Georgia Performance Standards Framework Mathematics Grade … · Georgia Performance Standards...

Georgia Performance Standards Framework

Mathematics – Grade Five

of 38 Unit 3 Organizer Unit 3 Organizer

May 8, 2007 FUNKY FRACTIONS

Unit 3 Organizer: “Funky Fractions”

(7 weeks)

OVERVIEW:

In this unit students will:

classify counting numbers into subsets;

find factors and multiples;

analyze and use divisibility rules;

find equivalent fractions;

simplify fractions;

use concrete, pictorial, and computational models to find common denominators;

compare fractions using <, >, or = and justify the comparison;

add and subtract fractions and mixed numbers with unlike denominators;

use fractions (proper and improper) and decimals interchangeably;

model multiplication and division of fractions (denominators not to exceed 12 – 2, 3, 4, 5, 6, 8, 10, 12);

estimate products and quotients;

use variables for unknown quantities; and

use formulae to represent the relationship between quantities.

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics

such as add/subtract decimals and fractions with like denominators, whole number computation, angle measurement,

length/area/weight, number sense, data usage and representations, characteristics of 2D and 3D shapes and order of operations should

be addressed on an ongoing basis.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under “Evidence of

Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely

replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks

in these units illustrate the types of learning activities that should be utilized from a variety of sources.





ENDURING UNDERSTANDINGS:

A fraction is another representation for division.

Equivalent fractions represent the same value.

Whole numbers can be classified into subsets.

Divisibility rules can be used to find equivalent fractions quickly.

Fractions and decimals are different representations for the same amounts and can be used interchangeably.

Variables are used to represent unknown quantities in algebraic expressions and formulae.

ESSENTIAL QUESTIONS:

How can I determine whether a number is odd or even?

How do I know if a number is prime or composite?

How can I find equivalent fractions?

How do I determine which factors a number is divisible by?

How does knowing the divisibility rules help me solve problems?

How are factors and multiples represented?

How are fractions and decimals related?

STANDARDS ADDRESSED IN THIS UNIT

Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities

as possible in order to emphasize the natural connections that exist among mathematical topics.

KEY STANDARDS:

M5N1. Students will further develop their understanding of whole numbers.

a. Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite).





b. Find multiples and factors.

c. Analyze and use divisibility rules.

M5N4. Students will continue to develop their understanding of the meaning of common fractions and will compute with them.

a. Understand division of whole numbers can be represented as a fraction (a/b = a ÷ b).

b. Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by

the same number because it is the same as multiplying or dividing by one.

c. Find equivalent fractions and simplify fractions.

d. Model the multiplication and division of common fractions.

e. Explore finding common denominators using concrete, pictorial, and computational models.

f. Use <, >, or = to compare fractions and justify the comparison.

g. Add and subtract common fractions and mixed numbers with unlike denominators.

h. Use fractions (proper and improper) and decimals interchangeably.

i. Estimate products and quotients.

M5A1. Students will represent and interpret the relationships between quantities algebraically.

a. Use variables, such as n or x, for unknown quantities in algebraic expressions.

b. Investigate simple algebraic expressions by substituting numbers for the unknown.

c. Determine that a formula will be reliable regardless of the type of number (whole numbers or decimal fractions)

substituted for the variable.

RELATED STANDARDS:

M5D1. Students will analyze graphs.

a. Analyze data presented in a graph.

b. Compare and contrast multiple graphic representations (circle graphs, line graphs, bar graphs, etc.) for a single set of

data and discuss the advantages/disadvantages of each.

M5D2. Students will collect, organize, and display data using the most appropriate graph.





M5P1. Students will solve problems (using appropriate technology).

a. Build new mathematical knowledge through problem solving.

b. Solve problems that arise in mathematics and in other contexts.

c. Apply and adapt a variety of appropriate strategies to solve problems.

d. Monitor and reflect on the process of mathematical problem solving.

M5P2. Students will reason and evaluate mathematical arguments.

a. Recognize reasoning and proof as fundamental aspects of mathematics.

b. Make and investigate mathematical conjectures.

c. Develop and evaluate mathematical arguments and proofs.

d. Select and use various types of reasoning and methods of proof.

M5P3. Students will communicate mathematically.

a. Organize and consolidate their mathematical thinking through communication.

b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

c. Analyze and evaluate the mathematical thinking and strategies of others.

d. Use the language of mathematics to express mathematical ideas precisely.

