Parts of a Set: Fractions
Students will be able to divide sets into equal parts and identify the parts using fractional names.
- Tell students that today they are going to learn how to represent parts of a set, or a group of things, that we call fractions.
- Tell them that a fraction represents a part of a set, and therefore it is not meaningful without knowing what the total of the set is.
- Show a set of four balls consisting of three soccer balls and one football.
- Ask students what fraction of this set of balls are soccer balls. Answer: three-fourths or three quarters.
- Tell students that you have to know what the whole amount, or total number of items in a set, is to know what the given part represents. Relate it back to your last example by bringing up that you have to know that there are four balls total to know that three quarters of them are soccer balls.
- Have five girls and three boys come to the front of the class. Ask the class what fraction of the group is girls. Ask the class what fraction of the group is boys. Remind them, if needed, that each is a fraction out of eight.
- Show a set of shapes containing four squares and three rectangles. Ask what fraction of these shapes are triangles. Answer: zero out of seven.
- If more examples are needed, you can collect shoes from students and determine what fraction require laces, or bring students to the front of the class and determine what fraction are blonde or brunette.
Explicit Instruction/Teacher Modeling(15 minutes)
- At this point, review the notion that we have to know what the total amount of the set is before we can say what the fraction is.
- If you feel the students are ready, you can introduce the notion of a denominator as being the total amount in the set. Create an example and write your denominator under the fraction line.
- Show a stack of text books and ask your class what fraction are math books, science books, or story books.
- Tell students that a numerator is the specific item within a set that the fraction is about.
Guided Practice/Interactive Modeling(20 minutes)
- Divide your students into groups.
- Give each group a set of counters or coins.
- Have each group choose twelve 2-sided counters and set them out on the desk, breaking them into three groups.
- Ask them to flip over one group so that they have two groups of four of one color and the third group is a different color.
- Ask what fraction of the whole set is one color, then ask what fraction of the set is the other color (or heads and tails if your class is using coins.)
- Ask students how many counters are in one-third of the set.
- Have students arrange the counters so that one-fourth of them are [a color of your choosing].
- Ask students to rearrange counters into six equal groups all with the same colored side up.
- Tell them to flip the counters in one group. Ask them what fraction of the set is [a color of your choosing].
- Tell your students to flip another group. Ask them what fraction of the set is [a color of your choosing].
- Have them flip another group. Ask them what fraction of the set is [a color of your choosing].
- Ask students to arrange the counters so that one-fourth of them have [a color of your choosing] sides showing.
- Ask students to share what they have found out from this activity.
Independent Working Time(10 minutes)
- Pass out Colorful Plants: Practicing Fractions.
- Have the students write and draw about fractions of a set in their math journals. If using the math journal, have them draw something easy to draw and color, such as circles or squares. You will collect these for assessing once they are finished. This will help you know what the students have learned.
- Enrichment: Give advanced students more information about denominators and numerators.
- Support: For students who are struggling, spend additional time helping them grasp the notion of parts of a whole. You might also draw a couple of examples in their journal and ask them to explain it to you that way.
- Circulate as groups are working and determine whether or not students understand the lesson.
- Grade the worksheets to check understanding of individual students.
- Mark the journal entries to determine the students' levels of understanding of fractions as parts of a whole.
Review and Closing(5 minutes)
- Have students take out their math journals and explain with pictures, numbers, and words what they learned about fractions today.