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Subject Matter:
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Mathematics
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Grade Levels:
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5-7
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Time Allotment:
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2-3 hours
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Overview
Adding and subtracting fractions with unlike denominators is a
major stumbling block for students, and it is made much more difficult
if students do not fully understand the concept of equivalent fractions.
Students often lack a sense of why they are doing what they are
doing, trying instead to memorize a series of steps that don't make
sense. Through a series of interactive activities on the Web set
up as computer stations, this lesson provides students with the
number sense of equivalent fractions. Knowledge is assessed at the
end when students are asked to show what they have learned about
equivalent fractions by creating their own game.
Learning Objectives
Students will be able to:
- Understand the concept of a fractional part of a whole.
- Understand how equivalent fractions show the same amount of
"stuff" in the whole, just divided into different numbers
of parts.
- Change fractions into useful equivalent fractions.
- Demonstrate their understanding of equivalent fractions in a
performance assessment.
Oregon Standards Available at:
http://www.ode.state.or.us/cifs
Mathematics - Calculations and Estimations
- Perform calculations on whole numbers, fractions, decimals and
integers using paper and pencil, calculators and/or computers.
- Demonstrate the relationships among whole number, decimal, fraction,
percent, exponent and integer operations (including relationships
involving ratio and proportion).
National Standards From the National Council of Teachers of Mathematics
(http://standards.nctm.org/)
In grades 5-8, the mathematics curriculum should include the study
of number systems and number theory so that students can:
- Understand and appreciate the need for numbers beyond the whole
numbers.
- Develop and use order relations for whole numbers, fractions,
decimals, integers and rational numbers.
- Extend their understanding of whole number operations to fractions,
decimals, integers and rational numbers.
Media Components
Video
Check the link at http://www.opb.org/edmedia/trs/
to find access to the video(s) from unitedstreaming™ referenced
in this lesson plan.
- "Mathica's Mathshop: Winter Warm-Up" (15:00)
- Clip: "Using Tanograms (02:41)
Web
Note: Some of these Web sites change games frequently, so
be sure to check the day of the lesson.
Materials
- A tangram set for every 2 students
- A pattern to make tangram sets (if you don't have access to
plastic ones and card stock or construction paper on which to
print the pattern)
- At least 7 computers that connect to the Internet - one for
each student would be ideal
- A computer that is connected to a projector or television on
which to show the video clip
- A copy of the Equivalent Fraction Stations Worksheet for each
student (at end of lesson plan)
- Signs to label computer stations (at end of lesson plan)
- Copies of the instructions for the games to put at each station
(at end of lesson plan)
Prep for Teachers
Photocopy the following items:
- A copy of the Equivalent Fraction Stations Worksheet for each
student
- Signs to label computer stations
- Copies of the instructions for the games to put at each station
Bookmark Web sites on computers that will be used for the stations.
Bookmark any tangram sites you want to show the students on your
projecting computer.
Familiarize yourself with the video clip. Cue the video
clip to the beginning.
Introductory Activity
Students will use tangrams to explore the concept of equivalent
fractions. Basic information on tangrams can be found on the Web
at http://www.tangrams.ca/,
as well as many other sites. If you don't have tangram puzzles in
your classroom, patterns to make tangrams are provided on that site
and others. (Card stock works well for creating tangrams, and construction
paper works okay. Regular photocopy paper is a little too flimsy.)
Step 1: Introduce tangrams to the students using the video
clip, "Using Tanograms" (02:41), from the video, "Mathica's
Mathshop: Winter Warm-Up" (15:00). Explain that the Mathmagician
is trying to help the Chinese Emperor find spring in his garden.
He uses tangrams to do this. Provide students with a Focus for
Media Interaction by asking them to notice the seven shapes
that make up a set of tangrams. Play the video clip from
the beginning and pause at approximately 00:31 when the Mathmagician
says, "… Cut the square into seven special pieces."