M5P4. Students will make connections among mathematical ideas and to other disciplines.

a. Recognize and use connections among mathematical ideas.

b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

c. Recognize and apply mathematics in contexts outside of mathematics.

M5P5. Students will represent mathematics in multiple ways.

a. Create and use representations to organize, record, and communicate mathematical ideas.

b. Select, apply, and translate among mathematical representations to solve problems.

c. Use representations to model and interpret physical, social, and mathematical phenomena.





CONCEPTS/SKILLS TO MAINTAIN:

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be

necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a

deeper understanding of these ideas.

Add and subtract fractions with like denominators

Number sense

Data usage and representations

Order of operations

SELECTED TERMS AND SYMBOLS:

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in

isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors

should pay particular attention to them and how their students are able to explain and apply them. The definitions below are for teacher reference only and are not to be memorized by the students. Teachers should present

these concepts to students with models and real life examples. Students should understand the concepts involved and be able to

recognize and/or demonstrate them with words, models, pictures, or numbers.

Simplify: To rewrite a fraction where the numerator and denominator are the smallest numbers possible.

Common denominator: A common multiple of the denominators.

Greatest common factor (GCF): The biggest number that will divide two or more numbers exactly.

Least common multiple (LCM): The lowest common multiple of the denominators.

Improper fraction: A fraction larger than one; the numerator is larger than the denominator.

Proper fraction: A fraction smaller than one; the numerator is smaller than the denominator.

Divisibility: The characteristic of dividing evenly into another number.

Multiple: The product of two whole numbers.

Factor: A number that is multiplied by another number to find a product.





EVIDENCE OF LEARNING:

By the conclusion of this unit, students should be able to demonstrate the following competencies:

classify counting numbers into subsets;

find factors and multiples;

analyze and use divisibility rules;

find equivalent fractions;

simplify fractions;

use concrete, pictorial, and computational models to find common denominators;

compare fractions using <, >, or = and justify the comparison;

add and subtract fractions and mixed numbers with unlike denominators;

use fractions (proper and improper) and decimals interchangeably;

model multiplication and division of fractions (denominators not to exceed 12 – 2, 3, 4, 5, 6, 8, 10, 12);

estimate products and quotients;

use variables for unknown quantities; and

use formulae to represent the relationship between quantities.

The following tasks represent the level of depth, rigor, and complexity expected of all fifth grade students. These tasks or a

task of similar depth and rigor should be used to demonstrate evidence of learning.

The Sieve of Eratosthenes

Exploring the Sieve of Eratosthenes

Number Riddles

The Quotient is Greater than 1

Fraction and Decimal Match Up

Fraction and Decimal Line Up

Picture This!

Birthday Cookout

My Multiplication and Division Fraction Book

You’re Invited to a Fabulous Fraction Party





Culminating Activity: “You’re Invited to a Fabulous Fraction Party!!!”

Students will plan a surprise party for their best friend. They will find recipes for what they will be serving and rewrite the recipes for

the correct number of people. They will check the cupboards to see what they have and make a grocery list of what they will need

grocery shop with a $50 limit, and create invitations.

STRATEGIES FOR TEACHING AND LEARNING:

Students should be actively engaged by developing their own understanding.

Mathematics should be represented in as many ways as possible by using graphs, tables, pictures, symbols and words.

Appropriate manipulatives and technology should be used to enhance student learning.

Students should be given opportunities to revise their work based on teacher feedback, peer feedback, and metacognition which

includes self-assessment and reflection.

Classroom Routines

The importance of continuing the established classroom routines cannot be overstated. Daily

routines must include such obvious activities such as taking attendance and lunch count, doing

daily graphs, and daily question and calendar activities as whole group instruction. They should

also include less obvious routines, such as how to select materials, how to use materials in a

productive manner, how to put materials away, and how to access classroom technology such as

computers and calculators. An additional routine is to allow plenty of time for children to

explore new materials before attempting any directed activity with these new materials. The

regular use of routines is important to the development of students’ number sense, flexibility,

fluency, collaborative skills, and communication. All of which will support students’

performances on the tasks in this unit and throughout the school year.





TASKS:

The collection of the following tasks represents the level of depth, rigor and complexity expected of all fifth grade students to

demonstrate evidence of learning.



Use a hundreds board to complete the following:

1) Cross out the number 1, because it is not a prime number.

