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Georgia Performance Standards Framework
Mathematics – Grade Five
Page 1 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.
Georgia Performance Standards Framework
Mathematics – Grade Five
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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).
Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
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Mathematics – Grade Five
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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.
Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
Georgia Performance Standards Framework
Mathematics – Grade Five
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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
Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
The Sieve of Eratosthenes
The Sieve of Eratosthenes
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.
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Georgia Performance Standards Framework
Mathematics – Grade Five
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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
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Mathematics – Grade Five
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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.
Exploring the Sieve of Eratosthenes
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Mathematics – Grade Five
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Exploring the Sieve of Eratosthenes
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.
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Georgia Performance Standards Framework
Mathematics – Grade Five
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Discussion, Suggestions, Possible Solutions
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
Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
All of my digits are different.
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.
The sum of my digits is 17.
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.
The sum of my digits is 14.
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.
The sum of my digits is 12.
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.
The sum of my digits is 8.
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.
All of my digits are different.
The sum of my digits is 14.
What number am I?
Challenge: Create two riddles of your own. Include the answer to your riddle.
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Mathematics – Grade Five
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Discussion, Suggestions, Possible Solutions
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.
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Mathematics – Grade Five
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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.
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Dividend
Divisor
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Mathematics – Grade Five
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Discussion, Suggestions, Possible Solutions
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.
Fraction and Decimal Line Up
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Mathematics – Grade Five
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Fraction and Decimal Line Up
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?
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Discussion, Suggestions, Possible Solutions
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.
Georgia Performance Standards Framework
Mathematics – Grade Five
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Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
Georgia Performance Standards Framework
Mathematics – Grade Five
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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.
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Mathematics – Grade Five
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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.
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Discussion, Suggestions, Possible Solutions
Materials: pattern blocks, paper, markers/crayons/colored pencils
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Mathematics – Grade Five
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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
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Mathematics – Grade Five
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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.
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Discussion, Suggestions, Possible Solutions
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:
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Mathematics – Grade Five
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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.
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Mathematics – Grade Five
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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.
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Mathematics – Grade Five
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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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 27 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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!
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 28 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
Discussion, Suggestions, Possible Solutions
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.
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 29 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 30 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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.
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 31 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 32 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 33 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
Rewrite the Recipes:
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 34 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 35 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
My Grocery List
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 36 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 37 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
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
Georgia Performance Standards Framework
Mathematics – Grade Five
Page 38 of 38 Unit 3 Organizer Unit 3 Organizer
May 8, 2007 FUNKY FRACTIONS
The Invitation: