Math 6 Unit 6: Fractions Tasks Onlybhmsparnell.weebly.com/uploads/2/2/7/3/22730444/500...Math 6 Fractions Unit 6 – Entry Assessment 2 3. United for Success is having a pizza party

Math 6

Unit 6: Fractions

Tasks Only

Math 6 Name: Date: Period:

Fractions Unit 6 – Entry Assessment

Fractions Assessment 1. Which of the following fractions are equivalent?

Explain or show how you know.

2. Erik has 4 34

bottles of soda. If he gives away 2 23

of them, how many

does he have left? _____________________


59

34

48

Math 6

Fractions Unit 6 – Entry Assessment 2

3. United for Success is having a pizza party in all 6 of the math classrooms. Ms. Chen is taking the left overs home with her. If

there is 38

of a pizza left in each box, how much total pizza

will she be taking home?

_____________________ Explain or show how you know.

4. Sharon is carrying her baby who weighs 8 25

pounds and a diaper bag weighing

4 12

pounds. How much total weight is she carrying?

_____________________


Math 6


5. What is 56• 45

? _____________________


6. What is 23

+ 38

?_____________________


7. Write a number sentence for the model shown below.

___________________

Math 6


8. Alejandra went to the grocery store. Her receipt is shown below but the total

is missing. What is the total of her purchase?

_____________________

If she paid with a $20.00 bill how much change did she receive?

_____________________ Show your work.

9. Carlos bought 365 pencils that cost $0.78 each. How much did he pay?

_____________________

Show your work.

GROCERY OUTLET Soda bottle $1.64 Sandwich $6 Chips $0.77 Cookie $1.50

Math 6 Name: Date: Period

Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)

Fractions on a Number Line

_______________________________________________________________

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_______________________________________________________________

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_______________________________________________________________

!!

.



Fractions on a Number Line ! ! ! ! ! ! !! ! ! ! ! ! Name:!

Do you agree with Genie’s method for solving this? Why or why not? What feedback would you give her? _______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

!


!

Do you agree with Genie’s reasoning when for solving this? What feedback would you give her? _______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________!

!

What is another way for Genie to know if her answer is correct on number 3? !



Cindy’s Cats !Cindy has 3 cats: Sammy, Tommy and Suzi.

!!1. Cindy feeds them on Cat Crunchies.

Each day Sammy eats of the box. Tommy eats of the box and Suzi eats of the box.

!

What fraction of a whole box do the cats eat, in all, each day? Show how you figured this out.

!!!!!!!!!!!

2. Tommy and Suzi spend much of each day sleeping.

Tommy sleeps for 3 5

of the day and Suzi sleeps for 7

10

!

of the day.

Which of the two cats sleeps for longer? !

!

How much longer does it sleep each day? Show how you figured this out.

12

18

14


3. Cindy’s cats often share a carton of cat milk. !

Sammy always drinks 1 3

!

of the carton, Tommy always drinks 5

12

!of the carton, and

Suzi always drinks 1 of the carton. 6

What fraction of the carton of cat milk is left over? Show how you figured it out.

!!!!!!!!!!!!!!

4. Cindy’s cats love to jump in and out of their cat door. !

!

Yesterday the cat door was used 40 times by her cats. !

!

Sammy used it for 1

of the times and Tommy used it for 3

!!!!of the times.

4 10

How many times did Suzi use the cat door?

!

Explain how you figured it out.

!!!!!!!!!!



Cindy’s Cats !! ! ! ! ! ! Name:!!Cindy has 3 cats: Sammy, Tommy and Suzi.

!!1. Cindy feeds them on Cat Crunchies.

Each day Sammy eats of the box. Tommy eats of the box and Suzi eats of the box.

!

What fraction of a whole box do the cats eat, in all, each day?

Show how you figured this out. !!!!!!!!! Is Bobby correct? ____________ Explain how Bobby got his answer. What feedback would you give Bobby about his work? _______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

12

18

14

Bobby


2. Tommy and Suzi spend much of each day sleeping.

Tommy sleeps for 3 5

of the day and Suzi sleeps for 7

10

!

of the day.