Pause and let students note the shapes they will find. Explain
that these seven shapes (2 large triangles, 1 medium triangle, 2
small triangles, 1 square and 1 parallelogram) always make up a
set of tangrams.
Step 2: Before continuing, provide students with a Focus
for Media Interaction by asking them to predict what the Mathmagician
will do for the Emperor to help him find his spring garden. Ask
them to whisper their prediction to a neighbor. Play the
clip until approximately 01:55 when the Mathmagician says, "…
The magic is in your hands and your imagination." Ask students
to reflect on their predictions.
Step 3: Give students a set of tangrams and ask them to
make a garden-oriented shape out of their tangrams and share with
neighbors. This will help students get the urge to play with the
tangrams out of their systems.
Step 4: Ask students what the tangram pieces could possibly
have to do with equivalent fractions. Using their tangram pieces
and a neighbor's, can students demonstrate some equivalent fractions?
Joanne Caniglia has written a lesson that incorporates fractions
into tangrams at http://explorer.scrtec.org/explorer/explorer-db/rsrc/813447516-81ED7D49.2.PDF,
and there is a PBS lesson that has the pieces of a tangram set related
to fractions at http://www.pbs.org/teachersource/mathline/concepts/asia/activity2.shtm.
This PBS lesson also has instructions for students to cut their
own tangrams out of a piece of paper by folding, rather than following
pre-printed lines. This would be appropriate for more capable students.
Step 5: Once students are familiar with the physical concept
of equivalent fractions, you can introduce the algorithm (multiply
or divide both parts of the fraction by the same number to get an
equivalent fraction). Then you are ready for the Fraction Stations
on the computer.
Learning Activities
You will need at least seven computers. Each computer will be set
up for one of the game stations listed in the following paragraphs.
If there are enough computers for each of your students, students
can play separately - or they can be divided into small groups to
accommodate the computers available. For simplicity, students/groups
will rotate through the seven games on different computers rather
than sitting at one computer and changing to a new game on that
computer. This also ensures that students will spend equal time
with each game, not continually play the one they find easiest or
most diverting. It also ensures that Web sites will not be overloaded
as all students try to access the same ones.
Step 1: Divide the available time into seven periods and
have students rotate in a specific direction through the game stations.
At each station, provide students with a Focus for Media Interaction
by placing a goal for that station on a strip of paper on the top
of the computer screen (these focus questions/statements are included
below and at the end of the lesson plan). Alternatively, these focus
questions/statements can be printed out on a student worksheet.
Print out a summary of the game and rules for each station.
- Station 1: One of the Cyberkids characters challenges
students to find 13 ways to shade one-half of a square.
http://pbskids.org/cyberchase/games/fractions/../index.html
- Focus for Media Interaction: Write a sentence that
describes how you found all 13 ways to shade in one-half of
the square.
- Station 2: Learning Planet game in which students can
click on equivalent fractions to beat the clock. Each level gives
students more fractions for which to find equivalents in the same
amount of time.
http://www.learningplanet.com/sam/ff/index.asp
- Focus for Media Interaction: Play the first game
and then write a strategy that can help you succeed at higher
levels.
- Station 3: The Fresh-Baked Fraction Game: students click
on the one fraction out of four that is not equivalent to the
others.
http://www.funbrain.com/fract/../index.html
- Focus for Media Interaction: Write your strategy
for finding the fraction that is not equivalent.
- Station 4: Cool Math 4 Kids is a site that provides colorful
explanations of math topics. This is less a game site and more
a chance for students to articulate what they know. In "Equivalent
Fractions Part 1," this site describes how to visualize and
calculate equivalent fractions. It also provides two chances for
students to do it themselves (with expanded games promised for
the future). http://www.coolmath4kids.com/lessons/fractions4.html
- Focus for Media Interaction: Choose one set of equivalent
fractions on the "Try It" page. Write an explanation
of why the two fractions are equivalent. Go back to the lesson
if you need help explaining it.