2) Circle the number 2 with yellow, because it is the smallest prime number. Cross out every multiple of 2 with yellow.

How do you know which numbers to cross out? Write an algebraic expression for the numbers you crossed out with

yellow.

3) Circle the number 3 with blue. This is the next prime number. Now, cross out every multiple of 3 with blue. What do

you notice about the number 6? What do you think it means when a number is crossed out with two colors – in this

case yellow and blue?

4) Circle the next open number, 5 with red. Cross out all multiples of 5 with red. Write an algebraic expression for the

numbers you crossed out in red.

5) Circle the next open number with orange. Cross out all multiples of 7 with orange.

6) Continue doing this until all the numbers through 100 have either been circled or crossed out.

7) Which numbers are circled? What do you notice about these numbers?

8) Write a short paragraph about your findings and conclusions.

*************************************************************************************************





Discussion, Suggestions, Possible Solutions

Each student needs a hundreds board (sample shown below) and colored pencils, markers, crayons, or highlighters.

You may choose to model the first one or two steps on the overhead. Discuss the patterns students see. Write these on

the board or chart paper as students share them.

1 2 3 4 5 6 7 8 10 9

12 11 13 14 15 16 17 18 19 20

22 21 23 24 25 26 27 28 29 30

32 31 34 33 35 36 37 38 39 40

42 41 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100





Students should use different colors or symbols (*, #, etc.) for each new prime number. This will help students see

patterns for the divisibility rules. Using different colors works better, but students might need to use a combination of

crayons, highlighters, colored pencils, and markers.

Extension:

The following internet links have interactive versions of the Sieve of Eratosthenes…

http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes - This website is part of Wikipedia. There is a brief definition

and an animation of a Sieve being completed.

http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm - This website is a Java Sieve of Eratosthenes. You can select

any number and its multiples will be eliminated. The end result will be all the prime numbers between 1 and 400.


http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm






Work with a partner to complete the first part of the chart. Complete the CHALLENGE and record your observations on

your own.

Find this number

on your

hundreds board:

What colors and/or

symbols were used to

cross out this number?

What numbers are

circled with these colors

or have the symbol?

Insert the numbers from the previous

column in the blanks

(be sure they are increasing in order)

6 1, , , 6

9 1, , 9

12 1, , , , , 12

15 1, , , 15

17 1, , , 17

21 1, , , 21

24 1, , , , , , , 24

29 1, , , 29

CHALLENGE: For each line below, select a number between 40 and 60. Write it in the first column. Complete the columns.

Reflection Time: Look at your chart. Record 3 observations from your work.

*************************************************************************************************






Each student needs his/her completed Sieve of Eratosthenes. Let students share their observations. Record these on

a chart or the board. This activity will help students determine factors and multiples.

Extension:

Students can write a letter to an “absent” classmate about how to use the Sieve of Eratosthenes to find factors of

numbers.

Number Riddles





Number Riddles

Use the clues to solve these number riddles.

Riddle #1 – I am a 4-digit decimal between 400 and

650.

My hundreds digit is divisible by 2 but not

3.

My tens digit is a multiple of 3.

My ones digit is ½ of my tens digit.

All of my digits are different.

The sum of my digits is 20.

What number am I?

Riddle #2 – I’m a 2-digit whole number between 30 and 80.

My tens digit is one more than my ones digit.

I am a prime number.

What number am I?

Riddle #3 – I am a four-digit whole number greater than

6000.

My thousands digit is prime.

My ones digit is the only even prime number.

I am divisible by 4.

My tens digit is ½ my hundreds digit.


What number am I?

Riddle #4 – I’m an odd number between 250 and 700.

I am divisible by 5.

My tens digit is 3 more than my ones digit.


What number am I?

Riddle #5 – I am a 5-digit decimal between 150 and 375.

All of my digits are odd.

My tens digit is 3 times my ones digit.

My hundreds digit is my smallest digit.

None of my digits is the same.

My tenths digit is 2 less than my tens digit.

What number am I?

Riddle #6 – I am a three-digit whole number between 300

and 500.

My ones digit is the largest single digit prime

number.

My tens digit is even.


What number am I?

Riddle #7 – I am a 3-digit odd number greater than

800.

My tens digit is 2 less than my ones digit.

I am divisible by 3 but not 5.


What number am I?

Riddle #8 – I am a four-digit whole number.

