Transcript pefect squares and irrational numbers - Mrs-Cook-8th

Bell Ringer
12-14-10
1. Create a table and write an expression for
the sequence
6, 13, 20, 27,….
Solve
2. -3x = 18
3. 2x + 5 = 17
4. -2 + 4x = 10
5. You go to the store to buy a $20 present
for Mrs. Cook. The tax rate is 8%. The
total comes out to $36. Will you pay this?
Explain.
1. Create a table and write an expression
for the sequence
6, 13, 20, 27,….
7n - 1
7(1) - 1
7-1=6
Position (n) 1 2 3 4
Term
6 13 20 27
7(2) - 1
14 - 1 = 13
7(3) - 1
21 - 1 = 20
7(4) - 1
28 - 1 = 27
-3x = 18
3 3
x = -6
3. 2x + 5 = 17
5 5
2x = 12
2
2
x=6
4. -2 + 4x = 10
2
2
4x = 12
4
x=3
4
5. You go to the store to buy a $20
present for Mrs. Cook. The tax rate is
8%. The total comes out to $36. Will
you pay this? Explain.
Absolutely NOT!
A total of $36 means you are paying $16
in tax for a $20 item. This is way too
much. It should only be $1.60 in tax.
Instead of paying .08 per dollar, you
were charged .80 per dollar.
Quiz
12-14-10
Tara bought three DVDs at the same
price and paid $4.07 in sales tax.
She spent $54.92 in all. How much
did each DVD cost?
Tara bought three DVDs at the same price and paid $4.07 in sales tax. She spent
$54.92 in all. How much did each DVD cost?
How much was each
DVD?
$54.92  $4.07  $50.85
3 DVDs
Tax: $4.07
Total: $54.92
To find the total spent on the DVDs before
tax, I subtracted the amount of tax from the
total paid. I divided this amount by 3 (the
number of DVDs) to calculate the cost for
one DVD.
$50.85
 $16.95 / DVD Each DVD was $16.95.
3
Speed Test
1. Get out a dry erase marker.
2. You have 1 minute to complete as
many problems as you can.
3.We will grade in 1 minute.
4. Graph your results. Keep the graph in
your notebook.
5. We will do this every day.
Problem of the Week &
Word Problem
#3-4
1. You have 5 minutes to work on the
problem of the week and word problem.
2. The problem of the week must follow
the Read, Think, Solve, Justify format.
3. When you are finished, turn them in.
4. They are due Friday.
Accelerated Math
1. You have 10 minutes to work on your
accelerated math.
2. Work out every problem.
3. When you complete the practice
problems, bring them to me. If you
have worked them all, I will allow you to
submit your answers.
4. This is INDIVIDUAL…NO TALKING!
Class Work
Perfect Squares Chart
Create the Perfect Squares Chart
Fill in the Dimensions, Square, and
Square Root Columns
We will go over this in 15 minutes
Class Work:
Perfect Squares &
Irrational Numbers
You need your notes. Title the notes:
Perfect Squares & Irrational Numbers
I will check your work at the end of class.
Perfect Squares
1. Calculate the square of 7
7  49
2
2. Calculate the square root of 81.
81  9
3.
121  ?
121  11
Irrational Squares
4.
5 ?
This is an example of an irrational
number. The answer will not be a whole
number.
Irrational Squares
5 ?
Place the irrational square between two
consecutive perfect squares.
4 5 9
Irrational Squares
4 5 9
Place the irrational square between two
consecutive integers.
2 5 3
Irrational Squares
2 5 3
Determine the range of answers.
Between 2 and 3
Go to the Tenths place
Range = 2.1 – 2.9
Irrational Squares
1
4
4 5 9
2 5 3
Range = 2.1 – 2.9
Determine which perfect square the
irrational square is closest too.
5 is closer to 4, so the square root of 5
is closer to 2.
Irrational Squares
2 5 3
Range = 2.1 – 2.9
Guess and check
(You want the answer that is
closest to the irrational square)
What # when multiplied by itself = 5?
Since it is closer to 2, we are going to
start on the low end.
Irrational Squares
2 5 3
Range = 2.1 – 2.9
2.1 2.1  4.41
2.2  2.2  4.84
2.3 2.3  5.29
I have found the number right
above and below 5.
Irrational Squares
2 5 3
2.2  2.2  4.84
2.3 2.3  5.29
Find the number closest to 5
5.00  4.84  0.16
5.29  5.00  0.29
Which number is closest to 5?
5  2.2
Irrational Squares
39  ?
Place the irrational square between two
consecutive perfect squares.
36  39  49
Irrational Squares
36  39  49
Place the irrational square between two
consecutive integers.
6  39  7
Irrational Squares
6  39  7
Determine the range of answers.
Between 6 and 7
Go to the Tenths place
Range = 6.1 – 6.9
Irrational Squares
3
10
36  39  49
6  39  7
Range = 6.1 – 6.9
Determine which perfect square the
irrational square is closest too.
39 is closer to 36, so the square root of
39 is closer to 6.
Irrational Squares
6  39  7
Range = 6.1 – 6.9
Guess and check
(You want the answer that is
closest to the irrational square)
What # when multiplied by itself = 39?
Since it is closer to 6, we are going to
start on the low end.
Irrational Squares
6  39  7
Range = 6.1 – 6.9
6.2  6.2  38.44
6.3 6.3  39.69
I have found the number right
above and below 39.
Irrational Squares
6  39  7
6.2  6.2  38.44
6.3 6.3  39.69
Find the number closest to 39
39.00  38.44  0.56
39.69  39.00  0.69
Which number is closest to 39?
39  6.2
Irrational Squares
115  ?
Place the irrational square between two
consecutive perfect squares.
100  115  121
Irrational Squares
100  115  121
Place the irrational square between two
consecutive integers.
10  115  11
Irrational Squares
10  115  11
Determine the range of answers.
Between 10 and 11
Go to the Tenths place
Range = 10.1 – 10.9
Irrational Squares
15
6
100  115  121
10  115  11
Range = 10.1 – 10.9
Determine which perfect square the
irrational square is closest too.
115 is closer to 121, so the square root
of 115 is closer to 11.
Irrational Squares
10  115  11
Range = 10.1 – 10.9
Guess and check
(You want the answer that is
closest to the irrational square)
What # when multiplied by itself = 115?
Since it is closer to 11, we are going to
start on the high end.
Irrational Squares
10  115  11
Range = 10.1 – 10.9
10.7 10.7  114.49
10.8 10.8  116.64
I have found the number right
above and below 115.
Irrational Squares
10  115  11
10.7 10.7  114.49
10.8 10.8  116.64
Find the number closest to 115
115.00 114.49  0.51
116.64 115.00  1.64
Which number is closest to 115?
115  10.7
Class Work
Solve
1. 36
6. 98
11. 62
16. 10
2. 41
7. 152
12. 75
17. 146
3. 193
8. 205
13. 144 18. 208
4. 11
9. 81
14. 54
19. 43
5. 84
10. 27
15. 38
20. 64