Summary
Students will use sports to learn about fractions, decimals and percents.
Materials
Attachments
Websites
- Major League Baseball
Students can get access to batting averages of professional players, click on "stats" (with parent permission).
- Mathletics
When your class has access to computers, have them visit the
following site. It allows them to compute batting averages online, as
well as many other sports-math connections.
For each group:
For each student:
Background for Teachers
This activity should be used after Coin
Conversions,
or after an introduction to the concept that parts of a whole can be
represented as decimals, fractions, and percents. This lesson uses real
basketballs and hoops, but can easily be adapted for use inside the
classroom using small balls and garbage cans. Make sure when you are
doing the paper/garbage can demo, that the can is close enough to you
that you can "rig" the number of shots made. This example should be
very simple so that all students are successful, and don't get scared right
away with more difficult problems.
Intended Learning Outcomes
1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
3. Reason mathematically.
5. Make mathematical connections.
Instructional Procedures
Invitation to Learn
Have students brainstorm names of sports and athletes they enjoy
playing or watching. Share their results in small groups. Hopefully, all
students will be able to list at least one. After the discussion, tell them
they will be learning how math is used in sports.
Instructional Procedures
- Say the following to
students:
- "How many of you consider yourself a true sports fan?"
- "Does anyone
keep track of a favorite athlete's stats?"
- "The word "stats" is short
for statistics, which are used in
sports to keep track, mathematically, of how well athletes
are playing."
- "Today we are all going to be athletes and we are going
to
record some stats for ourselves and our classmates. Before
we can do that, we need to learn some skills we'll need to
keep accurate stats."
- "Let's start with something easy. I am going to
toss some
paper into the garbage can. I need one volunteer to crumple
up these ten sheets of paper, and another volunteer to tally on
the board all the shots I make." Make 5 out of the 10 shots,
with students counting aloud and someone tallying on the
board.
- "How many total shots did I take?"
- "How many were successful shots?"
- "Please represent my shots as a
fraction in your math journal."
- "Good, 5/10 is correct. Did anyone write
this fraction in
simplest form?"
- "Who can think of a way to represent my number of shots
as a
decimal?"
- "And as a percent?"
- Discuss, and make sure all students know the
correct answers.
"That was pretty simple. It seems we're all pretty familiar with
the fact that 1/2 = .50 = 50%. But sometimes athletes' stats get a
little more complicated and can't be so easily computed
mentally."
- "I'm going to show you how to take any fraction, no matter
how difficult it looks, and represent it as a decimal and a
percent."
- Demonstrate how to convert a fraction to a decimal, reminding
students that the fraction bar is really just a division symbol. If
they remember that, the fraction tells them what to do. Review
the division process, and how a decimal must be placed if the
divisor is larger than the dividend. Point out that the answer can
be rounded, or can be represented with a repeat bar. In baseball,
batting averages are always represented as decimals rounded to
the nearest thousandths place.
- Write on the board some common decimals/percent
equivalencies
such as .25 = 25%, and .50 = 50%. Ask students if they see a
pattern, or if they can explain the difference. They should reply
with such answers as, "One has a decimal and one has a percent
sign," or, "The decimal disappears when it becomes a percent." Remind students
that all whole numbers could have a decimal
after them, but we don't usually write it if there are no digits after
the decimal. So actually, 25% could be written as 25.0%.
- Say to the class:
- "When we change from a decimal to a percent, we actually
multiply the decimal by a number, and that gives us our
percent. What kind of number do you think we could
multiply by and keep the digits the same, but scoot the
decimal over two places to the right?" Let the kids explore,
then explain the reason we multiply by one hundred is
because a percent is a portion of one hundred. Do several
exercises together as a class.
- Give directions for the basketball activity.
Each group will
receive one set of number
cards, a Sports Math worksheet for
each student, and one basketball. Each student selects a card--
the number on the card tells them how many shots they get to try.
Each student must tally the shots of every other student in his/her group.
The scores must be represented as fractions, decimals, and
percents. When everyone has made their shots (outside or in the
gym), they return to class to complete their calculations and the
rest of the problems. After students have had a chance to complete
the worksheet, discuss the results as a class. Let students explain
whether or not they think the total number of shots attempted
matters to an athlete. Did the student who got four tries have as
good of a chance as the student who got six tries?
Extensions
- During physical education,
assign different students to keep stats
for players in the games. This can be done with almost any sport.
Rotate the students so they all get a chance to keep stats.
- This is a great
opportunity to discuss appropriate calculator usage.
After students have had lots of practice converting manually,
allow them to compute stats with a calculator. This will act as a
fun extension for quick learners, and as a helpful tool for
struggling learners.
Family Connections
- Encourage students to have
a family basketball game, with the
student keeping stats for each player. Afterward, the student can
present a homemade trophy to the player with the best percentage
of shots.
- If someone in a student's family collects baseball cards, the
student can compare batting averages of each player, and convert
them to percents.
Assessment Plan
- Take notes during the basketball activity. Which students
appear
confident in their ability to record their shots as fractions? Are
students displaying a positive attitude toward the assignment?
- The Sports
Math worksheet should be completed with accuracy.
The questions at the end assess a student's understanding of not
just how to convert, but the concept of how percentages work.
Bibliography
Research Basis
Irwin, K.C. (2001). Using Everyday Knowledge of Decimals to Enhance Understanding.
Journal for Research in Mathematics Education, 32(4), 399-420.
"Half the pairs worked on problems presented in familiar contexts
and half worked on problems presented without context." This article
presents results of an investigation that showed students who were
presented decimal problems in a familiar context succeeded more often
than students who were given no context.
Verschaffel, L. & De Corte, E.
(1997). Teaching Realistic Mathematics Modeling in the
Elementary School: A Teaching Experiment With Fifth Graders. Journal
for Research in Mathematics Education, 28(5), 577--601.
"Recent research has convincingly documented elementary school
childrens' tendency to neglect real-world knowledge and realistic
considerations during mathematical modeling …" This article suggests
that using real-world modeling can help students have a better disposition
toward mathematical concepts.
Created: 01/27/2006
Updated: 02/05/2018
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