1. Bellringer 8/23/17 Head to Go formative!
Classify each number as Rational, Irrational, or Not a Real Number C A
B. −36
D. 𝜋 2

2. Bellringer 8/23/17
Which number is rational? C A
B. −36
D. 𝜋 2

3. Rational and Irrational Number Rap

4. Agenda ~Color Code sheet from Yesterday ~Estimating IRRATIONAL Numbers
~Comparing and Ordering

5. Solo Time Get your sheet from Yesterday and take 10 minutes
to complete
Rational
(BLUE) vs. 
Irrational 
(YELLOW).
Circle time-Rational/Irrational

6. Solo Time Get your sheet from Yesterday and take 10 minutes
to complete
Rational
(BLUE) vs. 
Irrational 
(YELLOW).
Circle time-Rational/Irrational

7. Comparing and Ordering
Rational & Irrational Numbers & placing on a Number line

8. Estimating expressions containing irrational numbers
Like estimating square roots, just multiply or divide your estimate.
4 10
Est the sqrt:
So, is between 3 and 4
If I multiply 4*3=12 and 4*4=16
Therefore, is between 12 and 16
More specifically, closer to 3.1 *4= 12.4

9. Estimating expressions containing irrational numbers
Like estimating square roots, just multiply or divide your estimate.
32 2
Est the sqrt:
So, is between 5 and 6
If I multiply 5/2=2.5 and 6/2=3
Therefore, 32 /2 is between 2.5 and 3
More specifically, closer to 5.7 /2= 2.85

10. Ana calculated the lengths of 4 hiking trails.
Length (in km)
Valley View
Butterfly Gulch
2 𝜋
Waterfall Perch
4. 275
Forest Walk
2 5
Ana calculated the lengths of 4 hiking trails.
Because some trails form a triangle or a circle, some lengths have square lengths have square roots or the 𝜋 symbol.
Identify the trails that have irrational lengths. Explain your reasoning.
List the lengths from shortest to longest. Explain your work.

11. Think Back 2.

12. How to Order Numbers Step 1: Change them all to decimals
Step 2:  Plot positive numbers
Step 3:  Begin at zero and plot your negatives to left (remember the negatives are backwards)

13. 1, 2, 3, … 3, 2, 1, … Least to Greatest Ascending Order Increasing
Greatest to Least
Descending Order
Decreasing
3, 2, 1, …

14. Graph on the number line:
How to Order Numbers
Graph on the number line:
Ex 1:
− − 2

15. Step 1-Change all to decimals
How to Order Numbers
Step 1-Change all to decimals
Ex 1:
4 9 =0.44… =1 − − 2 =−1.41

16. Step 2-Plot Positives to Right
How to Order Numbers
Step 2-Plot Positives to Right
Ex 1:
4 9 =0.44… =1 − − 2 =−1.41
4 9 1

17. Step 3-Plot Negatives to left
How to Order Numbers
Step 3-Plot Negatives to left
Ex 1:
4 9 =0.44… =1 − − 2 =−1.41
4 9
−0.5 1
− 2

18. Line ‘Em Up Activity
At each station, teams will work to put numbers on the number line. 

19. Line ‘Em Up Activity For example, my group has the following numbers:
-5.1,  20%, ½, 5 , -11/2
-5.1, 0.2, 0.5, 2.3?, -5.5

20. Line ‘Em Up Activity Check on desmos: ​

21. Line ‘Em Up Activity %
Ex 1

22. Line ‘Em Up Activity %
Ex 1

23. Line ‘Em Up Activity
Ex 2
Pink Team
− − %
− − −7.8

24. Line ‘Em Up Activity Pink Team 52 − 5 − 25 450% − 12 − 25 4 −7.8 Ex 2
− − %
− − −7.8
After ordering, have them go back and label I for Irrational or R for Rational

25. Line ‘Em Up Activity Yellow Team 9 3.5 400% 10 325%
Ex 3
Yellow Team
% % %

26. Line ‘Em Up Activity Yellow Team 9 3.5 400% 10 325%
Ex 3
Yellow Team
% % %

27. Exit Ticket 1.

28. Irrational numbers. Practice your script! You have 1.5 mins of video
POOLE FlipGrid
You may partner up. Create examples of Rational & Irrational Numbers. Discuss how to estimate expressions containing
Irrational numbers. Practice your script! You have 1.5 mins of video
Flipgrid.com
2nd CODE:  9e6c1f
3rd CODE:   04f6b9