Lesson: 8 - Irrational Numbers

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Lesson Objective

SWBAT identify rational and irrational numbers.

Lesson Plan





1. Opening - active

2. Mini-Lesson – passive

3. 4 Corners – active

4. Review – active

5. IP - passive

6. Exit / Closing - passive

-        When asked if a number is rational, ask yourself, “Is it fractional?”

-        Turning decimals into fractions: use the digits as the numerator and the place value as the denominator. IE: 0.345 = “zero wholes and three hundred forty five thousandths” = 345/1000

-        Non-repeating decimals that go on forever are “irrational”

-        Square roots of “non-perfect” squares are irrational.




SWBAT identify rational and irrational numbers.





1. Which of the following is an irrational number:

A. √225

B.  π

C. 0.45

D. 0.11111111…



1.  OPENING (8 minutes) ACTIVE


Have students answer mental math questions coming in thru door.


Students are prompted to switch from lesson 1 to this lesson by partnering up and answering the following Q’s:

Take turns READING the numbers below to your partner. They do not have a sheet to read. You must read it to them correctly, and then they must write it accurately as a fraction. Most correct team wins suckers.

Students are prompted again to follow TOUCHDOWN procedure to get into classroom / complete warm-up.



2.  Mini-lesson: CONTENT (10 minutes) PASSIVE


Irrational numbers ask yourself … “Is it fractional?” so youmust turn it into a fraction first.

 First part of mini lesson, let’s practice converting numbers into fractions. Start with decimal values. Move to whole numbers. Then square roots.


Now let’s try telling if these numbers are rational or irrational. Remember to turn them into fractions first.

Students listening and filling in notes sheet.

Notes 2.8


3.  Guided Practice (30 mins) ACTIVE


Back and forth with INM – read description above.


Give students white boards and allow them to convert to fractions / label rational and irrational after converting to fractions.





4. Independent Practice (20 minutes) ACTIVE


Practice problems on back.

Team with best participation / activity gets to work on carpet / clipboards



5.  Exit Ticket and Closeout (8 mins) PASSIVE


Close out activity – 3,2,1 to identify the 3 new things learned, 2 old things remembered, and 1 question you still have.


Exit ticket, silent volume.




Write “when finished…” directions on board.



6. Reflection


Most effective part of this lesson was me asking students repeatedly, "Is it rational?" and requiring them to ask back "Is it fractional?" I'd feign confusion and say I don't know and they'd respond yes or no, depending on the value presented. Besides being engaging, this strategy requires 100% participation and compliance, let's you know who "gets it" and encourages the link between the words rational and 'fractional' – a bit of a stretch, yes, but effective enough regardless.



Lesson Resources

Notes 2.8 Irrational Numbers  
Lesson 2 8 Irrational Numbers  


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