- Station 5: This site provides a match-the-fraction game
in which students identify equivalent fractions.
http://www.quia.com/mc/351.html
- Focus for Media Interaction: If you were going to
play with a partner, write down your strategy for winning
with the most matches.
- Station 6: Students translate line graph representations
of fractions into equivalent fractions.
http://www.visualfractions.com/EnterFraction.html
- Focus for Media Interaction: Keep a running tally
of how many you get right on the first try compared to those
that take more than one try. When you are done, turn these
tallies into a fraction by placing the number you got right
over the number you missed.
- Station 7: Melvin's Make a Match asks students to pair
potion bottles labeled by equivalent fractions.
http://pbskids.org/cyberchase/games/equivalentfractions/equivalentfractions.html
- Focus for Media Interaction: Which potion bottles
seem easiest to match? Why?
Culminating Activity
Students will demonstrate an understanding of equivalent fractions
by designing a game of their own, either individually or in groups,
that involves equivalent fractions. Students will exchange games
with other students/groups and play them in the classroom.
Games could include matching equivalent fractions in a number of
ways:
- Students could move around the board by drawing a card and moving
to the space that has an equivalent fraction.
- Students could roll two dice and create a fraction, then move
to an equivalent fraction.
- The matching game could be a bingo format.
- The game could involve timed sessions and the most matches in
a given time wins.
Urge students to come up with ideas for game boards that are not
copies of commercial games. Games related to other curricular areas
could be encouraged - for instance, an Egyptian theme if students
are studying Egypt in social studies.
Ground Rules for the Games:
- The game must involve players making equivalent fractions or
matching equivalent fractions.
- The game must have clearly written rules so other students will
know how to play. The rules should clearly tell players how to
start, continue play and win.
- The game must be ready to play by the due date, with all pieces,
boards and game cards written out.
- Players must be provided with a way to check their answers to
see if they are correct.
Set aside a day in class to play the games.
Cross-Curricular Extensions
Cooking
Reading
- Read Grandfather Tang's story and use the tangrams to create
the shapes of the animals in the story.
Social Studies
- Tangrams have connections to Japan and China. Search on the
Web for "tangram" and you will find many sites and activities.
Community Connections
- Students in middle school could take their equivalent fraction
games to a fourth- or fifth-grade class for a game day. They could
also share what they have learned about the computer games.
- You can invite a person to your class whose job involves working
with fractions. For instance:
- An independent bakery or restaurant planner can share how
they take a favorite dish and scale it up to serve to customers.
- An architect can share how they keep scales in mind when
building. Working with scales is working with equivalent fractions.
Summary of Rules for Game Stations
Print out these rules and place a copy at each game station. Game
7 (Fraction Man) is enhanced by sound, but not impossible without
it.
Station 1
Cyberkids fraction game: 13 ways to make one-half:
http://pbskids.org/cyberchase/games/fractions/../index.html
The first four screens explain about fractional parts of a square
that can make 1/2 of the square shaded. Click the arrow on the right
side of the screen to continue on to the next page.
The fourth screen is particularly important to pay attention to
because it tells you that the same shaded pattern flipped or rotated
does not count as a new pattern.
On the fifth screen, click "Play Game."
The Game
Click on the triangles in the big square. When you think you have
a new pattern for shading 1/2 of the square, click on the "Test
for 1/2" button. The correct ones are recorded across the top.
Station 2
Learning Planet game: http://www.learningplanet.com/sam/ff/index.asp
In this game, you will try to find equivalent fractions and beat
the clock. The levels go up automatically as you answer correctly.
A group of fractions will be displayed on the screen. You must
match equivalent fractions.
First click one of the fractions. Next click the equivalent fraction.
Continue until all fractions have been matched. The game is over
if you allow time to run out.
