Bell Ringer12-15-10

1. What is the 25th term in the sequence 2, 5, 8, 11, …, 3n-1,…

Solve2. 5x = -253. 4x - 6 = 144. 3 + 5x = -125. The area of a square piece of

wrapping paper is 64 in2. Calculate the length of each side.

1. What is the 25th term in the sequence 2, 5, 8, 11, …, 3n-1,…

3n - 1

3(25) - 1

75 - 1 = 74

Position (n) 1 2 3 4

Term 2 5 8 11

The 25th term is 74.

5x = -25

x = -53. 4x - 6 = 14

4x = 20

x = 54. 3 + 5x = -12

5x = -15

x = -3

5 5

6 6

4 4

3 3

5 5

5. The area of a square piece of wrapping paper is 64 in2. Calculate the length of each side.

lwAlw64

864 in8

Quiz12-15-10

Trish works for a straight salary of $32,000 a year plus a commission of 4% on the real estate she sells. Which expression could be used to find her yearly income, if x = the

total value of real estate sold?A. 32,000(0.04)xB. 32,000x + 0.4C. 32,000 – 0.04xD. 32,000 + 0.04x

Which expression can be used?

To find the amount of commission I would convert the % to a decimal and multiply by the amount of real estate sold (x). To find the total income, I would add the commission with the salary.

Trish works for a straight salary of $32,000 a year plus a commission of 4% on the real estate she sells. Which expression could be used to find her yearly income, if x = the total value of real estate sold?

Expression D can be used to find the income.

Salary: $32,0004% commissionx = total real estate sold

)(Re04.

:

talalEstateTo

Commission

xD 04.000,32:

SalaryCommissionIncome

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

#3-41. 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!

Math Sing-A-Long

Project due Monday, January 10 (one week after Christmas

break)

Class Work Pythagorean Theorem

You will create two models of the Pythagorean Theorem.

You will take notes and work examples.

Pythagorean Theorem

If two side lengths of a right triangle are known, you can find the third length by using the Pythagorean Theorem.

Pythagorean Theorem

Leg

Leg

Hypotenuse

The hypotenuse is the longest side!

Pythagorean Theorem

Leg

Leg

Hypotenuse

Legs:

Sides a and b

Hypotenuse:

Always side c

Pythagorean Theorem

a

b

c

Theorem:

a2 + b2 = c2

Pythagorean Theorem

3

4

On your graph paper, draw a 3 by 4 triangle.

Use the ruler to draw the diagonal.

Pythagorean TheoremShade in the squares, representing

the area of each side.

3 92

4 1 62

Pythagorean Theorem• Create a new square by

combining the two areas.

• Cut the square out.

Pythagorean Theorem• Glue the square against the

diagonal of the triangle.

• Count the units.

• Calculate the sides of the square.

2 5 5

5 2 52

Pythagorean Theorem

3

4

c

Theorem:

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

2 5 2 c

5 = c

5

Pythagorean Theorema=8; b=?; c=10

On your graph paper, shade in squares, representing the area of each side.

 

8 6 42 1 0 1 0 02

Pythagorean TheoremCut the squares out.

Lay the smaller square on top of the larger square.

Calculate the number of squares that are not covered.

 

36 squares

Pythagorean Theorem

Create a new square with an area of 36.

 

3 6 66 3 62

Pythagorean Theorem

6 

8

On your graph paper, draw a 6 by 8 triangle.

Use the ruler to draw the diagonal.

Place the 3 different squares on the sides.

Pythagorean Theorem

8

10b

Theorem:

a2 + b2 = c2

82 + b2 = 102

64 + b2 = 100-64 -64

b2 = 36b 2 3 6

b = 66

Pythagorean Theorem• A jogger runs north for 7 miles.

• He then runs East for 4 miles.

• How far away is the jogger from his starting point?

HINT: Draw a Picture.7

4

Pythagorean Theorem

Theorem:

a2 + b2 = c2

72 + 42 = c2

49 + 16 = c2

65 = c2

6 5 2 c

c = 8.1

Guess & Check!7

4

He is 8.1 miles from his starting point.

Pythagorean Theorem

a

cb

If a2 + b2 = c2, then the triangle is a right triangle.

Pythagorean TheoremIf a2 + b2 = c2, then the triangle is a

right triangle.

If a2 + b2 = c2, then the sides are Pythagorean triples.

a=3, b=4, c=5

32 + 42 = 52

9+ 16 = 25

25 = 25

Right triangle

3,4,5 are Pythagorean Triples

Pythagorean TheoremIf a2 + b2 = c2, then the triangle is a

right triangle.

If a2 + b2 = c2, then the sides are Pythagorean triples.

a=2, b=4, c=6

22 + 42 = 62

4+ 16 = 36

20 = 36

Not a right triangle

2, 4, 6 are Not Pythagorean Triples