What's Rational About That? Day 2

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SWBAT sort numbers as rational or irrational and explain why. They will also be able to order rational and irrational numbers on a number line.

Big Idea

To reinforce the previous day's lesson, Students will create a human number line. They will then collaborate to sort given number cards and order those cards from least to greatest.


7 minutes

As students enter the classroom today, I hand them a neon pink number and tell them to save it for later.  I then remind them to get their journals and get started on the day's Warm Up problems.

Building on the previous day's warm-up, the first question is another percent benchmark problem. I circulate to check to see who still needs reinforcement of the benchmark concept. I remind students to ask their tablemates if they are not sure what to do.

I also remind students to use their resources from their notes section to help them with question 2 if they are unsure of the correct answers.  I notice several students flipping to their rational/irrational number T-tables from the day before.

I use class sticks to randomly select students to share their answers to the warm up.  To check and make sure all students agree with the answers, I ask them to give me a thumbs up or thumbs down for each problem.  If the majority of the class gives a thumbs up then I know we have mastered this standard and can move on. If I see a lot of thumbs down, I will go over the problem in detail and then ask students to share what mistake they made in the problem

Ordering Rational and Irrational Numbers

16 minutes

After Warm Up, I ask students to look at their pink numbers that I gave them as they entered class.  I explained that if they thought the number they had was rational, they needed to move to the left side of the room.  If the number they had was irrational, they needed to get up and move to the right side of the room.  I told them they had 15 seconds and began counting down. 

We went through each student's card on the rational side of the room and confirmed its correct placement.  I expect some confusion when we get to square root of 48 For that card you are going to ask the class to vote on which type of number they think it is.  If students are unsure, you will ask if 48 is a perfect square.  Students should be able to realize that it can’t be since 49 is a perfect square. This should help lead the kids to the answer.

Next, we verified the irrational numbers using the same procedures. I then ask the student with zero to come to the center of the room so that the rest of class can then order their numbers along a class wide number line, a task for which I give 30 seconds to complete.

When I reached zero, the students were standing in the line, so I explained that we would be verifying every number's placement.  I began with the largest number and moved left asking, "Is ____ smaller than ___?" If confusion happens, I hand a student a calculator to verify our work.

Once we finish verifying the other numbers, I give students ten seconds to put their pink numbers in a stack and return to their seats. I then explained the next part of the day's lesson.

Rational/Irrational Card Sort

12 minutes

I hand each pair of students a set of rational or irrational cards.  I tell them they have two minutes to sort the cards into two piles. At the end of two minutes, I tell them to compare with the other group at their table and make any changes.  I then poll the groups to determine placement of the number on a T-chart on the Smart board.

Once we have consensus, I explain that I now will give them three minutes to order the numbers from least to greatest just like we did with our human number line.  Before we start, I tell them to take out the fraction 8 divided by 0 and set it aside.  I explain this is a special case that we would deal with later.  I start the timer and wander the room eavesdropping on student conversations.

When time is up, I ask student groups to compare answers at tables and discuss any discrepancies. Then, as a class, we order the numbers on the number line on the Smart board

Exit Tickets

5 minutes

To help me assess students' level of understanding, I distributed rational irrational exit tickets for closure. I want to know if students need additional work with identifying rational and irrational numbers. I want to know if they have internalized the definition and are able to come up with examples of each on their own.