LESSON ONE
COMPARING UNIT VALUES USING FRACTION TOWERS
OBJECTIVES:
The student will demonstrate an understanding of the relationship between the
value of a whole unit and its parts.
The student will construct fractions and compare fractional parts using a concrete
model.
TEKS:
7.1 (A) – The student is expected to compare and order integers and positive
rational numbers.
7.14 (A) – The student is expected to communicate mathematical ideas using
language, efficient tools, appropriate units, and graphical, numerical, physical, or
algebraic mathematical models.
7.15 (B) – The student is expected to validate his/her conclusions using
mathematical properties and relationships.
TOOLS AND MATERIALS:
One fraction tower for each student.
Fraction card set for each student.
Scissors to cut the fraction cards apart.
(Note: The fraction towers should be made before the lesson, either by the
students, teacher, or by volunteers. See directions on how to construct the
towers).
EXPLORE:
The student will use the fraction tower to explore unit values. Have the student
demonstrate different unit values on the fraction tower.
Lesson sequence and facilitation questions:
-
Tell students that we are going to explore unit fractions as we did in the
previous lesson except we are going to use the fraction towers this time
instead of the fraction bar charts.
-
Have students demonstrate and explain the value of a whole unit on the
fraction tower using the slinky.
-
How much of the tower would be covered by the slinky to show one whole
unit? The whole tower is one unit.
-
How is this value represented? By the number 1 or 1/1.
-
What does the symbol 1/1 tell us? It means that the number has only one part
and that one part is the whole unit.
-
How much of the tower is covered when the slinky is “at rest” at the bottom?
None.
-
What value is this? Zero.
-
Ask the students to show 1/2 on the fraction tower. Discuss how they chose
where they placed the slinky.
-
1/2 divides the fraction tower into two parts. Are the two parts different sizes?
No, they are the same size.
-
Is it necessary for the parts to be equal in size? Yes. Why? Because
according to the definition of a fraction, they have to be the same size. 1/2 =
1/2.
-
Continue as a whole group to demonstrate unit fractions on the fraction tower
and on paper with symbols. Demonstrate 1/2, 1/3, 1/4, 1/5, 1/6, etc. to 1/12.
PRACTICE:
Have students work in pairs demonstrating the value of the various fractions on
the fraction tower.
DISCUSSION:
Discuss with students the relationships between the different values.
EVALUATION:
Play the fraction tower card game.
FRACTION TOWER CARD GAME
For two players.
1/2
Materials:
one fraction tower
one set of fraction cards
How to play: Deal all the decimal cards out into two piles, face down. Player one
turns over his/her top card and models the value on the fraction tower. The other
player agrees or disagrees with the placement. If they disagree, discussion
determines the correct placement. A correct placement counts as one point. The
second player now turns over the top card in their pile and models the fraction.
The first player agrees or disagrees and discussion ensues as needed. At the
end of the game, players count up the number of correct placement cards. The
player with the highest number of cards correctly placed wins. Players may have
the option of putting incorrectly represented cards back into their pile at random
to remodel later.
NOTE: improper fractions should be modeled by stretching the slinky higher than
the “whole” (top of tower). Students should be able to justify their placement
above the top by a certain amount.
1/2
1/3
2/3
1/4
2/4
3/4
4/4
3/2
4/3
5/2
1/5
1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8
9/8
10/8
1/9
1/10
1/12
2/12
0/12 3/12 4/12
5/12
6/12
7/12 8/12 9/12
1/20
1/15
3/15 5/15 9/15
2/5
3/5
4/5
10/5
1/6
2/6
3/6
4/6
5/6
6/6
7/6
8/6