I am divisible by 5 but not 10.

My thousands digit is neither prime nor

composite.

My hundreds digit is 2 more than my tens digit.


What number am I?

Riddle #9 – I am a 3-digit decimal less than 10.

My tenths digit is 3 times my ones digit.

My hundredths digit is an even prime.



What number am I?

Challenge: Create two riddles of your own. Include the answer to your riddle.

*************************************************************************************************






This can be used as a tic-tac-toe or students can complete all of the riddles. Some students may want to use their

completed Sieve of

Eratosthenes to help solve the riddles.

Riddle #1 – 463.7 Riddle #2 – 43 Riddle #3 – 7632

Riddle #4 – 485 Riddle #5 – 193.75 Riddle #6 – 347

Riddle #7 – 813 Riddle #8 – 1205 Riddle #9 – 3.92

Extension: Students can write their riddles on separate index cards. These can be collected and used as warm-ups,

centers, problem solving activities, etc. These types of riddles can also be used as warm-up problems to reinforce

critical thinking and mathematical vocabulary. They can be adapted to include a variety of mathematical concepts.

http://www.stfx.ca/special/mathproblems/grade5.html - This website has many problem solving activities and

math riddles.

http://www.justriddlesandmore.com/math2.html - This websites has math riddles, patterns, multiplication

problems, problem solving, and more.

http://www.stfx.ca/special/mathproblems/grade5.html

http://www.justriddlesandmore.com/math2.html





The Quotient is Greater than 1 (Q > 1)

The Quotient is Greater than 1 (Q > 1)

> 1

(1) The dividend and divisor are 25 and 75. Which number goes where and why?

(2) If the dividend is 36, what is the largest number the divisor can be? Why is that true?

(3) If the divisor is 18, what is the smallest number the dividend can be? Tell why.

(4) Fill in the chart so that the quotient would be > 1.

*************************************************************************************************

Dividend

Divisor






This task is designed to help students understand that fractions are also division problems. Discuss responses to

each of the questions.

(1) 75 is the numerator and 25 is the denominator – otherwise you will have a proper fraction and it will not be

greater

than 1.

(2) The largest number the divisor can be is 35…36 will give you 1 and 1 is not greater than 1. Anything more

than 36 will

give you a proper fraction which will result in a number less than one.

(3) The smallest number the dividend can be is 19…18 will give you 1 and 1 is not greater than 1. Anything less

than 18

will result in a proper fraction which is less than 1.

(4) Answers will vary but the divisor should be smaller than (but not equal to) the dividend.

Extension:

Students can rewrite their decimals as mixed numbers.

Change the sign so that the students are finding quotients that are less than 1. Use common fractions such as ½,

¼, ¾, etc. to help students connect fractions with their decimal equivalents.







It’s time to hang up the wash! But, you must hang the clothes in order on the clothesline. Before you can put your

laundry on the line, you should use the recording sheet and put it where you think it should go. Work with your team

to determine where to hang your clothes. Put your team’s clothes on the recording sheet.

Go up with your team to hang your clothes. You can rearrange the clothes if you need to, but you have to explain

why you changed the order.

Reflection Time: How did you determine where to put your clothes?

*************************************************************************************************


Preparation – Materials needed – “laundry” cards, clothesline and clothespins (or string and tape)

Prior to activity:

1. Select beginning and ending numbers for your line up (the numbers used will be determined by your

students). You may choose 0 and 5, 0 and 10, 0 and 2, etc.

2. Count enough laundry cards for each student to have a complete outfit.

3. On each card, write a fraction (it may be proper, improper, mixed number, simplified, “un-simplified”) or

decimal.

4. Put up the clothesline and place the clothespins in a small basket nearby.

5. “Pin” the beginning and ending laundry cards on the clothesline. (You have a clothesline number line.)

Sample laundry cards are shown below.





Print enough copies of the “outfits” so that each child has a complete outfit.

You might want to laminate the clothes before you write on them.

Write a different fraction or decimal on each clothing piece. You can use fractions (simplified, non-simplified,

improper), mixed numbers or decimals.

**Note - The fractions or decimals for the top and bottom do not need to go together.

Activity

1. Give each student an outfit and a recording sheet.

2. Discuss what they see on their outfit and what they did with the clothesline in the previous activity.

3. Have students record where they think their laundry should go on the recording sheet.

4. Select a team to hang their laundry up to dry. (Students should hang their laundry on the clothesline

according to where it belongs on the number line.)

