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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? _____________________
Explain or show how you know.
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?
_____________________
Explain or show how you know.
Math 6
Fractions Unit 6 – Entry Assessment 3
5. What is 56• 45
? _____________________
Explain or show how you know.
6. What is 23
+ 38
?_____________________
Explain or show how you know.
7. Write a number sentence for the model shown below.
___________________
Math 6
Fractions Unit 6 – Entry Assessment 4
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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Math 6 Name: Date: Period:
Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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? _______________________________________________________________
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Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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Do you agree with Genie’s reasoning when for solving this? What feedback would you give her? _______________________________________________________________
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What is another way for Genie to know if her answer is correct on number 3? !
Math 6 Name: Date: Period:
Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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
Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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.
!!!!!!!!!!
Math 6 Name: Date: Period:
Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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? _______________________________________________________________________________
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12
18
14
Bobby
Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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? _______________________________________________________________________________
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Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
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? _______________________________________________________________________________
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!!!
Unit 6 Fractions – Lesson Series 0 Adapted from Mathematics Assessment Resource Service (MARS)
!!!
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?
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Math 6 Name: Date: Period:
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?
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? _____________________
Explain or show how you know.
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?
_____________________
Explain or show how you know.
Math 6
Fractions Unit 6 – Entry Assessment 3
5. What is 56• 45
? _____________________
Explain or show how you know.
6. What is 23
+ 38
?_____________________
Explain or show how you know.
7. Write a number sentence for the model shown below.
___________________
Math 6
Fractions Unit 6 – Entry Assessment 4
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 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.
Math 6 Name: Date: Period:
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?
Math 6 Name: Date: Period:
!
Unit 6 – Fraction Lesson Series 1
Natasha, Gabriel and Da’Jon are sharing 12 of
a chocolate bar. How much of the whole bar
will each person get?
Math 6 Name: Date: Period:
!
Unit 6 – Fraction Lesson Series 1
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?
Math 6 Name: Date: Period:
!
Unit 6 – Fraction Lesson Series 1
Katherine has 35 cups of flour. Her pancake
recipe calls for 14 cups of flour. How many total
recipes can she make?
Math 6 Name: Date: Period:
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
Math 6 Name: Date: Period:
Unit 6 – Fraction Lesson Series 2
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?
Math 6 Name: Date: Period:
!
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
Unit 6 Fractions – Lesson Series 2
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
Math 6 Name: Date: Period:
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:
spelling, grammar, neatness of drawings,
scripting etc.)
More than 4 errors in presentation (example:
spelling, grammar, neatness of drawings,
scripting etc.)
Math 6 Name: Date: Period:
Unit 6 Fractions – Lesson Series 3 Adapted from Mathematics Assessment Resource Service (MARS)
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
Make up this problem yourself!
12÷ 1
4
Math 6
Unit 6 Fractions – Lesson Series 3
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?
Student Materials Interpreting Multiplication and Division S-2 © 2013 MARS, Shell Center, University of Nottingham
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
Student Materials Interpreting Multiplication and Division S-3 © 2013 MARS, Shell Center, University of Nottingham
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?
Student Materials Interpreting Multiplication and Division S-4 © 2013 MARS, Shell Center, University of Nottingham
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?
Student Materials Interpreting Multiplication and Division S-5 © 2013 MARS, Shell Center, University of Nottingham
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
Student Materials Interpreting Multiplication and Division S-6 © 2013 MARS, Shell Center, University of Nottingham
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
Make up this problem yourself!
4 ÷ 13
5
Make up this problem yourself!
13÷ 1
6
Math 6 Name: Date: Period:
Unit 6 Fractions – Lesson Series 0
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?
Math 6 Name: Date: Period:
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?