Summary
This activity uses money as a way to introduce the relationship between fractions, decimals and percents.
Materials
For each student:
Background for Teachers
This activity uses money as a way to introduce the relationship
between fractions, decimals, and percents. Most students have a good
understanding of money by fifth grade, even if their reading, language,
and/or math skills are not at grade level. This lesson works well with
photocopies of coins, but if you have access to plastic coins the lesson
would be even more lifelike. Students should already have an
understanding of fractions as a way to represent parts of a whole, and of
how to simplify fractions. They should also be familiar with the concept
of decimals and how to read them.
This lesson uses math journals, assuming that each student has been
using one throughout the year. A math journal is a great way for students
to record their thoughts about math lessons, new discoveries, example
problems, and math definitions. Any type of notebook works well. If
you do not use math journals, students can write the results on a piece of
paper.
Intended Learning Outcomes
1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections.
Instructional Procedures
Invitation to Learn
Distribute a Coin Combinations worksheet and one set of coin
manipulatives to each student. (Students may also work in small groups.)
Ask students to find as many combinations of coins as they can to make
50¢ using pennies, nickels, dimes, and/or quarters. Students use the
manipulatives and record each combination on the sheet.
Instructional Procedures
- Say the following to
students:
- Using your manipulatives, show me the way to make 50¢
using only two coins.
- What two coins did you use?
- Record in your journal the way this
amount of money
would look on a price tag in a store.
- Good. Money is usually written
using decimals. On
which side of the decimal would you find the whole dollar
amount? On which side of the decimal would you find the
coin amount? Today we will be working with digits to the
right of the decimal, or the money that is not enough to
make a whole dollar.
- I see everyone has two quarters out. How many
quarters
would it take to make a whole dollar? (4) And how many
quarters are we using right now? (2) Can anyone tell me
what fraction of a dollar were using? Record that fraction
right next to your previous answer in your journal. What is
that fraction in simplest form?
- Write the percent symbol (%) on the
board and say, Raise
your hand if youve seen this symbol before. If you know the
name of it, please write that name in your journal. (pause) If
you wrote percent, you are correct. If you didnt, please
write this word now. Look at the word and underline a hidden
four-letter word that starts with c. What is that word?
Wow, weve just been working with cents! How many cents
does it take to make one whole dollar? One way to write the
percent of a number is to write how many cents you have.
Then we write this percent symbol (%) after the number.
Please try to write as a percent the amount of money you have
with your two quarters.
- Youve just written 50¢ as a decimal, fraction,
and percent.
Did the amount of money we used change? Can anyone make
a mathematical statement about your decimal, fraction, and
percent? (They are all equal.) Write that statement in your
journals. We can represent parts of a whole as a decimal,
fraction, percent, or all three!
- Repeat the steps above asking students
to make certain amounts
using a different coin each time (e.g., 25¢ cents using quarters =
.25, 1/4, and 25%. 10¢ using dimes = .10, 1/10, and 10%, etc.).
- Try having
students make the same amount using different coins
and discussing why the decimal and percent look the same, but
the fraction looks different until you simplify (e.g., 80¢ using
pennies = .80, 80/100, and 80%, while the same amount using
dimes = .80, 8/10, and 80%).
- When students are comfortable with this concept,
allow them to
try the Coin Conversions and Price Problem worksheets.
Most students should be able to work independently, allowing you time
to work with those who may still be struggling.
Extensions
- For students who have difficulty
with the Price Problem worksheet, you can have students act it out
for the class. Students can make signs advertising each sale, and use their
play money to actually make purchases. This may help all students understand
that the same amount was spent at each store.
- Allow students who were able
to solve the challenge question on
Coin Conversions to present their reasoning to small groups of
students who were unable to find the solution.
- This type of activity could
be used with other money systems,
connecting with the fifth grade social studies curriculum.
Specifically, the money system used in colonial times,
representing farthings, pounds, etc. as fractions, decimals, and
percents.
Family Connections
- Gather spare change from around
the house. Have family
members sit around the coins. One person selects some coins. (It
is easiest to select only one type of coins, but can be done using a
variety.) Have a race to see which family member can write the
selected amount as a decimal, fraction, and percent first.
- Go shopping with
your family. Watch for signs that advertise
sales. Does the sign show the discount in decimal, fraction, or
percent form? What would the discount be in the other two
forms?
Assessment Plan
- Keep mental notes during the initial lesson. Which
students are
not willingly participating in discussion? Which students seem
reluctant to write in their journals? Which students were already
familiar with the percent symbol? Record these notes
immediately following the lesson.
- Journals can be collected and reviewed
periodically. They should
not be tied to a grade, as they are meant to be a means for
students to practice and explore. However, a journal is a great
assessment tool in which a teacher can observe a students
understanding of mathematical concepts.
- Coin Conversions is an assessment
of a students ability to
independently convert common money-related decimals to
fractions and percents.
- Price Problem is an assessment of a students ability
to apply
what s/he learned about equivalent representations, along with
problem-solving skills, to obtain a reasonable solution.
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), 577601.
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.