5. Ask students to share why they hung their clothes where they did. Discuss as a class these placements. How

did they decide where to place the laundry? Do any adjustments need to be made? If so, where? Why?

6. Have another team of students hang their laundry on the clothesline. If they get stuck, they may ask for help.

7. Discuss the placement of their clothes on the clothesline. How did they decide where to place the laundry?

Do any adjustments need to be made? If so, where? Why?

8. Repeat steps 6 and 7 until all laundry has been placed on the clothesline.

A sample clothesline is shown below.





Extension:

Students can select 8-10 laundry items from the class clothesline and place them appropriately on their recording

sheet.

After students do this activity you break them into teams and then give them a “basket of laundry” and have

teams race to put them in order.

Record the beginning and ending numbers below.

Record your numbers on the clothesline where you think they will go.





Picture This!

Picture This!

Part 1

1) Use the pattern block pieces to create a picture of your own design.

2) Transfer your picture to plain paper and color it (you do not have to use the pattern block colors). Label all the

pieces with the appropriate fractions – the hexagon has an area of 1 units. You have to find the values of the

other pieces.

3) Find the total area of your design.

4) Write the value as an improper fraction and a mixed number.

5) Convert the total value to a decimal.

6) Write a short paragraph describing your design. Be sure to use appropriate mathematical vocabulary.

Part 2

1) Trade pictures with a partner.

2) Remove pieces totaling an area of 1 ½ units.

3) Find the new area.

4) Write the value as an improper fraction and a mixed number.

5) Convert the total area to a decimal.

6) With your remaining pieces make a new picture.

7) Write a short paragraph describing your design. Be sure to use appropriate mathematical vocabulary.

*************************************************************************************************


Materials: pattern blocks, paper, markers/crayons/colored pencils





Pattern Block values – hexagon – 1, trapezoid – ½, rhombus – 1/3, triangle – 1/6. Reinforce that these values

represent areas, not just numbers. Students should write sentences to describe the relationships of the different

areas. The area of the trapezoid is ½ the area of the hexagon. The area of the triangle is 1/3 the area of the

hexagon. The area of the triangle is 1/6 the area of the hexagon. Have students record as many different ways to

make 1 using the trapezoid, triangle, and rhombus pieces.

Extension: Students can display their pictures from smallest to largest (or largest to smallest). They can work

together in teams to order the pictures.

Graph the number of each pattern block used to make your picture. After exchanging pictures with your partner,

how does your number compare with your partner’s?

My Multiplication and Division of Fractions Book





My Multiplication and Division of Fractions Book

A major mathematics textbook company is asking for your help. They are looking for ideas on how to model

multiplication and division of fractions using fraction circles and/or arrays.

You need to create a mini-book to model multiplication and division of fractions using circles and arrays.

Include pictures, appropriate story problems and a brief statement of what your answer means.

You need to complete 3 examples for each operation.

******************************************************************************************


Fractions should be common fractions (denominators do not exceed to 12). Have students connect multiplication

and division of fractions with multiplication and division of whole numbers.

Multiplication is groups of – ½ x ¼ means ½ of a group of ¼

Division is how many groups? ½ ÷ ¼ means how many ¼’s are in ½?

Each page should have a problem written at the top. To help students connect multiplication of fractions with

multiplication of whole numbers, it is a good idea to have them write a question that can be answered using the

multiplication problem on the page. From there, students can include pictures to model their problem.

Multiplication Example:





Students should understand what multiplication of fractions means…not just the algorithm for finding the answer.

From working problems similar to the one above using manipulatives and reasoning, students can generalize the

procedure for fraction multiplication.

Division Example: The algorithm for fraction division is not as clear when using manipulatives. However, it is

important for students to understand what the answer to a fraction division problem means. Students can work

with fraction division through multiplication in order to find the procedure for dividing fractions.

8

1

4

1

2

1

What is ½ of a group of ¼?

This shaded part shows ¼. If I want ½ of this shaded section (which is 1 out of 2 pieces),

then I need to have an equivalent fraction so that ¼ has 2 parts. That would be 2/8.

Now, 1 out of 2 pieces is 1/8.

So, ½ x ¼ is 1/8.





