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Exploring Fraction
(Fraction Fridays)
For grades 6 – 8
Erin Richgels
North Pole High School
[email protected]
Tom Liapis
Blackduck Public School
[email protected]
These ten activities are meant to be done on Fridays in the fall or spring depending on the
grade level. Some activities may take more than one Friday. This project is meant to
have students develop a connection between equivalent fractions and ratios. We will meet
this goal by doing activities that involve, computers, manipulatives, graphing, and
collecting data.
We will be addressing the following Number and Operation standards.
• 1st Friday 6.1.1.4
• 2nd Friday 6.1.1.4
• 3rd Friday 6.1.1.7
• 4th Friday 6.1.1.4 and 6.1.1.7
• 5th Friday 6.1.2.1
• 6th Friday 6.1.2.2 and 6.1.2.3
• 7th Friday 6.1.2.4
• 8th Friday 6.1.2.1 and 6.1.2.2
• 9th Friday 6.1.2.1 and 6.1.2.2
• 10th Friday 6.1.2.2
Table of Contents
• 1st Friday Fraction Circles ………………………………………………....3
• 2nd Friday Fraction Symbols……………………………………………...17
• 3rd Friday Mixed Numbers and Improper Fractions……………………..23
• 4th Friday Mixed Numbers and Improper Fractions on the computer……30
• 5th Friday Introduction of Ratios…………………………………………34
• 6th Friday Comparing Ratios……………………………………………..35
• 7th Friday Area and Ratios………………………………………………..37
• 8th Friday M&M Project………………………………………………….41
• 9th Friday More M&M’s………………………………………………….44
• 10th Friday Graphing M&M’s on your computer………………………...46
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1st Friday
Standard: Number and operation standard 6.1.1.4. Determining the equivalence among
fractions
Materials Needed: Fraction circles
Launch: How would you divide a candy bar between two people, between four people?
When you look at the pieces what are you hoping for, how would you make it fair?
Would dividing a pizza be different than dividing a candy bar? How would you cut a
pizza to make it fair?
Explore: Cutting out fractions circles. Have each student write down 10 observations
while playing with their fraction circles. Can you use brown pieces to cover a yellow,
what about blue? What colors do cover yellow? What colors don’t cover yellow?
Share: Have each student share one interesting thing they observed on the board, then
discuss.
Summary: Have students gain a general knowledge about equivalent fractions. You
fractions are equivalent when you can cover it entirely without any extra hanging over the
edge.
Fraction circle material can be found at:
http://www.education.umn.edu/rationalnumberproject/rnp1.html
Under fraction circle master – blank or filled with color.
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2nd Friday
Standard: Number and operation standard 6.1.1.4 Determining equivalence among
fractions.
Materials: Fraction circles, and a copy of lesson five can be found at the web site
http://www.education.umn.edu/rationalnumberproject/rnp1/lev1les05.pdf
Launch:
Explore: Lesson five of the rational number project. We recommend that the lesson be
done in groups to facilitate more discussion.
Due to the length of the activity you may want to only do part of the activity or plan on
more than one Friday.
We recommend that you do pages 51-54, you may want to look at page 58 the lesson
reflection.
Share: Discuss any of the pages that students thought were easy, challenging, and try to
focus on different ways of thinking about the fractions in terms of what is equivalent to
one whole.
Summarize: Your unit doesn’t always have to be one whole, it can sometimes be half of
a whole. Three fourths is still three fourths but they may not cover the same area if the
size of the unit is not the same. Teachers may want to take the time to fill out the post
lesson reflection to help you in the future.
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3rd Friday
Standard: Number and Operation standard 6.1.1.7. Convert between equivalent
representations of positive rational numbers.
Launch:
Explore: Lesson 17 of the rational project. We recommend that this lesson be done in
groups. Lesson 17 can be found at the following web site. We will save pages 138 and
139 for next Friday.
http://www.education.umn.edu/rationalnumberproject/rnp1/lev1les17.pdf
Share: What did students find true about fractions that were bigger that one whole? What
is bigger 3 ½ or 7/2? How can you tell? Is there more than one way of writing fractions
bigger than one whole?
