This document outlines a lesson plan on classifying rational and irrational numbers. It includes a pre-test for students to determine if example numbers are rational or irrational. The lesson then covers key concepts like different forms of rational numbers as decimals, fractions, and square roots. Students work in groups to organize numbers on a poster as rational with terminating decimals, rational with repeating decimals, irrational and non-repeating decimals. A post-test reviews the concepts and has students determine the rationality of additional numbers, explaining their reasoning.

1. Classifying
Rational & Irrational
Numbers
Pretest
Lesson
Posttest

2. Math Goals
• Classify Rational & irrational
numbers
• Moving between different
forms of numbers

3. Pretest- Is it Rational
• For each number below rational/Irrational?
• Explain your reasoning
1.) 5 2.) 5/7 3.) 0.575… 4.)√ 5
5.) 5 + √7 6.) (√10) ÷ 2 7.)5.75…
Continue to the next screen to finish
the pretest…

4. Pretest #8.)
• Several students discussed whether
0.575757575757… was a rational number or
not. Agree/Disagree
Ario: It is an irrational # _____________
Hao: It is rational, because ____________
it can be written as a fraction
Eli: Rational it equals 57/100____________
KB: 0.57 goes on forever _______________
Hank: Irrational because the
decimal goes on forever_______________
What do you think? Explain.

5. Questions to discuss…
• Are all fractions less than one?
• How do you write a repeating decimal as a fraction?
• What is the difference in 0.3 and 0.3333333…?
• What is a perfect square?
• Can you only take the square root of whole
numbers?
• What is the difference in the square root of a perfect
square and not a perfect square root?
• Are all fractions rational?
• How do you write ⅓ as a decimal?

6. More questions to ponder….
• Does every rational number have a
terminating decimal expansion?
• Does every irrational have a non-
terminating & non-repeating decimal
expansion?
• Which non-terminating decimals can be
written as fractions?

7. Whole class Activity
• Materials needed:
• Whiteboard, marker, and eraser
• Display the next slide

8. • COPY THIS table down on your whiteboard
• Write down an example of each section
CLASSIFYING RATIONAL & IRRATIONAL #
Rational Irrational
Terminating
Decimal______________________________
Non-terminating
Repeating decimal______________________
Non-terminating &
Non-repeating decimal___________________

9. Questions whole class activity
• What did you notice on your white board?
• What does the bar over the digit(s) mean?
• Which section would 0.123123123… go?
• Summarize what your table shows in terms of
decimals and types of numbers.
• COLLECT MATERIALS

10. Small group work
• Each group needs: poster paper, scissors,
Poster headings, the 2 sheets of numbers,
glue stick and scrap paper.
• Organize your class into groups.
• Follow the instructions.
• ALL students should be able to give a
reason for every card’s placement!
• TEACHER DOES NOT HELP!

11. Small Group Instructions
• Cut poster headings apart and number cards.
• Take turns to choose a number card.
• When it is your turn,
-decide where your # card goes on the poster
-does it fit in 1 or more places?
-give reasons for your choice
When it’s your partner’s turn,
-if you agree with your partner explain it in your own
words
-if you disagree, explain why and decide together where
card goes
When you have reached an agreement:
-write reasons for your decision on the number card
- if the card fits in one place, glue it on the poster.
- if not, put it to one side.
BONUS-Make up a # to go into an empty cell on the poster
with the blank card.

12. • Ambassadors jot down your group’s answers
on scrap paper and go to another group
compare your answer with theirs.
• Glue down all answers after comparing and
reaching a group consensus on every card’s
placement.
• Using tape post posters up on the walls around
the room
• Make sure names are on the posters
• Teacher have class compare posters explain
why they place numbers where they did.
• Check to see if class agrees/disagrees.
• How did someone else do this differently?

13. Hand back pretest
• Let students revise their answers first on
their pretest
• Then go over pretest questions with class
• Then do post test on next screen or
handout from website.

14. Post test
• Decide whether each number is rational or
irrational. Explain your reasoning.
1.) 0.21 2.) 3 3.) (√12 ) – 2
12
4.) √12 5.) 4.125… 6.) 12.52
4
CONTINUE TO NEXT SCREEN

15. Decide if each are correct or not? Explain your answers
clearly.
7.) Otis said (√3) ÷ 8 is rational because it can be
written as a fraction.
8.) Lulu said its irrational because √3 is irrational
9.) Joe said its rational because 3 is a perfect
square
10.) Ray said it is rational because it’s a
terminating decimal
11.) Sue says it is irrational because it is a
repeating decimal
12.) What do you think and why?

16. •THE END!