This lesson is designed to review the process of converting between mixed numbers and improper fractions. Students have varying levels of mastery at this concept. This lesson will provide all students with a common experience to refer back to. Emphasizing modeling (vs. algorithms) first will allow students to better understand how/why the algorithms work.
To launch this lesson, I use a dip sticking approach to determine what the students know as well as their comfort level with these skills. I survey the students by asking them to raise their hand to show if they:
• Have heard, or used, the words improper fractions or mixed number before
• Are very familiar with working with improper fractions or mixed number
• Have some idea about improper fractions or mixed number
Next, to make sure there is a clear understanding of these terms and how they are related, I facilitate a class discussion.
• What is a mixed number?*
• Can you give and example?
• What is an improper fraction?*
• Can you give and example?
• In what real life situation are improper fractions or mixed numbers used?
• Why do we need to know how to convert between these two types of numbers?
Improper fractions are defined as any fraction that is equal or greater than 1 where the numerator is larger than, or equal to the denominator
Mixed numbers are defined as a whole number and a fraction combined. They represent numbers between whole numbers.
I use the guided practice piece of this lesson to demonstrate the purpose of modeling in converting between improper fractions and mixed numbers.
Using a think a loud and interactive modeling, I demonstrate the process first by converting an improper fraction to a mixed number and then by converting a mixed number to an improper fraction.
Based on the initial survey of the students and evidence of their thinking shown in their school work, I know that a handful of students know the procedures for these conversions. I emphasize the importance of using models for this lesson (and the requirement that they do so). Then before students break off to practice, I quickly model the procedures.
The reason I demonstrate the procedure quickly is strategic. I want to recognize that there is a procedural way for changing mixed numbers to improper fractions because the students who already know this "trick" will want to use it. I would rather they use it appropriately to check their work than to attempt it incorrectly. Also, I want to show students that there are many ways to accomplish the goal of converting between mixed numbers and improper fractions - exposure to the procedures lets them have a preview of what is coming.
Students work in pairs to convert two improper fractions 2 mixed numbers, demonstrating their thinking by using models. This lesson is designed to help students develop the mathematical practice of modeling (MP6).
I circulate around the room to monitor students and based upon what I see, some students are invited to the board to share their approaches.
Because of the classroom schedule today, I didn’t have time to close with students. If time had allowed, I would have focused the group share on the problem 4 and 7/10 because while the students were working, I noticed two students used different entry points to approach this conversion. One student drew each of the 10 parts in tall of the wholes. The other student wrote out 4 tens, then drew just the fractional part. I'd ask them each to share their approaches shows the progression toward the algorithm.