6th Grade Math : Unit #5 - Introduction to Fractions : Lesson #2

Improper Fractions and Mixed Numbers

Objective: SWBAT understand the relationship between improper fractions and mixed numbers.
Standards: 6.NS.A.1 MP1
Subject(s): Math
60 minutes
1 Do Now - 10 minutes

The Do Now is based on the previous day's lesson on Simplifying Fractions.  This is a quick assessment of how much students have understood and retained.

Simplify the following fractions.  Show your work.

1.     63/108


2.     36/84

After about 7 minutes, we will review the answers.  I will randomly select 2 students to show their work on the board.  If other students used a different strategy, we will discuss their method.

  Overall, I want to see if students use the divisibility rules in simplifying fractions and if they are able to simplify the fractions completely.

2 Vocabulary Review - 10 minutes

Most students have seen improper fractions before, so we will formulate a definition together.  In your own words, what is an improper fraction?

An improper fraction has a numerator that is larger than or equal to the denominator.

 I will select 8 students to come up to the board and write their own examples based on the definition.  The students I select will be lower level math students who I need to assess their ability to write an improper fraction.  For the visual learners, I will share an example of what an improper fraction looks like.  Improper Fracions.png

 Some students will be familiar with a mixed number.  I will ask these students to share their ideas.  This will lead to the definition.

A mixed number is an integer and a proper fraction combined.

I will select 8 more students (lower level math students) to come up to the board and write an example of a mixed number.  For the visual learners, I will share an example of a mixed number.  Mixed Number.png

*Do not erase the students' examples on the board, they will be used throughout the lesson. 

3 Mini Lesson - 10 minutes

Using one of the student's examples of a mixed number written on the board, I will work through converting it to an improper fraction.  Students have the option of writing down the steps in their notebooks, but I always recommend that they do so.

Mixed Number to an Improper Fraction

 Ex. 1 - Change 4 1/7 to an improper fraction.

Step 1 - Multiply the denominator and the integer.

For this example, what numbers should I multiply?

Step 2 - Add the numerator to the product of step 1.

How can you show your work?

Step 3 - The denominator stays the same.

Using one of the student's examples of an improper fraction written on the board, I will work through converting it to a mixed number.

Improper Fraction to a Mixed Number

Ex. 2 - Change 39/8 to a mixed number.

Step 1 - Divide the denominator into the numerator.

Step 2 - The quotient will be the integer part of the mixed number.

Step 3 - The remainder is the new numerator.

What happens if you don't have a remainder? 

Step 4 - The denominator stays the same.

How can you check your work?

Helpful Foldable
Checks for Understanding

For an additional resource, students created a foldable (See Improper-Mixed Number Foldable and Improper-Mixed Number Foldable Cover) summarizing working with mixed numbers and improper fractions.  Although we went over the steps, I advised students to write the steps in their own words.

The foldable is a fun alternative or addition to note-taking.  Students can use the foldable throughout the unit to help them.

4 Independent Practice - 10 minutes

Students will complete the remaining student created problems on the board; changing the improper fractions to mixed numbers and vice versa. This activity helps motivate the lower level math students because their examples are being used.

I will encourage students to compare answers and check one another's work.  As students work, I will circulate throughout the room, observing students' work.  The most common mistakes made by students are in their basic multiplication and addition.

After about 10 minutes, we will review the answers together.  I will select students to share their answers and explain their steps.

5 Lesson Review - 5 minutes

I will post a visual representation of an improper fraction and mixed number.  Visual Representation.jpeg Students will have to explain what fraction it represents and why.