LESSON THREE
COMPARING PERCENT VALUES USING FRACTIONTOWERS
OBJECTIVES:
The student will demonstrate an understanding of the relationship between the value of a whole unit and its parts by comparing percent values using a concrete model.
TEKS:
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.
Percent card set for each student.
Scissors to cut apart the percent cards.
EXPLORE:
The students will use the fraction towers to explore the following percent values:
25%, 50%, 75% and 100%. Have students demonstrate these values on the fraction tower.
Lesson sequence and facilitation questions:
-Tell students that we are going to explore percent values using the fraction tower.
-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.
-How is this value represented as a percent? 100%
-What does the value 100% tell us? It means that all the parts of a whole unit are all together.
-How much of the tower is covered when the slinky is “at rest” at the bottom? None. What value is this equal to? Zero
-How is this value represented as a percent?0%
-Ask the students to show 50% on the fraction tower. Discuss how they chose where they placed the slinky.
-What decimal value is 50% equal to? .5
-What fraction value is 50% equal to? 1.2
-50% divides the fraction tower into two parts. Are the two parts different sizes? No, they are the same size.
-If the tower is divided into four equal parts, what is the value of one of these parts? 25%
-What decimal value is equal to 25%? .25
-What is the value of two of the 25% parts added together? 50%
-What is the value of three of the 25% parts added together? 75%
-What decimal value is equal to 75%? .75
-What is the value of four of the 25% parts added together? 100% (25%+25%+25%+25%=100%)
-What is the value of two of the 50% parts added together? 100% (50%+50%=100%)
-What is the value of a 75% part and a 25% part added together? 100% (75%+25%=100%)
-What is the value of a 75% part and a 50% part added together? 125% (75% + 50% = 125%)
-What does 100% represent on the fraction tower? All the parts of a whole unit together
-Continue as a whole group to demonstrate different percent values on the fraction tower.
DISCUSSION:
Discuss with the students the relationships between the different values.
EVALUATION:
Play percents card game.
PERCENT CARD GAME USING FRACTIONTOWER
For two players.
Materials:
one fraction tower
one set of percent cards
How to play: Deal all the percent 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: Percent values higher than 100% should be modeled by stretching the slinky higher than the “whole” (top of tower). The student should be able to justify their placement above by a certain amount.
/ 25% / 33.33% / 41.6% / 50%58.3% / 66.6% / 75% / 5% / 66.6%
20% / 033.3% / 60.0% / 40% / 60%
80% / 200% /
16.6% /
33.3% / 50.0%
66.6% / 83.3% / 100% / 116.6% / 133.3%
50% / 33.3% / 66.6% / 25% / 50%
75% / 100% / 150% / 133.3% / 250%
20.0% / 12.5% / 25% / 37.5% / 50.0%
62.5% / 75.0% / 87.5% / 100.0% / 112.5%
125% / 11.1% / 10.0% / 8.3% / 16.6%