Grade level
Fourth grade
Area of Math Engaged/Emphasized
Fractions
Description of Activity (3), (4), (5), (11), (12)
(1)In this activity, students will be asked to find ten fractions between 0.25 and 0.30. (9)The materials needed for this activity are paper coins that express $ .25, $ .05, and $ .01 (enough so that each student has one $ .25, one $ .05, and four $ .01). Students should also have paper and regular lead and color lead pencils for their area model drawings. A black board and chalk will also be needed for students to post their examples during the class discussion.
(2)Before proceeding with this activity, students should have prior experience working with fractions and be aware of their relationship to decimals. Also, students should have experience expressing fractions using the area model. To lead students into the activity, allow them to begin thinking about decimals by giving them money values. (10)Distribute one .25 cent paper coin, one .05 cent paper coin, and four .01 cent paper coins to each student. Tell students that they can use the coins to express their money values in decimal form (ex: .25, etc.) Students should be told that they can use the money amounts to help them come up with their fractions. (2)Tell students to come up with combinations of coins that fit between $ .25 and $ .30 using the paper coins they have been given. Students should be told to write down their answers in decimal form. (7)Students will come up with answers of $ .26, $ .27, $ .28, and $ .29, using the paper coins. (2)Students should be asked to describe how they came up with their answers.
Students should then be told to think of the money values (decimals) they came up with and try to express them in fraction form. Ask students to think of the values they first started with (0.25 and 0.30). Tell students to come up with the fraction form for 0.25. (15)If students have difficulty, ask them to think of the money values again. There are one hundred $ .01 in one dollar, thus there are twenty-five $ .01 in one dollar (25/100). Another way is to think of what the coin $ .25 is called-one quarter. Ask students to think of how "one quarter" is usually expressed (1/4). Once students come up with the fraction for 0.25, then ask them to come up with the fraction form for 0.30 using the same technique they did for 0.25.
(2)Ask students to guess how many fractions will fit between 0.25 and 0.30. Students will probably state that they can come up with four fractions because of the answers they got using the paper coins. Tell students that it is possible to come up with more than four fractions that will fit between 0.25 and 0.30. (1)Ask them each to come up with ten fractions that will fit between 0.25 and 0.30.
Students can be told to begin by starting the same way they began with the coins-expressing 0.25 through 0.30 in fractions. Students should be told to use the area model to express each of the fractions. (7)Possible student responses are as follows:
25/100 26/100 27/100
28/100 29/100 30/100
(4), (5)Students should then be asked to use these area models to come up with other fractions-fractions that fit between 0.25 and 0.30. Students should be left to find these fractions on their own by finding groups within the area models that they came up with. (7)Possible student solutions are that they will find that in their area model of 28/100, they will find that they can create four groups of 7/25 and so forth. (15)If students have difficulty, show them how the area model of 25/100 can be broken into groups expressing 5/20 or 1/4.
(6)After working for a while, the class should reconvene and students should discuss their answers and how they came up with them. Students should take turns drawing their examples on the board and how they created their groups within the area models to come up with other fractions. They should also be asked to describe how their fractions are the same and how they are different. The teacher should write these responses on the board.
(8), (13)Through the discussion, students should discover that some fractions, through they have different numerators and denominators are the same. For example: 25/100, 5/20, and 1/4 are the same value. A follow-up activity could consist of students coming up with four fractions that equal a certain decimal value. For example: students could come up with 50/200, 25/100, 5/20, and 1/4 to equal 0.25. Students could then discuss the relationship between these fractions.