Fractions are more fun when we can eat them!
numerator, denominator, fraction, whole number
Before the Lesson
Students should have some basic exposure to fractions before this lesson, which offers hands-on practice in finding a fractional part of a whole number (for example, 1/2 of 4).
Count out kernels or pop up a batch of popcorn and give each student a handful (at least 30 pieces) of it. If you popped the popcorn, tell students not to eat the popcorn -- yet. "First we are going to do some math"
Write the simple fraction 1/2 on the board. Talk about what 1/2 half represents. Talk about what 1/2 of an object looks like. Tell students that they can also divide groups of things in half. For example, if they had four pieces of popcorn and wanted to share it with a friend, how many pieces of popcorn would each person get? (Some students will suggest that each student will get half of the popcorn, or two pieces of it.) Help students see the answer to this by asking them to do a hands-on activity:
The denominator concept is one that students might not yet grasp, but, as you continue with the activity, it will begin to make more sense.
Ask students to use their popcorn to figure out what 1/2 of 10 pieces of popcorn would be. How many pieces of popcorn should they count out? (10) If they are to divide that popcorn in half, how many groups will they divide it into? (two, the same number as the denominator in the fraction) How many pieces are in each group if you divide those 10 pieces of popcorn into two equal groups? 5 pieces
Next, write on the board 1/3 of 6. Ask students to identify the total number of pieces of popcorn they need to count out to figure out the answer to this problem in a hands-on way. (6 pieces) In order to figure out what 1/3 of 6 pieces of popcorn is, into how many groups will they need to divide the popcorn? (3 groups, the same as the number in the denominator position) Have students divide their 6 pieces of popcorn into three equal groups. How many pieces of popcorn are in each group? (2 pieces) What is 1/3 of 6? (2) Write on the board 1/3 of 6 = 2
Write on the board 2/3 of 6 = ___ Ask: What if you wanted to know what 2/3 of 6 is? How many pieces of popcorn would you need to figure that out? (6 pieces) Into how many groups would you need to divide the popcorn? (3 groups, the same number that appears as the denominator in the fraction 2/3) How many pieces of popcorn is 2/3 of 6? (4 pieces) Write on the board 2/3 of 6 = 4
As a reward, let student eat those four pieces of popcorn [if you are using popped popcorn, of course].
Set up another fraction problem for student to solve in a hands-on way: write on the board 2/3 of 9. Ask: Does anyone remember what the bottom number of the fraction is called? (denominator) What does the denominator tell us? (It tells the total number of groups that you will divide the whole number, 9, into.) So if we are going figure out what 2/3 of the 9 pieces of popcorn is, into how many groups will we divide the popcorn? (3 groups) If we divide 9 pieces of popcorn into 3 equal groups, how many pieces of popcorn will be in each group? (3 pieces) Ask students to identify the top number in the fraction on the board. (2) Explain that the top number in a fraction is called the numerator. Write the word numerator on the board and draw a line to the number 2 in the fraction 2/3. And what does the numerator tell about the fraction? (It tells how many of the groups are being used/counted.) So in our fraction 2/3, how many of the 3 groups are we going to use/count? (2 groups) Have students separate 2 of the 3 groups of popcorn. Then ask: How many total pieces of popcorn do you have in those 2 groups? (6 pieces) So 2/3 of 9 = 6.
As a reward, let student eat those six pieces of popcorn.
Write another problem on the board: 3/5 of 15 =
Ask students to figure out the answer to that problem and to raise their hands when they have the answer. You might provide scrap paper on which they can write their answers. Wander among students watching them as they work out the answer to the problem by
How did they do? Did they figure out that 3/5 of 15 = 9?
As a reward, let student eat those nine pieces of popcorn.
Repeat the activity. Ask students to identify the number of pieces of popcorn that is represented by the mathematical statement 3/4 of 16 = __ The answer is 12. Have them show you how they figured that out.
As a reward, let student eat the rest of the popcorn.
Assess students' understanding of the concepts and processes involved. Judge whether you need to provide more practice. If students seem to be grasping the concept, provide more problems for them to solve. (See Assessment section below.)
AssessmentFollow up this activity with a worksheet of about 10 problems. This activity may be done individually or with partners. Some students might continue to use the popcorn to figure out the answer; that's fine. Some suggested fraction problems include:
Diane Meehan, Trinity Lutheran School in Freistatt, Missouri