Relating Fractions, Decimals, and Percents Activity
Objective: Reinforce equivalent fractions as part of a set
Relate common fractions, decimals and percents
Materials:
Transparency of large 10 x 10 grid and 1 copy per student
50 transparent overhead counters
Transparency of Student Grid Sheet and 1 copy per student (copied on front and back
for plenty of practice)
50-100 counters per student
1. Ask the following questions and have students discuss each: “Can someone tell me what you
think one hundred percent means?” “What does a coach mean when he says he wants you to
give one hundred and ten percent?” “If I have a two percent chance of winning the raffle at our
school fair, what do you think about my chances? “Can anyone explain what the word percent
means?
Inform students that the word percent is derived from the Latin per centum, which means “per
hundred” or “out of one hundred.”
2. Continue the discussion by posing several problems:
 If there were 100 problems on a test, what would a score of 100% mean?
 If there were only 20 problems on a test, not 100, how many would you have to
answer correctly to get a score of 100%?
 If you only answered 10 problems out of 20 correctly, what would your score be?
3. Discuss that 20 out of 20 questions is the same as 100 out of 100, and that 10 out of 20 is the
same as 50 out of 100. Write on the board:
 100 out of 100 = 100%
 20 out of 20 = 100%
 50 out of 100 = 50%
 10 out of 20 = 50%
4. Ask, “How do you think percents are related to decimals? To fractions? What percent of the whole
is one-tenth? What percent of the whole is twenty-five hundredths?” Write on the board:
 0.1 is 10% of one whole
 0.25 is 25% of one whole
5. Distribute grids and counters to students. Select a common fraction, such as 1/4. Throughout the
activity, choose fractions where the denominator is divisible by 100. For example: ¾, 1/10, 7/10,
1/5, ½
6. Place beans (or counters, etc) in the squares to match the fraction. For example, if the fraction is
1/4, that represents 1 out of 4. You place one counter in every fourth square. As the teacher is
modeling on the overhead, students should be manipulating with counters on large 10 x 10 grid
sheet at their desks. You are building equivalent fractions.
7. Have students tell you equivalent fractions as you fill the squares and record the equivalent
fractions, 2 squares out of 8 total have counters, 3 squares out of 12 total. Repeat until you count
all 100 squares. There are 25 squares out of 100 total with counters.
8. You and the students shade in the grid (Student Grid Sheet) to match the pattern as built on the
large 10 x 10 grid. (See example on the next page) Once you and the students have completed
shading the grid, you may rearrange the counters on your large 10 x 10 so that all 25 counters
have moved to the left side, but do not add or remove counters from the grid. (See example on
the next page)
9. Have students shade in the new grid with all 25 shaded squares moved to the left side.
10. On the Student Grid Sheet, write the fraction (1/4) in three ways:
 As a fraction out of 100 (25/100)
 As a decimal to the hundredths place (0.25)
 As a percent out of 100. (25%) Remind students that the word percent means “out of 100.”
For example, for 1/4, you shade in the grid as shown:
Do at least 2-3 fractions as a class, then let students select their own, and shade it in. Remember to
choose fractions divisible by 100.
Then you would write it the following ways:
Fraction
Fraction
out of 100
Decimal
Percent
____1____=___25___=__.25___=__25%__
4
100
Once you have done at least 2-3 fractions, students may choose their own fractions
to build, shade and write.
Example
Student
Shade 3 squares gray
for every 4 squares total
Fraction
Shade 3 out of 4 columns gray
Fraction
out of 100
Decimal
Percent
75 “for every 100”
____3____=______75_____=__.75___=__75%___
4
Rearrange counters so it looks like
a model of a decimal.
100
Rearrange counters so it looks like
a traditional fraction model.
5 hundredths
7 tenths
Name ______________________________________
Fraction
Fraction
out of 100
Student Grid Sheet
Relating Fractions, Decimals & Percents
Decimal
Percent
__________=___________=__________=_________
Fraction
Fraction
out of 100
Decimal
Percent
__________=___________=__________=_________