Summarize: You should be able to recognize that there is more than one way to write a
number that represents something bigger than one. 3 ½ is the same as 7/2. One is given
the name improper fraction one is given the name mixed number. Teachers may want to
take the time to fill out the post lesson reflection to help you in the future.
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4th Friday
Standard: Number and operations standards, 6.1.1.4, and Determining equivalents
between fractions decimals and percents. 6.1.1.7 Converting between equivalent
representations of positive numbers.
Materials: Pages 138 and 139 from lesson 17 of the rational numbers project. Follow the
link
http://www.education.umn.edu/rationalnumberproject/rnp1/lev1les17.pdf
We will also be using computers for this lesson. Use the Illumination web site (fraction
model II)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=44
Launch: From last week who remembers one way to write a fraction bigger than one
whole? Can someone write this fraction in a different way? Do they represent the same
amount? Does anyone remember the two fraction names for what’s on the board?
Explore: Students will use the illumination web site to model fraction by changing the
numerator and denominator based on worksheets 138 and 139 from lesson 17 of the
rational number project. Have students make note of interesting patterns.
Share: Have one student share their results using a computer projector. Does anyone
have anything different? Is there more than one way of showing the same fraction? What
did they noticed when they adjusted the numerator and denominator on the slide bar of
the computer screen? Did you find any equivalent mixed numbers when you moved the
denominator bar?
Summarize: You should have created equivalent mixed numbers 2 ¼ is equal to 2 2/8.
The amount shaded in both mixed numbers is equal. If they didn’t see look at a few more
examples. Teachers may want to take the time to fill out the post lesson reflection to help
you in the future.
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5th Friday
Standards: Number and Operation standard 61.2.1. Identify and use ratios to compare
quantities.
Materials: Bring in a newspaper ad involving ratios. Ex. 2 cans of soup for $0.88 or any
other ratio example.
Launch: Show the newspaper ad, discuss how 4 cans of soup would be or 8 cans and so
on. Have students come up with a list of ratios from the real world.
Explore: Give each group a section of the newspaper. Have students find their own
ratios, have students prove it’s a ratio. Have student take their favorites ratio and make a
list of terms of their ratio. Have students come up with a list of observations about the list
of ratios. Begin a discussion on how the ratios are in proportion.
Share: Have students share their observations. What conclusion can be made based on
their observations. This is an example of a list of ratio terms 2/88 = 4/176 = 6/264 …
Students my notice the following:
• All the numbers are even
• The top number goes up by two the bottom number goes up by 88
• When you cross multiply (2*176 = 4*88) they are equal
• All the ratios can be simplified to the same fraction 1/44
• All the ratios are equal
• The ratios are written like fractions, fractions are written like ratios
Summarize: You should notice that all the ratios are the same. You can show that no
matter how many cans of soup you buy they are all proportionate to 1/44 or 2/88. No
matter what your ratio is when you make a list of terms they will be equivalent.
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6th Friday
Standards: Number and Operation standard 6.1.2.2. Apply the relationship between
ratios, and equivalent fractions. And 6.1.2.3 determining the rates for quantities with
different units.
Materials: Scott Foresman Addison Wesley Mathematics Grade 6 Enrichment Masters
Workbook. P. 69
Launch: What are some equivalent ratios to 2/88? How do you know they are
equivalent? What were some of the observations we listed last week? What areas of life
do ratios appear in?
Explore: Have each student complete the Circling proportions work sheet. These
questions may want to be asked. If ratios are not equal why aren’t they? Can you make
them equal?
Share: How could you tell if ratios were equal or not? If they were not equal were you
able understand why or change them so they were.
Summarize: Activity was meant to further the understanding of equivalent ratios and
fractions. Students should notice they were equivalent or not equivalent by;
• using a ratio series (from last Friday)
• cross multiplying
• finding equivalent denominator
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7th Friday
Standard: Number and operation standard 6.1.2.4. use reasoning about multiplication
and division to solve ratio problems.