Which of the two cats sleeps for longer? !

!

How much longer does it sleep each day? Show how you figured this out.

!

!!!

!!

!!!

!Is Bobby correct? ____________ Explain how Bobby got his answer. What feedback would you give Bobby about his work? _______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________


3. Cindy’s cats often share a carton of cat milk. !

Sammy always drinks 1 3

!

of the carton, Tommy always drinks 5

12

!of the carton, and

Suzi always drinks 1 of the carton. 6

What fraction of the carton of cat milk is left over?

Show how you figured it out. !!!!!!!!!!!!!! Is Bobby correct? ____________ Explain how Bobby got his answer. What feedback would you give Bobby about his work? _______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

!!!


!!!

4. Cindy’s cats love to jump in and out of their cat door. !

Yesterday the cat door was used 40 times by her cats.

Sammy used it for 14

of the times and Tommy used it for 13

of

the times. !

!

!

How many times did Suzi use the cat door? !

Explain how you figured it out. !!!!!!!!!!!!!!!! Is Bobby correct? ____________ Explain how Bobby got his answer. What feedback would you give Bobby about his work?

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

!


Unit 6 Fractions – Lesson Series 0

A Pizza Problem!

On Friday night, Ruben had pizza for dinner. He ate 13

of the pizza and saved

the rest for lunch on Saturday. On Saturday, Ruben ate 12

of the pizza he had

saved. How much of the whole pizza did Ruben eat on Saturday for lunch? Lauren says that Ruben ate 1

6 of the pizza. Here is how she figured it out:

Raymon says that Ruben ate 2

6 of the pizza. This is how he figured it out.

Work with your team or partner to create a mini-poster showing whether Lauren or Raymon has the correct answer. Make sure to demonstrate more than one method for finding the answer. How would you explain to the incorrect person what mistake they made?


Fractions Unit 6 – Entry Assessment

Fractions Assessment 1. Which of the following fractions are equivalent?


2. Erik has 4 34

bottles of soda. If he gives away 2 23

of them, how many

does he have left? _____________________


59

34

48

Math 6


3. United for Success is having a pizza party in all 6 of the math classrooms. Ms. Chen is taking the left overs home with her. If

there is 38

of a pizza left in each box, how much total pizza

will she be taking home?

_____________________ Explain or show how you know.

4. Sharon is carrying her baby who weighs 8 25

pounds and a diaper bag weighing

4 12

pounds. How much total weight is she carrying?

_____________________


Math 6


5. What is 56• 45

? _____________________


6. What is 23

+ 38

?_____________________


7. Write a number sentence for the model shown below.

___________________

Math 6


8. Alejandra went to the grocery store. Her receipt is shown below but the total

is missing. What is the total of her purchase?

_____________________

If she paid with a $20.00 bill how much change did she receive?

_____________________ Show your work.

9. Carlos bought 365 pencils that cost $0.78 each. How much did he pay?

_____________________

Show your work.

GROCERY OUTLET Soda bottle $1.64 Sandwich $6 Chips $0.77 Cookie $1.50


Unit 6 – Fractions Entry Task!

How Can I Share Equally? Today in class you will be sharing licorice; it will be passed out to be shared amongst groups. If your group has 3 members, you will get 5 pieces of licorice. If your group has 5 members, you will get 9 pieces of licorice. If your group has 6 members, you will get 10 pieces of licorice. Work with your teammates to show how you could divide the licorice fairly amongst your group. Your poster presentation should include:

• A diagram or diagrams showing how the licorice was divided

• A division number sentence representing the problem.

• Words that explain what portion of licorice each person gets and why.

• An explanation of how you know that you are sharing fairly.

• An explanation of which groups you think got the most licorice.


Unit 6 – Fraction Lesson Series 1

Geetha is making goodie bags for her birthday

party. She bought a 4- pound bag of candy that

she is going to split it into baggies with 1/3

pound in each. How many goodie bags can

she make?


!


