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Summary:
Students will use dominos to learn about common denominators and fractions.
Main Curriculum Tie:
Mathematics - 6th Grade
Standard 1 Objective 2
Explain relationships and equivalencies among rational numbers. Materials:
- Set of dominos (ideally
double twelves, but
smaller sets will work)
- Set of coins or round
plastic chips
Web Sites
Background For Teachers:
The use of dominos represents a graphical model for adding unlike
fractions. A key concept for students to understand is the common
denominator. A common denominator is a common multiple of two or
more denominators. A multiple is the lowest number that both (or all)
numbers (denominators) can “go into,” or be divided into.
In the case of adding or subtracting, unlike fractions, the Least
Common Multiple (LCM) needs to be found. The dominos in this
activity illustrate the need for a common or matching set of dominos in
order to add. That is where we need the common denominator.
As a teacher, you can even explain the use of the term common
denominator in everyday speech. For example, the common denominator
in the Civil War was hatred of each side for the other. That is what was
shared in common—the common cause of the war.
Intended Learning Outcomes:
1. Demonstrate a positive learning attitude toward mathematics. Instructional Procedures:
Invitation to Learn
Kids enjoy dominos—whether playing a game or setting them up in
a pattern only to tip them over. Students will use dominos to assist
them in understanding addition of fractions during this activity.
Have pairs or small groups of students set up two unequal lines of
dominos standing on their short end. They can use straight lines or
curves—as long as the lines have an unequal amount with a difference of
at least three.
When the lines are set up, have students tip them at the same time.
What do they notice? Did the shorter line finish first? Of course. They
are not even. One line has more than another. Explain that you will use
the dominos to add unlike amounts of fractions together.
Instructional Procedures
- This activity works best with unlike fractions with small
denominators. How large the fractions are depends on how many
dominos you have. Pass out sets of dominos and plastic chips or
coins to pairs or small groups.
- Explain that they will use the blank side of the dominos to add
unlike fractions. Model the first problem with them.
Example:
Remind students that the denominators represent the total number,
in this case, of dominos. Have them arrange two lines parallel to
each other that look like this, representing the denominators:
Another way to remember is to use the term “domino
denominator.”
- Next, using the coins or plastic chips, place two chips on top of
two dominos in the group of three, and one chip on top of one
domino in the group of six, representing the numerators:
- Ask the students how many dominos they would have to add to
the group of three to equal the group of six. The answer is three.
Remind them that if they add three more dominos, they also need
to add a chip or coin to two of them, like this:
- Now that both lines have the same total amount of dominos, six,
ask the students to add up all of the dominos with chips or coins
on the tops. The answer is five. So, five-sixths (5/6) of the
dominos have coins or chips on top of them.
- This process can be checked by adding the traditional way, as
follows:
- Again, this technique is more effective with “smaller fractions,”
as determined by the number of dominos and coins or chips.
- This exercise may also be used to demonstrate simple subtraction
of unlike fractions. The difference being you subtract the lesser
amount of chips/coins from the greater amount.
Attachments
Extensions:
Another activity using the dominos is done with the numbered
sides. With all dominos face down, have a student (in a pair or
group) turn over two dominos. On each domino, the smaller
number represents the numerator, and the larger number
represents the denominator. Have students practice adding and
subtracting these fractions on the dominos. Paper and pencil may
be needed.
Family Connections
Dominos is a popular game for many families. Many games
involve grouping and patterns with a need for number sense and
operations. Encourage students to play domino games with
families. In the event a student has no access to dominos, at your
discretion, they may check out your set.
Assessment Plan:
An ideal assessment method for this activity combines a
performance test with a traditional summative test. Students,
given a set of problems, model and solve equations using the
dominos in this activity. This assessment would indicate
conceptual understanding of the process of addition and
subtraction of fractions.
Bibliography:
Research Basis
Tankersley, K. (1993). Teaching Math Their Way. Educational Leadership, 50, 12-13.
This article follows the development of a methodology of using
manipulatives for elementary math that fosters discovery and positive
attitudes toward math. It also reflects an increase in testing results in
math.
Rust, A. L. (1999). A study of the benefits of math manipulatives versus standard curriculum
in the comprehension of mathematical concepts. Knoxville, TN,
ERIC 436395.
This dissertation attempted to test first graders using both standard
text-book based instruction and the use of manipulatives in math.
Conclusions indicated little difference in tested results, though standard
curriculum methods did show slightly higher results. However, the
article points out that students’ enjoyment of the different methods wasn’t
studied. Author:
Utah LessonPlans
Created Date :
Feb 27 2006 12:17 PM
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