These games and activities help students investigate the relationship between fractions and decimals, focusing on equivalence.
Background for Teachers
Students should use models and other strategies to represent
and study decimal numbers. Fractions and decimals both represent
parts of a whole, and both can represent numbers greater than one.
Learners need to investigate the relationship between fractions and
decimals, focusing on equivalence. Any fraction can be rewritten
as an equivalent decimal and any decimal can be rewritten as an
equivalent fraction. Help them understand that a fraction such as 1⁄2
is equivalent to 5/10 and that is has a decimal representation of (0.5).
After developing and understanding of equivalent fraction and decimal
forms, students need to recall fluently the decimal equivalents for
common fractions such as 1⁄4= 0.25, 1⁄2= 0.5 and 3⁄4= 0.75. For other
fractions divide the numerator by the denominator. It is important for
students to understand the traditional algorithm, but also be able to
use a calculator to convert fractions to decimals. In addition, students
can examine that some fractions are terminating decimals and others
Decimals are part of our every day life. We see them in the amount
of rainfall in weather reports, sports statistics (e.g. batting averages),
and stock market reports. It is important to connect fractions to
decimals by numerous conceptual experiences, rather than just
memorizing the algorithm.
Intended Learning Outcomes
1. Develop a positive learning attitude toward mathematics.
6. Represent mathematical ideas in a variety of ways.
Invitation to Learn
Ask students if they have ever created new words by taking
a word and rearranging its letters. Explain that they are going to do
a similar activity only using numbers. Have the students cut three
index cards in half the wide way. Then, have students label the card
as follows: 7, 5, 4, 0, and a decimal point. Tell the students you
are going to ask them to make numbers that will fit a specific rule.
Remind students that each number and the decimal must be used for
each problem. Have students work in small groups and discuss their
findings and discoveries. Start giving rules such as: "Build a number
that is greater than 750", "Build a number that is less than 5", "Build a
number that is between 70 and 70.5", etc.
Part One: Rolling For One
- Tell the students they are going to play a game to investigate
decimals in more depth. They will be looking at the whole,
which is one, 1, and/or 1.0, and exploring adding tenths and
hundredths. Students will create a written accounting of all
addition of decimals.
- Model the game as a whole class the first time. To play the
game, have students set up a T-chart like this by folding a blank
piece of copy paper in half and labeling it as shown:
Play the game with the class using the following rules:
- Each player must roll the die 7 times.
- After each roll of the die the player will decide whether it should
be tenths or hundredths. (e.g. a roll of 3 could be 0.3 or .03)
- A running total is kept of all seven rolls.
- To win the game, students must get as close to one without
going over 1 whole.
- If you have a class that is struggling with this concept, show
the tenths and hundredths in money form. For example, six
hundredths is $0.06 and six tenths is $0.60. Students are trying
to reach $1.00. This is great for understanding, but students
need to be able to remove the dollar sign and the zeros and
still realize that $0.06 is equal to .06 and $0.60 is equal to 0.6.
Students will make this transfer quickly if they can clearly see
the connections between representations.
- An example of play: One player rolls a six, they must decide
whether it is six tenths or six hundredths. Player two repeats
the process with his/her own roll. Player one rolls again and
adds the roll to the previous total. For example, player one had
six tenths and rolled a six again, the player can not make that
into six tenths because it will go over one whole after only two
rolls, so the players must make it six hundredths. So, 0.6 + .06=
.66. Play continues with each player adding to his previous sum.
After seven rolls, the player closest to 1 (without going over) is
- Practice the game as a class.
- Check for understanding of the game. If students are still a little
confused have them play the game partners against partners.
Circulate questioning the students during the game. If students
grasp the idea, play in partner groupings. As you circulate,
continue asking questions to see if students can see any patterns
that will help them win the game.
- After everyone has had a chance to play, have the students
examine their results. Have students discuss in small groups
how numbers were recorded. Did it matter if a student didn't
put the zero after a number? (i.e. 0.6 instead of .60), How did
each student keep track of their score, etc.
- Students will record in their math journals their responses to
the journal prompt "My strategy for playing Rolling One is..."
Part Two: Get the Hint?
- Explain to the students they are going to explore decimals using
a calculator. Many times when students use calculators they get
an answer with many digits after the decimal point; students
find it difficult to deal with all those decimals. Teachers hear
questions like What do the decimals mean?, and What's the
real answer?, stated in the classroom. This activity is a simple
engaging way to look at decimals. Before starting, be sure to
have the students create a recording sheet by folding a regular
sheet of 81⁄2" x 11" copy paper into thirds and labeling each
column as shown here(information in parentheses is for teacher
help, do not have students write it on their page).
- For the whole class modeling use an overhead calculator. The
first couple of times you model this activity show students the
- The goal is to figure out the secret number. (Note: When
playing with a partner and not the class as a whole, be sure to
remind students to keep the calculators hidden so their partner
can not see the secret number.)