Natasha, Gabriel and Da’Jon are sharing 12 of

a chocolate bar. How much of the whole bar

will each person get?


!


Kenji has two- thirds square yards of wood. It

takes three-fourths of a square yard of wood to

make a chair for his daughter’s dolls. How

many chairs can he make?


!


Katherine has 35 cups of flour. Her pancake

recipe calls for 14 cups of flour. How many total

recipes can she make?


Unit 6 Fractions – Formative Task

Lucy’s Dollhouse Lenny and his uncle want to build a dollhouse for Lenny’s little sister, Lucy. They picked up left-over materials from another project, but are not sure if they have enough to make what they want. Below is the list they made of their materials.

Here is a list of what they want to make and how much of each material they need.

Room (floor and walls): 13

yard of plywood Windows: 324

yard of plastic

Tables: 316

yard of cardboard Beds: 415

yard of fabric

Create a mini-poster that will help Lenny and his uncle know how many or what fraction of a whole they can make of each item. Draw a model and write a number sentence to prove to them your calculations are correct.

Plywood- 59

yard

Cardboard- 23

yard long

Plastic- 5 sheets, 14

yard each

Fabric- 78

yard



Michael has 12 of a yard of fabric to make book

covers. Each book cover is made from 18 of a yard of

fabric. How many book covers can Michael make?


!

Unit 6 – Fraction Lesson Series 2 2!

A recipe requires 23 of a cup of yogurt. Martha

has 12 of a cup of yogurt from a snack pack.

How much of the recipe can Martha make?

Math 6


Dividing Fractions Explanation Quiz

Facilitator

Get the conversation started and keep it going. Make sure everyone shares ideas. Did anyone think about it abother way? What do you think, ____?

Team Captain

Keep your team together and on task. Your weekend sounds cool, but let’s get back to this problem. Does everyone know where we got that?

Resource Manager

Get resources for your team, including calling the teacher when you have a team question.

Does everyone know the question we want to ask?

Recorder/Reporter

Keep the task in the middle of the table so everyone can see it. Organize how to record your team’s ideas.

What should I write down from what we just said? Which model should we use for this?

You have been learning how to divide fractions. Today your team will work together to divide fractions in an explanation quiz. You can start with any problem you’d like. Work on a separate sheet of paper. When you have an equation written and have used 2 different models, call your teacher over to quiz your group. Everyone on your team must be able to explain your group’s reasoning and work.

28÷ 75

68÷ 34

56÷ 45

79÷ 13

12÷ 16

32÷ 54

23÷ 45


Unit 6 Fractions - Expert Task!

Create Your Own Story Part 1: Create a story, in the form of a comic strip, poster, video or other approved project around the problem:

34÷

12

Your story should place this expression and the quotient in a real world situation.

Part 2: Your story should include a visual and written explanation as to how to solve the problem using both a model and the algorithm.

Part 3: The end of your story should draw connections between the two strategies you used to solve the problem.

4 3 2 1

Mathematics

The story correctly represents the

mathematics in a real world context.

1 mathematical error or inconsistency in the

story line

More than 1 mathematical error

and/or several inconsistencies in the

story

Story does not illustrate the problem

Explanation

Two methods for solving the problem

are clearly explained with words, drawings

and math.

The methods for solving the problem is clearly explained with ONE of the following: words, drawings, or

math.

The explanation is confusing, unclear or incomplete, OR only

one method is explained.

Explanation is missing or unrelated to the

problem.

Presentation

Little to no presentation errors Story is original and the format is well chosen and used.

1-2 errors in presentation (example:

spelling, grammar, neatness of drawings,

scripting etc.)

3-4 errors in presentation (example:


scripting etc.)

More than 4 errors in presentation (example:


scripting etc.)



Sewing Sandy is sewing pants for herself.