Station 3
Fresh-Baked Fraction Game - equivalent fractions:
http://www.funbrain.com/fract/../index.html
The word on the street is that Fraction Jackson is a dog who loves
pie (pi?). If you answer 24 problems correctly, you can put your
name on Jackson's list of Master Pie Bakers.
How to Play
- You are shown four fractions.
- Three of the fractions are equivalent. They can all be simplified
to the same fraction.
- Click on the fraction that is not equal to the others.
- If you get the answer correct, Jackson gets another piece of
pie.
Equivalent fractions are different fractions that name the same
amount. For example, these are all equivalent fractions:
Choose a level of difficulty by clicking on the words
"Easy," "Medium," "Hard" or "Super
Brain." The game will start after you click on your level.
Station 4
"Equivalent Fractions Part 1" from Cool Math 4 Kids:
http://www.coolmath4kids.com/lessons/fractions4.html
The first screen shows you how equivalent fractions work. On the
left side of the screen, a green triangle says "Try It."
Click on that green triangle.
You will see a picture of two equivalent fractions. Answer in your
head or tell a partner your answer. Roll the mouse over the rectangle
to see if you were right.
Station 5
A match-the-fraction game:
http://www.quia.com/mc/351.html
Click on a fraction and then click on the equivalent fraction.
If you get it right, stars will appear. When all of the fractions
are matched up, you get a star and can start a new game.
Station 6
Use the line graphs to figure out the equivalent fraction:
http://www.visualfractions.com/EnterFraction.html
This game will ask you to identify the numerator and denominator
that are represented in the line graph. Once you have entered your
answer, click “OK.” If you missed it the first time, use
the hints to keep trying until you get it right. If you are completely
stumped, click “Explain” to get some helpful hints. Once
you've correctly identified the equivalent fraction, click “New
Example” for another problem.
Station 7
Melvin’s Make a Match asks students to pair potion bottles
labeled by equivalent fractions:
http://pbskids.org/cyberchase/games/equivalentfractions/equivalentfractions.html
Melvin will show you a growing number of potion bottles to be placed
in pairs according to their fraction labels. Select two bottles
that are labeled with equivalent fractions. If you pair all of the
potion bottles, it will move on to a more challenging game.
Name: ___________________
Equivalent Fraction Stations
Start at the station to which you have been assigned and work your
way numerically through the stations. Follow the directions provided
at each station and complete each section of this worksheet.
Station 1
Write a sentence that describes how you found all 13 ways to shade
in one-half of the square.
Station 2
Play the first game and then write a strategy that can help you
achieve at higher levels.
Station 3
Write your strategy for finding the fraction that is not equivalent.
Station 4
Choose one set of equivalent fractions on the "Try It"
page. Write an explanation of why the two fractions are equivalent.
Go back to the lesson if you need help explaining it.
Station 5
If you were going to play with a partner, write down your strategy
for winning with the most matches.
Station 6
Keep a running tally of how many you get right on the first try
compared to those that take more than one try. When you are done,
turn these tallies into a fraction by placing the number you got
right over the number you missed.
Station 7
Which potion bottles seem easiest to match? Why?
Computer Station Labels
These labels are identical to what is on the Equivalent Fraction
Stations Student Worksheet and may be used instead of the worksheet
or in addition to it.
Station 1
Write a sentence that describes how you found all 13 ways to shade
in one-half of the square.
Station 2
Play the first game and then write a strategy that can help you
achieve at higher levels.
Station 3
Write your strategy for finding the fraction that is not equivalent.
Station 4
Choose one set of equivalent fractions on the "Try It"
page. Write an explanation of why the two fractions are equivalent.
Go back to the lesson if you need help explaining it.
Station 5
If you were going to play with a partner, write down your strategy
for winning with the most matches.
Station 6
Keep a running tally of how many you get right on the first try
compared to those that take more than one try. When you are done,
turn these tallies into a fraction by placing the number you got
right over the number you missed.
Station 7
Which potion bottles seem easiest to match? Why?
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