1. Warm Up  Grab a handout from the “Algebra Handouts” basket. Sit in the same seat you sat in yesterday. Silently answer the following three questions on the back of your handout: 1.(2 + 6 x 2 + 2 – 4) 2 2.Do we always multiply before we divide? Why or why not?

2. Today’s Objectives  Students will understand how a weekly tracking sheet works.  Students will be able to identify rational and irrational numbers.  Students will be able to estimate the value of irrational numbers.  Students will be able to order rational and irrational numbers from least to greatest.

3. Tracking Sheet  This tracking sheet will make up the portion of your grade that is homework/participation.  Each Monday, you will get a new tracking sheet from the handouts basket.  As soon as you sit down at your desk, you will place it on the top left corner of your desk and your homework on the top right corner of your desk.  Each stamp is worth 5 points. 4 stamps x 5 days = 20 stamps. 20 stamps x 5 points = 100 points. You should earn an easy 100 each week.  What are the 4 possible stamps you can earn each day?  On Fridays, you will place your tracking sheet in Mrs. Inscoe’s inbox on your way out of class. I will not accept late tracking sheets UNLESS you have an excused absence on Friday.

4. Warm Up #2  When is our first quiz?  What do you think is the most important rule in this classroom and why?

5. Homework Questions?  We have time to go over 1 or 2 homework problems IF we need to.

6. Math time  What does the word rational make you think of?  How about irrational?  Do you think those meanings can apply to math as well?

7. Rational Numbers  The “math definition” of rational numbers is that they can be written as a fraction.  Rational numbers are usually numbers that are easier to work with. They make sense, and they aren’t too messy.  Let’s work together to come up with a few examples of rational numbers.  Types of rational numbers:  Integers  Fractions  Terminating or repeating decimals  Square roots of perfect squares** (these are also integers, but you’ll see why I mention them on the next slide)

8. Irrational Numbers  Irrational numbers are messy. They don’t follow a pattern, and they never end.  Irrational numbers always have a decimal, special symbol, or square root sign.  Types of irrational numbers:  Decimals that do NOT repeat or end  Pi  Square root of numbers that are NOT perfect squares.  It’s hard for us to imagine the exact value of irrational numbers, so it helps us to be able to estimate their value.  What does it mean to estimate something?

9. Estimating the value of Irrational Numbers  We can use our knowledge of perfect squares to help us when we’re trying to figure out the value of nonperfect squares.  To start, let’s list some perfect squares together:  Okay, now we have our toolset. Let’s use them to figure out some non-perfect squares!  Between which two consecutive integers does √20 fall?  We know that 20 is in between the perfect squares 16 and 25. The square root of 16 is 4, and the square root of 25 is 5.  So, since 20 is in between 16 and 25, we know its square root must be somewhere in between 4 and 5.  Still tricky? Let’s try a couple more.

10. Estimating the value of Irrational Numbers.  How about these?  √92  √40  -√40  -√5

11. Why is estimating helpful?  It helps us picture in our heads how much a weird looking number actually is.  It also helps us compare these weird, irrational numbers to other numbers and answer the questions:  Which number is bigger?  Which number is smaller?

12. Let’s put our knowledge to good use.  Put the following numbers in order from least to greatest:

13. How about these?  Put the following numbers in order from greatest to least: 20/3, √50, 5.6, 8

14. Work with your group  I will pass out a set of 4 numbers on index cards to each group.  Work with the two other people in your diagonal row to put the numbers in order.  I will come around to ask certain groups why they put their numbers in the order that they did.  When I say “switch” pass your index cards to the next group and repeat.

15. Homework  Complete the worksheet on the back of your guided notes sheet.

16. Cool Down 1.Are the following numbers rational or irrational √25, √37, 3.44444…., 123/15, -2.5? 2.Which two consecutive integers is √30 in between? How do you know? 3.Put the following numbers in order from least to greatest: 5.2, 18/3, √15, π

17. Leaving class  Straighten your desk before you leave the classroom, and take everything with you—don’t forget your homework!  Remember, return to the same desk tomorrow that you sat in today.