Sandy’s pattern calls for 2 14

yards of fabric for each pair of

pants she needs to make. If she has 312

yards of fabric, how many pairs of pants

can she make? ______________ Sandy wants to buy everything she needs for her another pair of pants at JoAnn’s Fabric Store. Complete the chart below to help her figure out the cost. $

2 14

yards of fabric at $18 a yard

17 spools of thread at 35¢ a spool

3 buttons at $1.25 each

1 Zipper $1.85

Total before sales tax

Sales tax at 8% (Round to the nearest cent)

Total

Student Materials Interpreting Multiplication and Division S-1 © 2013 MARS, Shell Center, University of Nottingham

Multiplication and Division Complete the gaps in the table. The first row has been done for you. The diagram should show the structure of the problem. The calculation should show a single multiplication or division.

Problem Explain how to do the problem, and draw a diagram to help Calculation Answer

1

I buy three boxes of yogurt. Each box contains four yogurts. How many yogurts do I buy altogether?

Calculate three groups of four.

3 x 4

or

4 x 3

12

2

Two pizzas are shared equally among five people. How much does each person get?

3

Max cuts a cake into three equal slices. He eats one half of a piece. What fraction of the cake does he eat?

4

Make up this problem yourself!

3 ÷ 12

5


12÷ 1

4

Math 6


Interpreting Multiplication and Division Participation Quiz

Facilitator Get the conversation started and keep it going. Make sure everyone shares ideas. Did anyone think of another way? What do you think, ____?

Team Captain Keep your team together and on task. Your weekend sounds cool, but let’s get back to this problem. Does everyone know where we got that?

Resource Manager Get resources for your team, including calling the teacher when you have a team question. Does everyone know the question we want to ask?

Recorder/Reporter Keep task in the middle of the table so everyone can see it. Organize how to record your team’s ideas. What should I write down from what we just said? Which model should we use for this?

Work with your group to match cards (expressions, words, diagrams). As you work with your group, ask and answer the following questions to help you find matches:

• What is the problem asking? • What are we trying to find? • How could we approach this? • What operation do we need to use? • How can we set up an expression that shows what the scenario is saying? • What is a good plan for solving this? • How can we prove that the cards match?


Card Set: Calculations

C1 C2 C3

C4 C5 C6

6 ÷ 3 3 x 6

C7 C8 C9

C10 C11 C12

6 x 3

C13 C14 C15

3 ÷ 6


Card Set: Words and Diagrams

W1 What is three groups of one sixth?

W2

What is one third of six?

W3

How many one-sixths are there in one third?

W4

Six groups of three. How many altogether?

W5

W6

Six groups of one third. How much altogether?


Card Set: Words and Diagrams (continued)

W7

Six divided into three equal groups. How many in each group?

W8

Three divided into six equal parts. How much is each part?

W9

W10

Six divided into thirds. How many slices?

W11

How much is one third of one sixth?

W12

What fraction of one third is one sixth?


Card Set: Pizza Problems

P1

Three boxes of pizza are delivered to a party. Each box contains six pizzas. How many pizzas are delivered altogether?

P2

Six boxes of pizza are delivered to a party. Each box contains three pizzas. How many pizzas are delivered altogether?

P3

Six boxes, each containing one pizza, are delivered to a party. I divide each pizza into three equal slices. How many slices are there altogether?

P4

Six pizzas are placed in three boxes. The same number go into each box. How many is this?

P5

Six people are each given one third of a pizza to eat. How many whole pizzas are they given altogether?

P6

There are six pizzas. One third are vegetarian. How many are vegetarian?

P7

I cut a pizza into six equal slices. I then eat a third of the whole pizza. How many slices do I eat?

P8

Three pizzas are divided equally among six people. What fraction of a whole pizza does each person get?

P9

I am given one sixth of a pizza. I eat only one third of this piece. What fraction of the whole pizza do I eat?

P10

A whole pizza is divided into six equal slices. I eat three of these. What fraction of the whole pizza do I eat?

P11

At a restaurant, each person is given one third of a whole pizza. I eat one sixth of a whole pizza. What fraction of my piece do I eat?

P12

I cut a pizza into three equal slices. I then eat a sixth of one piece. What fraction of the whole pizza do I eat?

Interpreting Multiplication and DivisionProjector Resources

What do these mean?

