Improper Fractions and Mixed Numbers

Mika Voith

Math Lesson #2

Improper Fractions and Mixed Numbers

Fourth Grade

OBJECTIVES:

The students will be able to recognize and interpret improper fractions and mixed numbers. The students will be able to convert improper fractions to mixed numbers, and the other way around. The students will be able to recognize equivalence among improper fractions and mixed numbers.

CONTENT:

The students will begin by recognizing that fractions can represent numbers that are larger than one. Fractions that represent numbers that are larger than one can be written either as an improper fraction (when the numerator is larger than the denominator) or as a mixed number (where there is a whole number written with a proper fraction). The students will learn how to convert improper fractions to mixed numbers by working with manipulatives to see how wholes can be “pulled out” to create the mixed numbers. Finally, the students will test their ability to see equivalence between mixed numbers and improper fractions by quickly matching terms together.

MATERIALS:

The following materials will be needed to complete the activities in this lesson: M&Ms candies, extra-small plastic cups (mouthwash size), index cards with matching improper fractions and mixed numbers written on them.

INTRODUCTION:

Length: 10 minutes

As the students are walking in have the following problem written on the board or overhead projector: What are the next two terms in each pattern? Under each fraction, draw a picture of it.

1. 1/3 2/3 3/3 4/3

2. ¼ ½ ¾ 1

3. 1/8 ¼ 3/8 ½

When all students have had an opportunity to work on the problems discuss the answers and how each student came up with the next two terms. Once all students have figured out the patterns and how to come up with the next two terms, ask the students how they could simplify the two new terms from the first and second patterns. Use this discussion to lead into the activities.

ACTIVITIES:

Activity One – 30 minutes

To begin this activity make sure that the students understand the definitions of numerator and denominator. For this activity it is especially important that they understand that the denominator is the “size of the pieces” and that the numerator is the “number of same sized pieces.” It is also important that the students know that ONE cup is going to be our whole. That means that if there are two cups that means that there are two wholes, not a new one whole. Then place three to four M&Ms in one cup and ask them to tell you what one M&M equals (1/3 or ¼). Ask them to tell you what fraction of one color M&M there is in the sample cup. When they have done this successfully get one more M&M and one more cup and place the M&M in that cup. Now ask the students what the new total number of pieces is (numerator) and ask them if the denominator (size of the pieces) has changed. What could make my denominator change sizes? Now divide the students up into groups of two or three and give those groups 6 cups and a handful of M&Ms (already pre-sorted out by you). Explain to each group or pair that they need to, first, determine the denominator (the “size” of one M&M) and the improper fraction and mixed number value of all colors of M&Ms in their cups. Once all of the groups have found the denominator, the improper fraction and the mixed number of their M&Ms, the members will be invited to share their results with the class and explain how they got them. Finally, working all together and using patterns that we have found in our data, we will all determine the mathematical way to convert improper fractions to mixed numbers.

Activity Two – 15 minutes

Before this activity begins you need to make sure that all of the students are not capable of converting mixed numbers to improper fractions, based on the conversation the class had at the end of Activity One. You will then divide the class up into groups of three where they will play “Mixed Number Go Fish.” This game is played just like Go Fish except that in order to make a match the students must match the equivalent mixed number and improper fraction. Each player begins with five cards and the rest are put into a pile in the middle. The person with the most recent birthday starts and play moves to the left. When a student believes that a match had been made the rest of the group must check for correctness. The person who collects the most pairs wins the game. As many rounds of this game can be played as time permits.

CLOSURE:

A mini-closure can be done by the teacher by walking around to each of the Go Fish groups and making sure that they are being successful at the game. To assess how much they know about improper fractions and mixed numbers ask the members of the group to explain to you their strategy for making sure that matches are correct. How do they know that their strategy works?

REFLECTIONS: See attached