Strategies for Dividing Fractions Day 2 + Show What You Know

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want student analyze this student’s work.  The student committed a common mistake of misinterpreting the remainder.  I want students to realize that the leftover 1/3 needs to be related to the 2/3, rather than the whole.  One-third is ½ of two-thirds, so the answer is 1 ½. 

I have a student explain their answer for each of the problems.  I ask the class if his/her answer makes sense.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.  I ask students what Ameila could have done to prevent this mistake.  Some students may say that she could have done the problem two ways and used the second way to check her answer.

Notes:

• Students started working on the practice problems during the previous lesson.
• For this lesson, each student needs a fraction kit to help model problems.  Example: Fraction Kit
• I print out a copy of the Extra Practice Multiplication and Division Problems for each student.

I have volunteers pass out the fraction kits.  I call on students to read through the to do list.  Then I ask a student to clarify the order of the tasks he/she needs to work on.  I explain that they should be working on these problems independently.  If they get stuck, they can ask a neighbor a question before they ask me.  I show students where I have set out the materials for the games.  I explain to students that before they play a game they need to find me and show me their work.  This way I can ensure that students are on the right track and also that they are solving the problems in two ways.

Note:

• I use the ticket to go data from Strategies for Dividing Fractions to see if there are any students who are severely struggling with dividing fractions.  If this is the case, I will pull this small group during the work time.  We will work together on a couple problems and then students will try the remaining problems on their own.

As students work, I walk around and monitor student progress.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason Abstractly and Quantitatively and MP4: Model with mathematics.

If I have a small group I am working with, I get up every few minutes and check on how students are doing.  If students struggle, I encourage them to use the fraction kit to model what is going on.  If they need ideas for another way to solve the problem, I have them go up and look at the Strategies poster we created in the previous lesson.  The hard part is for students to understand that the remainder needs to be compared to the divisor, rather than one. 

Here are some additional questions I may ask:

• What is going on in this problem?
• Do you think the answer is more or less than 1?  Why?
• What is your estimate for the problem?  Why?
• Look at the strategies on the poster.  Which strategy do you want to use?
• What is a different way we could solve this problem?
• What does your answer mean?
• How could you check to see if your answer works?

If students are finished with the division problems students work on Extra Practice Multiplication and Division Problems.  This will help them to review for the quiz.

For the last 7 minutes, we review the strategies for dividing fractions and the answers to the extra practice problems.

I give students the Quiz.  Students engage with MP1: Make sense of problems and persevere in solving them and MP4: Model with mathematics.  If students do not finish in the allotted time, they set up a time (preferably that day) to come in and complete it.  I use this data to inform my instruction.   If students struggle with a concept, I will spiral it into do nows and homework assignments.  I may also add a few problems on that topic to the next quiz.