 12 lbs of almonds. She puts them in bags, so that each bag has the same weight. In terms of pounds and bags of almonds, what would 12 ÷ 6 mean?

Open Ended

A baker has 12 pounds of almonds. She puts them in bags, so that each bag has the same weight. Explain what each division expression would mean in the context of the bags of almonds. Write a multiplication equation to show how you are thinking about the expression (or a diagram in your notebooks or piece of paper, be prepared to share it with your class):

a. 12 ÷ 4

b. 12 ÷2

c. 12 ÷ 1/2

Let's talk about it:

• a. 12 ÷ 4

  b. 12 ÷2

  c. 12 ÷ 1/2

• How many bags do you end up with in A? in B? in C?

• Predict how many lbs each bag weighs. How did you solve it?

Shoveling Sidewalks

When it snows, Ms. Kuqi and her friends help their neighbors by shoveling their sidewalks. Each person who shows up to help shovel an equal area. The pictures of people show how many people are helping and the picture of the tape diagrams show how many sidewalks need to be shoveled on different days. Let's use fractions to show the areas of each helper will have to shovel and write a division problem "equation" to represent each situation.

What do you notice about the Sidewalks and People helping? How can we write this as a division problem. How can we rewrite this division problem as a fraction?

What do you notice about the Sidewalks and People helping? How can we write this as a division problem. How can we rewrite this division problem as a fraction?

What do you notice about the Sidewalks and People helping? How can we write this as a division problem. How can we rewrite this division problem as a fraction?

What do you notice about the Sidewalks and People helping? How can we write this as a division problem. How can we rewrite this division problem as a fraction?

Let's use minecraft to better tackle these statements

Look at the 4th row of stone, let's say 4 stones make up this row, how many 1/2s are in 4 of the stone?

what is 1/2 + 1/2+ 1/2 + 1/2?

Look at the 3rd row of stone, let's say 3 stones are in a row, how many 2/3s are in 3 of the stone?

what is 2/3 + 2/3 + 2/3 + 1/3?

Look at the 2nd row of stone, let's say the 2nd row of stone contains 1 and a 1/2, how many 1/6s are in 1 and a 1/2 of the stone?

We can think about this problem as 1 and a 1/2 being 1+1/2 and find the fraction of 1/6 in each of them separately.

What's the easiest way to think about these types of problem in terms of fractions (and ratios) or division problems?

Multiple Choice

How many 1/6 are there in 1 whole?

• 6 because 1/6+1/6+1/6+1/6+1/6+1/6=1

• 6 because 1/1+1/1+1/1+1/1+1/1+1/1=6

Multiple Choice

How many 1/6 are there in 1/2?

• 3 because 1/6+1/6+1/6=3/6=1/2

• 12 because 1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6=1/2

Open Ended

You need 3/4 yards of ribbon for one gift box. You have 3 yards of ribbon. How many gift boxes do you have ribbon for? *hint make a division equation*

Open Ended

The distance around a park is 3/2 miles. Ms. Kuqi rode her bicycle around the park for a total of 3 miles. How many times around the park did she ride? *hint make a division equation*

Using Diagrams to Find the Number of Groups

Lesson # 6

TODAY'S GOALS

I can use a tape diagram to represent equal-sized groups and find the number of groups.

Multiple Select

How many 2/3s are in 3? Select ALL the possible ways to figure out this answer.

• ?*2/3=3

• 3÷2/3=?

• 4 groups of 2/3s in 3

How many 2/3s are in 3? There are 4 groups of 2/3 in 3.

Multiple Select

How many 3/4s are in 1? Select ALL the possible ways to figure out this answer.

• ?*3/4=1

• 1÷3/4=?

• There is 1 group of 3/4s in 1

How many 3/4s are in 1? There are 1 group of 3/4 in 1.

Multiple Choice

How many 3/4s are in 2? Write a multiplication equation and a division equation that can be used to answer the question:

• 2 ÷ 3/4 = ?

• 3/4 ÷ 3/4 = ?

• 3/4 ÷ 2 = ?

Multiple Choice

There is 1/3 gallon of water in a 3-gallon container. What fraction of the container is filled?

• 1/3 ÷ 3 = ?

• 3 ÷ 3 = ?

• 1/3 ÷ 1/3 = ?

• 3 ÷ 1/3 = ?

Dividing by Unit and Non-Unit Fractions

Lesson # 10-11

TODAYS GOALS

KEEP CHANGE FLIP - KCF

Multiple Choice

How many 3s are there in 12? *Select the correct division equation*

• 12÷3=?

• 3÷12=?

Multiple Choice

How many 6s are there in 12? *Select the correct division equation*

• 6÷12=?

• 12÷6=?

Open Ended

4 ÷ 5/9

Explain the possible steps we can take to solve this problem

THE RULE IS CALLED "KEEP CHANGE FLIP" WE KEEP THE FIRST FRACTION THE SAME, CHANGE THE DIVISION SIGN INTO MULTIPLICATION AND FLIP THE FRACTION.

Open Ended

Solve 5/6 ÷ 10/12 through the *keep change flip rule*

NOW WE HAVE WHOLE NUMBER FRACTION

Open Ended

Solve 1 5/6 ÷ 10/12 through the *keep change flip rule*

UNIT 4 EXAM REVIEW

DIVIDING FRACTIONS EVERYTHING YOU NEED TO KNOW

FRACTIONS ARE RATIOS

• THEY HAVE A NUMERATOR OVER A DENOMINATOR

• BUT THEY ARE ALSO DIVISION SIGNS AND RATIO'S IN DISGUISE

FRACTION COMPARING N AND D

• WHEN WE COMPARE NUMERATOR AND DENOMINATOR WE CAN SAY

• WHEN NUMERATOR = DENOMINATOR THE FRACTION IS EQUAL TO 1

• WHEN THE NUMERATOR IS > DENOMINATOR THE FRACTION IS >1

• WHEN THE NUMERATOR IS < DENOMINATOR THE FRACTION IS <1

NOW THAT YOU KNOW SOMET STUFF ABOUT FRACTIONS LET'S LOOK INTO HOW WE DIVIDE THEM

So far we learned things like tape diagrams

KCF

and the aid of turning a mixed number into a fraction

Multiple Choice

Jana has a beget that is 5 feet long. How many 1/3 foot sections can she cut from this bread

• 3/5 section

• 1 2/3 section

• 8 section

• 15 section

Open Ended

Rony has 3/5 box of diamonds in minecraft. He uses it to make 6 diamond helmets. What fraction of the box does he put in each helmet construction?

Open Ended

Ms. Markon buys a bag of cat food that contains 18 cups of food. Ms. Markon feeds her cat 1 and 1/2 cups each day. Ms. Markon says she will be able to feed her cat for 27 days. Is she correct?

Open Ended

Thea has 2 and 1/2 cups of cereal. How many 3/4 cup full servings can she make? Will she have any cereal left over?

Multiple Choice

Which word problem best represents this expression: 1/2 ÷ 3 and 1/6

• Bella has 3 and 1/6 cups of yogurt. How many 1/2 cup servings can she make?

• A rectangular piece of land has an area of 1/2 square mile. The land is 3 and 1/6 miles long. What is its width?

• Rodney drives 1/2 the distance to his house in 3 and 1/6 hours. At this speed, how long will the entire trip take?

• A chef has 3 and 1/6 pounds of beef. He uses 1/2 of this to make stew. How many pounds of beef does he have left?

Multiple Select

Evaluate 1/2 ÷ 3 and 1/6

• 6/38

• 3/19

• 19/3

• 38/6