The rules of the game are as follows:
a. Partner A will choose a secret number between 1-100.
b. Partner B will try to figure out what partner A's secret
number is by guessing a number.
c. Partner A will take partner B's guess and divide it by the
d. Partner A records the decimal on the Record Sheet.
e. Partner B finds the decimal point and draws a box around
the 3 numbers on the right side. Then, determines the
approximate percentage of the decimal.
- If it has a 1 to the left of the decimal point= 1.34567877679.
This means that your guess is greater than the secret
- If it has does not have a 1= 0.67895546565. Box
0.67895546565. This means that your guess is less than the
secret number. It is only approximately 68% of the number.
f. With your new information, make another guess.
g. Try to guess the secret number in less than 5 guesses.
- After modeling and checking for understanding, students will
play several games in partners, recording their work on their
self-made record sheet.
Part Three: The Tile Company
- Students are going to look at decimals using a model, the 10-by-
10 grid. Discuss how many squares make up a 10-by-10-square
grid. Remind the students that one grid represents 1 whole that
has been divided into 100 equal parts.
- Using the Blank 10x10 Grid Sheet, have the student shade in
three tenths of grid #1. Have students compare their shading
to their partners. Discuss the written notation for this picture in
fraction form, decimal form, and as a percent. If needed, have
a mini-lesson on how to figure out each one of these notations
and how it relates to the illustration.
- Continue giving the students other numbers to represent in
picture and written notation: .25, .4 .66 and so forth until you
are confident that the students understand.
- Inform the students that they have just been hired by the Tile
Center Company as financial consultants. Tell them they will be
examining different kitchen tile patterns which the Tile Center
Company sells. All tiles are 10 inches by 10 inches and sell for
$1.60. The company is losing money and needs the students'
assistance in determining which tiles need to be changed to
have the company make more money, but are still pleasing to
the eye. All the white squares are one cent. The shaded squares
are twice as expensive.
- The task: In small groups, "Consultants" (students) will create a
presentation to the President of the Tile Center Company.
1. Students need to determine the fraction, percent, and
decimal form of each The Tile Center tiles.
2. Determine the cost of each tile.
3. Make a recommendation about which of existing tiles
should continue to be manufactured (provide profit) and
which should be eliminated and why.
4. Create six unique grid patterns that will make the company
money. State the cost of each tile and the fraction, decimal,
and percent shaded for each tile.
5. Finally suggest a new price that would make the tile
company at least $0.05 profit per tile.
6. Write a one page letter to the President discussing #2, #3,
#4, and #5.
- The Tile Company is wanting to release a new line of tiles that
are 20 x 20. Suggest to the company a tile price and 6 different
tile designs that would make the company money on every sale.
- Play I Have, Who Has? Commercial sets are available for
purchase, or a Google search of "I Have, Who Has" will return
many pre-made sets you can print and use.
- Have the students play Get the Hint? with a family member.
- Have the students find batting averages for 10 different baseball
players in the newspaper. Record the players names and rank
order the players from the best batting average to the worst.
- Watch the nightly news or read a newspaper to find the Dow
Jones rate 10 days. Find the difference each day in the decimals.
Record and chart.
- Log on the www.weatherbug.com and create a bar graph of the
rainfall for two different regions.
- Have students write in their math journals about how decimals
relate to fractions and percents.
- Have students self assess how well their presentation met the
criteria on a student created rubric.
- Complete the tile company activity with accuracy. During the
activity, ask the students to explain the steps they are taking.
Check for accurate expression of fractions, decimals and
percents, both in written form and in conversation.
National Council of Teachers of Mathematics. (2000). Principles and standards for school
mathematics. Reston, VA.
Teaching and learning mathematics is a complex, active, and social
activity. The research on problem solving and mathematical reasoning
clearly states the great need to create mathematically rich environments
for students to deepen their understanding of mathematics. The
instructional strategies chosen should match the varied learning needs
of students. Effective instruction occurs when teachers choreograph the
learning experience by carefully choosing select problems, standard-
based materials, and conducting formal and informal assessments.
The end goal is to empower students in problem solving by blending
conceptual, procedural, and factual knowledge into a powerful learning
Van de Walle, J. A. (2001). Elementary and middle school mathematics: Teaching
developmentally (4th ed.). New York: Addison Wesley Longman.
Van de Walle clearly states the importance of constructivism.
"Constructivism provides us with insights concerning how children
learn mathematics and guides us to use instructional strategies that
begin with children rather than ourselves" (2001, p. 26). The whole
learning process focuses on learning the concept, instead of the small
pieces or procedural parts in the learning process. Effective teachers
know their students' strengths and weaknesses and plan instruction
to challenge all learners to meet high standards. To do this, teachers
must find ways to learn students' prior mathematics knowledge
and misunderstandings so that knowledge gaps can be addressed,
inconsistencies resolved, and understanding deepened.