P-1

3× 613×6

6÷3

3÷ 6


Multiplication and Division (revisited) Complete the gaps in the table. The first row has been done for you. The diagram should show the structure of the problem. The calculation should show a single multiplication or division.

Problem Explain how to do the problem, and draw a diagram to help. Calculation Answer

1

I buy three boxes of golf balls. Each box contains six balls. How many balls do I buy altogether?

Calculate three groups of six.

3 x 6

or

6 x 3

18

2

Three pizzas are shared equally among eight people. How much does each person get?

3

Max cuts a cake into two equal slices. He eats one third of a piece. What fraction of the whole cake does he eat?

4


4 ÷ 13

5


13÷ 1

6



Fractions, Decimal, Percent Explanation Quiz

Facilitator Get the conversation started and keep it going. Make sure everyone shares ideas. Did anyone think of another way? What do you think, ____?

Team Captain Keep your team together and on task. Your weekend sounds cool, but let’s get back to the problem. Does everyone know where we got that?

Resource Manager Get resources for your team, including calling the teacher when you have a team question. Does everyone know the question we want to ask?

Recorder/Reporter Keep task in the middle of the table so everyone can see it. Organize how to record your team’s ideas. What should I write down from what we just said? Which model should we use for this?

Work with your group on the series of questions on a separate sheet of paper. Make a model or diagram to show how you solved it. You may do them in any order you wish, but be sure that you call your teacher over as you finish each one. Each team member should be ready to explain their reasoning.

The elephants at the Oakland Zoo are fed 7/10

of a barrel of corn each day. The buffalo are fed

4/5 as much corn as the elephants. How many

barrels of corn are the buffalo fed each day?

You give 1/3 of a pan of brownies to Susan and

1/6 of the pan of brownies to Patrick. How

much of the pan of brownies did you give away?

How much do you have left?

Unit 6 Fractions – Lesson Series 0 2!

Ms. Hankins teaches 125 students. 60% are

girls. How many students are girls? How many

students are boys?

Sheila wants to make little sweaters for her

dog. She has yards of fabric. A sweater is

made with yard of fabric. How many

sweaters can she make?

Jonathan earns $11.75 per hour. If he works

21.75 hours, how much money will he make?

There are pounds of bricks in a bag. Each

brick weighs of a pound. How many bricks

are in the bag?


Unit 6 Fractions - Summative Task

Fraction Division Summative Task 1. Write a division equation for the following model: ____________________ 2. Draw an area model or a number line model for the following problem:

€

3 ÷34

3. Julia has two opened bottles of iced tea. One has45 of a liter in it and the

other has 23 of a liter in it. If a cup holds

116 of a liter, how many cups can

she fill up with what she has?

Unit 6 Fractions – Summative Task 2

4. Alice bought 4 23

yards of terry cloth to make collars for some of the costumes

for the school play. It takes 25

of a yard of fabric to make each collar. How

many collars can Alice make?

Write a number sentence and model how to solve the problem. 5. Estelle has a ribbon that is 0.7 inches long. Mara gives her another one that is

0.62 inches. How much ribbon does Estelle have now? 6. Erik’s hair is 0.6 feet long. He has 0.48 feet cut off. How long is Erik’s hair

after his haircut?

Unit 6 Fractions – Summative Task 3

7. Jorge has a plot of land that is 0.9 km2 long. It takes 0.23 km2 of land to build a fort. How many forts can Jorge build?

8. What is the area of a city that is 0.86 miles long and 0.97 miles wide? 9. Xiao is packing a suitcase that has 369.8 inch2 of space. If his shoes take up

25% of the space, how much space does he have left for his other things?

10. Sotida wants to buy a shirt that costs $45.55. She is using a coupon that

reduced the price of the shirt to 75% of the original price. If Sotida’s mom gives her the money for half of the price, how much does Sotida need in order to buy the shirt?

Documents

Math 6 Unit 6: Fractions Tasks Onlybhmsparnell.weebly.com/uploads/2/2/7/3/22730444/500...Math 6 Fractions Unit 6 – Entry Assessment 2 3. United for Success is having a pizza party