Think Multiplication – ½ x (______) = ¾. I might not know right away, but I do know that ½ x 2/1 is 1. I also

know that 1 times any fraction is that fraction. So, 1 x ¾ is ¾. Therefore, ½ x (2/1 x ¾) = ¾. And, I do know

how to multiply fractions. So, 2/1 x ¾ is 6/4…which is the same as 1 ½. Note: The 2/1 x ¾ is the same

multiplication problem you get when you invert and multiply to “divide” fractions with one slight difference…the

order of the fractions is reversed.

2

11

2

1

4

3

How many ½’s are in ¾?

This shaded part shows ¾. If I want to see how many ½’s are in ¾, then I need to “cover” the ¾

with ½ pieces. When I do, I can see that it takes 1 entire ½ piece and ½ of another one to

completely cover ¾ of the circle. There are 1 ½ one-half pieces in ¾.

So, ¾ ÷ ½ is 1 ½.

This is

one ½

piece.

This is

one-half

of a ½

piece.





Extension:

The pages can be combined and turned into a class book of fraction multiplication and division problems.

Students can share their problems with their groups and the class.

http://wme.cs.kent.edu/kimpton/fraction_multiply.html?index=/kimpton/fraction_index.html&indexname=Fra

ctions+module

This website uses arrays to model multiplication of fractions.

http://www.europa.com/~paulg/mathmodels/eggmult.html

http://www.europa.com/~paulg/mathmodels/eggdiv.html - These two websites use egg cartons to model

multiplication and division of fractions.

http://www.homeschoolmath.net/teaching/f/division_fractions.php - This website offers some ideas to help

explain and understand division of fractions.

Birthday Cookout

http://wme.cs.kent.edu/kimpton/fraction_multiply.html?index=/kimpton/fraction_index.html&indexname=Fractions+module

http://wme.cs.kent.edu/kimpton/fraction_multiply.html?index=/kimpton/fraction_index.html&indexname=Fractions+module

http://www.europa.com/~paulg/mathmodels/eggmult.html

http://www.europa.com/~paulg/mathmodels/eggdiv.html

http://www.homeschoolmath.net/teaching/f/division_fractions.php





Birthday Cookout

**********************************************************************************************

Bob turned 60 this year! His family celebrated by having

a cookout. Marcy took orders and found one fifth as

many people wanted chicken as wanted steaks, one fourth

as many people wanted steaks as wanted hot dogs, and

one half as many people wanted hot dogs as wanted

hamburgers. She gave her son-in-law, the chef, an order

for 80 hamburgers.

How many people asked for chicken?

How many people asked for steak?

How many asked for hot-dogs?

Write to help explain your best thinking using words, numbers, or

pictures. Be prepared to share!






Students can work with a partner or in small groups to work on this task.

How many people asked for chicken? (1/5 of 10 is 2)

How many people asked for steak? (1/4 of 40 is 10)

How many asked for hot-dogs? (1/2 of 80 is 40)

Extension:

Students can find the percent of the guests who ordered each type of entrée.

Culminating Task This culminating task represents the level of depth, rigor and complexity expected of all fifth grade students to demonstrate

evidence of learning.





Unit Three Task: “YOU’RE INVITED TO A FABULOUS FRACTION PARTY”

You are planning a surprise party for your best friend. You plan on inviting 6 more people to come to the party.

There’s a lot to do in order to get everything ready in time. You have to find recipes for what you will be serving

– not just pizza and cokes either. Your friend likes special dishes. After that you need to rewrite the recipes for

the total number of people coming to the party. Then, you need to check the cupboards to see what you have and

make a grocery list of what you will need. Then, you have to go grocery shopping – you only have $50 to spend

on food. Finally, you need to create the invitations. There’s not much time left…only a week. You better get

busy!

INVITATION – Create a mosaic design for the party invitation. Each color “square” is worth a different value.

(red = ½, blue = ¼, yellow = 1/3, orange = 1/12) Write an algebraic expression to represent the value of each

color. The total value of the picture must be between 20 and 25 ½. Each color must be represented. Use grid

paper to record your design.

Party Planning Agenda

1. Food – find recipes for punch, trail mix, brownies, fruit salad, etc.

2. Rewrite recipes for 8 people.

3. Inventory cupboards to see what ingredients I have and what I still need.

4. Make a grocery list (with amounts of items needed)

5. Go grocery shopping (only $50 to spend)

6. Create the invitations





Suggestions for Classroom Use

While this task may serve as a summative assessment, it also may be used for teaching and learning. It is important that all

elements of the task be addressed throughout the learning process so that students understand what is expected of them.

