What's Rational About That? Day 1

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SWBAT classify real numbers as rational or irrational.

Big Idea

Students will learn identifying properties of rational and irrational numbers.


12 minutes

I continue to reinforce procedures from the first week of school by providing students warm-up problems to complete when they first enter class. Today's warm-up questions are a review of several 7th grade concepts on which we will build this year:  Working with integers and percent benchmarks.

As students work, I walk around to get a sense about who was struggling with these concepts. If I find the majority of my students are having difficulty retrieving previous knowledge of these two concepts, I can stop the clock and guide the students toward remembering or at least making sense of the questions.

Rational or Irrational?

22 minutes

I refer to the day's objective on the board and then show a page of Rational Numbers on the SmartBoard.  I explain that all of these numbers have something in common and I ask the table groups to talk for two minutes about what they notice. I also remind students in seat 3 at each table to record for their group. After two minutes, I ask each group to contribute their ideas.

I get very low-level responses including, "They all have numbers.", "They are all black".  Luckily, I expected these responses, so I said, "What if I showed you this?" and I began clicking next to each of the examples of rational numbers and an equivalent fraction appeared in blue.  I gave the groups 15 seconds to explain what they saw and then I wrote the word 'equivalent' on the board and asked students to give me a thumbs up if they had heard that word before. Most had so I went on to explain that all of these numbers were examples of rational numbers. I then shared the definition of rational numbers.

Next, I showed another page of numbers (this time all irrational numbers) and asked students to talk for one minute in their groups how these numbers were different from the rational ones we just saw. Several groups recognized pi as a number that was not equivalent to a fraction. I explained that they had discovered one important feature of these numbers, but several other qualities could put them in this category:  an elispe, a zero in the denominator, pi, or a square root of a non-perfect square.

I wanted my students to have a resource for future reference, so we then created a T-table in their notes section of their journal in which we listed all the attributes of rational and irrational numbers. We then looked at five numbers and decided whether they were rational or irrational by citing attributes from the table. While sample "a" was clearly irrational because of the elipse, several tables disagreed on the classification of square root of eight (sample "b").  I realized I should have reviewed perfect square numbers, so quickly pulled up a page of perfect squares for reference. Once we clarified "perfect squares", students were able to easily classify the last three samples.

Finally, I shared a page of Let's Practice that had five numbers that students had to classify as rational or irrational. I told the students to record their answers in their journals. As students worked, I moved about the room checking for understanding. When all students had finished, I asked students to help me label each on the Smartboard.


6 minutes

For closure, I wanted to get a sense about how well students were grasping the difference between rational and irrational numbers, so I asked them to complete two sentences titled In Your Journal.  I gave them the sentence starters:

-A number is rational when...

-A number is irrational when...

As the students wrote, I circulated throughout the room in an attempt to identify any misconceptions that students revealed through their writing that I would incorporate into future lessons.