Materials: Curriculum and Evaluation Standards for School Mathematics Addenda
series grades 5-8 Understanding rational numbers and operations pages 72 and 73 also a
separate piece of graph paper.
Launch: As you look at the shapes on page 72 what do you notice about the figures. Are
their any similarities, differences? What could you do to rectangle B to make it look like
rectangle A? What have we done in the last couple of Fridays to compare a small number
to a big number?
Explore: Have groups work on pages 72 and 73. For questions 6 and 7 have groups use
the extra sheet of graph paper to explore possible answers.
Share: Discuss the data that they collected on the rectangles. What kinds of drawings did
each group come up with for questions 6 and 7?
Summarize: You should have seen a connection between rectangle B and rectangle A.
You can multiply rectangle B by 4 to get rectangle A, or divide rectangle A by 4 to get
rectangle A. The same concept works for all of the rectangles. Given the ratio of the
lengths of a rectangle student should be able to develop a ratio of areas of a rectangle.
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8th Friday
Standard: Number and operation standard 6.1.2.1 Identify and use ratios to compare
quantities, and 6.1.2.2 apply the relationship between ratios.
Materials: Curriculum and Evaluation Standards for School Mathematics Addenda
series grades 5-8 Understanding rational numbers and operations pages 54 and 55. A
small bag of M&M’s for each student or pair of students will be needed.
Launch: Who likes M&M’s? What is your favorite color? How many M&M’s are in a
bag? How many of the M&M’s are your favorite color, why do you think that?
Explore: Have students do questions 1-5 before they open their bag of M&M’s. The rest
of page 54 and 55 will be done once the students have opened their M&M’s. Once the
students have counted their M&M’s they may eat them. Note: you may want to break up
this activity into two Fridays.
Share: Discuss their results and estimation to see how accurate they are? Did anyone
guess exactly right? How did you come up with your guesses for colors? What did you
really find out? Is one color more likely to occur? What fraction of your bag is your
favorite color? What other ratios did you find? Did anyone get the same ratios?
Summarize: This activity is meant to bring ratios into real world situations. It’s not just
something found in math. M&M’s get kids excited and forget the fact that they are doing
math.
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9th Friday
Standard: Number and operation standard 6.1.2.1 Identify and use ratios to compare
quantities. 6.1.2.2 Apply the relationship between ratios.
Materials: Curriculum and Evaluation Standards for School Mathematics Addenda
series grades 5-8 Understanding rational numbers and operations pages 56 and one big
bag of M&M’s.
Launch: Review the different ways of expressing rational numbers. Review last weeks
M&M activity. What would happen if we dumped everyone bag into a bowl would the
ratios of colors to total in the bowl be the same as the ratio of colors to total in your
individual bag?
Explore: Get into small groups of 3 or 4 and collect data on your group record sheet.
Share: Discuss group findings. How did your individual ratios and proportions compare
to the groups ratios and proportions? Have students guess the total number of M&M’s
and the total number of each color in a big bag. The group that is closest will win the big
bag of M&M’s.
Summarize: Students will be able to draw connections between their ratios the group
ratios to predict the ratios in the big bag. As data varies you may not see a strong
connection between the ratios. You may want to discuss how the ratios vary.
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10th Friday
Standard: Numbers and Operations standard 6.1.2.2 relationship between ratios
decimals and percents.
Materials: Computer and M&M activity data sheets. Illumination web site at the
following link
http://illuminations.nctm.org/ActivityDetail.aspx?ID=60
Objective: Student should be able to start to see connections to ratios and fraction to
decimals and percents by creating their own graphs of their M&M data.
Launch: Show students how the illuminations web site works by using sample data from
the M&M’s activity.
Explore: Students use their individual data from the M&M activity data to make a circle
graph (from page 54).What do they notice about the estimated data graph versus their
actual data graph? Do the value and the percents change? Have students make notes of
their observations.
Share: Have students share their observations, looking for understanding of why their
graphs were different. What caused the differences?
Summarize: The students should notice that there is equivalence to their graph, the
fraction, the decimal and the percent that it generates. 20/100 = 20% = .2 = 1/5
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