Peer Review

Display for parent night

Place in portfolio

Photographs

Discussion, Suggestions and Possible Solutions

Discuss with students the total number of people attending the party. They should determine that it is 8 – you,

best friend, and 6 additional people. Students can use the recipes included or find their own. *NOTE – these

recipes have been modified so that the results would work with the usual measuring cups that are found in the

kitchen.

For the invitation, students should use paper squares or grid paper to create a picture. You can change the

fraction/color for the squares. But, be aware that you should use fractions that will not require denominators

larger than 12 when they find common denominators.

Algebraic expressions: Red (1/2 x or x/2); Blue (1/4 x or x/4); Yellow (1/3 x or x/3); Orange (1/12 x or x/12)

Supplemental materials to support this task are included below.





Recipes:

CHEX MIX PUPPY CHOW

9 cup Chex

1 cup chocolate chips

1/2 cup peanut butter

1/4 cup butter

1/4 teaspoon vanilla

1 1/2 cup powdered sugar

Put cereal in large bowl. Melt chocolate

chips, peanut butter, and butter. Remove

from heat and stir in vanilla.

Pour over Chex cereal, put into a large

plastic bag with powdered sugar and

shake well to coat.

Spread mixture evenly on wax paper and

allow to cool.

Yield: 12 servings

NO BAKE PEANUT BUTTER

BROWNIES

4 cups graham cracker crumbs

1 cup peanuts, chopped

½ cup powdered sugar

¼ cup peanut butter

2 cups semisweet chocolate chips

1 cup evaporated milk

1 teaspoon vanilla extract

Combine first 4 ingredients with a pastry

blender. In a small saucepan, melt the

chocolate chips with milk over low heat,

stirring constantly until smooth. Remove

from heat; add vanilla. Remove 1/2 cup and

set aside.

Pour remaining chocolate mixture over

crumb mixture and stir until well blended.

Spread evenly in a greased 9-inch square

baking pan. Frost with the reserved chocolate

mixture. Chill for about 1 hour.

Yield: 2 dozen





More Recipes:

FRUIT SALAD

2 cups watermelon balls

2 cups strawberries, halved

2 cups blueberries

3 medium bananas, sliced

2 cups sliced peaches

2 cups sparkling white grape juice

Combine the watermelon, strawberries and

blueberries in a glass bowl, cover and chill

until ready to serve.

To serve, add the sliced bananas and

peaches; pour the white grape juice over top.

Serve with a slotted spoon.

Yield: 6 servings

EASY FRUIT PUNCH

3 cans frozen fruit punch

9 cans of lemon-lime soda, chilled

Pour fruit punch into large container or punch

bowl. Slowly add each can of COLD soda.

Carefully stir after each addition of soda. (The

carbonization in the soda seems enhanced when

mixed with the cold punch. Chilling the soda

will help, but stir slowly or punch will fizz

over.)

Yield: 12 servings

http://www.cooksrecipes.com/salad/summer_fruit_compote_recipe.html








Rewrite the Recipes:





What’s in the cupboard?

Chocolate

Chips

2 cups

Peanut

Butter

1 cup

Evaporated

Milk

1 cup

Powdered

Sugar

2 cups

Chex

Cereal

12 cups

Peanuts

3 cups





My Grocery List





Shopping for Groceries:

Strawberries & Blueberries Bananas

2 pkgs for $4.00 $0.69/pound

(each pkg. contains 2 cups) about 3 bananas per lb.

– Buy 1 Get 1 Free Chocolate Chips Peaches

$3.19 each – 64 oz. bottle $2.89 – 12 oz. (1 ½ cups) 2 for $1.00 – 1 peach = ½ cup





Watermelon Vanilla Extract Graham Cracker Crumbs Butter

$4.99 each 8 oz. - $2.39 1 box (2 cups) - $2.79 $1.89 – 4 sticks

Powdered Sugar Lemon-lime Soft Drink Frozen Fruit Punch 16 oz. - $1.79 12 pack - $3.49 2 for $1.50





The Invitation:

Georgia Performance Standards Framework Mathematics Grade … · Georgia Performance Standards...

Documents

Transcript of Georgia Performance Standards Framework Mathematics Grade … · Georgia Performance Standards...