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October 15, 2007

Bellwork: Overhead Problems

Times Tables for 3’s.

Write out all integer operations rules

1. -4x = 32

2. x/7 = 5

3. x + -12 = 3

Page 179, problems 43 – 54.

Notes: Multiples and Divisibility

Multiple – a number that is a product of that number and an integer.

0, 5, 10, 15, 20, 25, 30,

Divisibility – any multiple of a number is divisible by that number

Any multiple of 10 is divisible by 10

Divisibility rules for

2 – A number is divisible by 2 if it is even.

3 – A number is divisible by 3 if the sum of the digits is divisible by 3.

4 – A number is divisible by 4 if the last two digits are divisible by 4.

5 - A number is divisible by 5 if the last digit is 0 or 5.

6 – A number is divisible by 6 if it is divisible by both 2 and 3.

9 – A number is divisible by 9 if if the sum of the digits is divisible by 9.

10 - A number is divisible by 10 if the last digit is 0.

Assignment: Section 3.1 Exercises 1 – 40, pages 177 – 178.

October 16, 2007

Bellwork: Overhead Problems

Times Tables for 4’s

1. X + -12 = 3

2. X/-2 = 3

3. 5X + 7 = -3

4. 7 = X/3 + 10

5. How can you tell if a number is divisible by 3? By 6? By 9?

6. Page 177, 59 – 62.

Notes: Review one and two-step equations

Assignment: Create and Solve 8 one-step equations. Make 2 each of ASMD.

Solve the following.

1. -3 x + 5 = -16

2. x/3 + 12 = 5

3. 28 = 10 + 6x

4. 6 = x/-3 + 15

October 17, 2007

Bellwork: Overhead Problems.

Times tables 6’s.

1. X + -2 = 13

2. X/-5 = 3

3. 5X + 7 = -3

4. 7 = X/3 + 10

5. How can you tell if a number is divisible by 4?

Notes: None

Assignment: In Class Activity – Review 1 and 2 step equations.

October 18, 2007

Bellwork: Overhead Problems

1. -2 + A = -1

2. 13 = B – 13

3. 75 = 25 C

4. 5 = D/-10

5. 7 E – 16 = 12

6. 7 = F/6 - - 4

Notes: Factorizations

- List all factors of a number

- 20: 1, 2, 4, 5, 10, 20

Prime - Only factors are one and itself.

Composite – Has more than 2 factors

Prime Factorization – all prime factors whose product is the number

- Bottom of a factor tree is a prime factorization.

Assignment: Section 3.2 Exercises 1 – 56, pages 184 – 185.

October 19, 2007

Bellwork: Overhead Problems

Times Tables for 7’s

1. 5x - -13 = -7

2. X/-4 + 15 = 6

3. Prime Factorization of 84.

4. A number is divisible by 6 if it _____________.

Page 195, Problems 67 – 72.

Notes: Fractions and Fraction Notation

Fractions – Numerator/Denominator

If a pizza is cut into 8 pieces and 5 pieces are left…

5/8 of the pizza is left.

3/8 of the pizza is eaten

Parts of an inch ½’s ¼’s 1/8’s 1/16’s (Paper folding activity)

Ratio – comparison of 2 numbers (like a fraction, right?)

- The order of the numbers is important.

o Culleoka’s basketball team plays 28 games. They win 22 and lose 6.

o What is the ratio of wins to losses?

o What is the ratio of wins to total games played?

o What is the ratio of losses to total games played?

Anything divided by itself is one. 8 pieces of pizza is left out of 8 total pieces.

8/8 = 1

Zero divided by anything is zero. 0 pieces of pizza is left out of 8 total pieces.

0/8 = 0

Anything divided by zero is not defined. 8 pieces of pizza is left out of 0 total pieces.

8/0 = undefined.

Anything divided by 1 is itself. 8/1 = 8

Assignment: Section 3.3 Exercises 1 – 64, pages 192 – 195, you may omit any 5 problems.

October 22, 2007

Bellwork: Overhead Problems

Times Tables for 8’s

1. 3x - -20 = 35

2. X/-8 + -4 = -6

3. Prime Factorization of 100.

4. A number is divisible by 3 if it _____________.

Page 203, Problems 53 – 64.

Notes: Multiplying Fractions

Fraction times an Integer 4 (2/3)

Multiply the integer by the numerator, keep same denominator.

8/3

Fraction times a Fraction

Multiply numerators by numerators, denominators by denominators.

2/3 x ¾ = 6/12

The high school is 4/13 of all the students at Culleoka Unit School. 1/5 of the students at Culleoka have some Indian ancestry. What fraction of CUS is high school Indians? 4/13 x 1/5 = 4/65

Assignment: Section 3.4 Exercises 1 – 50, pages 201 – 202.

October 23, 2007

Bellwork: Overhead Problems

Times Tables for 9’s

1. 12x - -1 = -35

2. X/6 + 6 = 6

3. Prime Factorization of 45.

4. A number is divisible by 6 if it _____________.

Page 211, Problems 71 - 80.

Notes: Simplifying Fractions

Equivalent fractions

- multiply a fraction by 1, get the same fraction.

- ¾ x 5/5 = 15/20 SO… ¾ = 15/20

- Use a pizza example ½ = 2/4 = 4/8 = 8/16

Reducing

- 18 (Use factoring) 2 x 3 x 3 = 3 x (2 x 3) = 3

24 2 x 2 x 2 x 3 2 x 2 (2 x 3) 4

- 105 = 21 x 5 = 21 = 7 x 3 = 7

135 27 x 5 27 9 x 3 9

Canceling – cancel out obvious like factors if you can.

512/1024 (Both are even – “cancel out” a factor of 2

256/512 (and so on)

Checking for equality

Cross multiply - if equal, then fractions are equal.

- if not equal, the larger number is the larger fraction

Assignment: Section 3.5 Exercises 1 – 68, pages 210 – 211.

October 24, 2007

Bellwork: Overhead Problems

Times Tables for 7’s

1. -x - -13 = -19

2. X/-9 + 6 = 3

3. Prime Factorization of 120.

4. A number is divisible by 2 if it _____________.

Page 221, Problems 73 - 78.

Notes: Reciprocals and Division

Reciprocal of a fraction

– just flip it.

– Product is 1.

– 0 has no reciprocal.

– To divide fractions, you must multiply by the reciprocal!

o ¾ ÷ 1/2

o ¾ ● 2/1

o 3/2

o 12 ÷ 2/3

o 12 ● 3/2

o 18

Solving Equations with Fractions

Get rid of a fraction coefficient by multiplying by the reciprocal

4/5 x = 5

5/4 ● 4/5 x = 5 ● 5/4

x = 25/4

Assignment: Section 3.7 Exercises 3 – 54, every 3^rd problem, pages 225 – 226.

Section 3.8 Exercises 1-36, 3 problems out of every 10 (at least one even problem per 3), pages 231-232.

October 25, 2007

Bellwork: Overhead Problems

Times Tables for 12’s

1. 2x - -13 + 3x = -7

2. 10 + X/-4 + 5 = 6

3. Prime Factorization of 128.

4. A number is divisible by 5 if it _____________.

Page 226, Problems 57 - 54.

Notes: Multiplying, Simplifying, and Area

Review multiplying and simplifying fractions.

Simplifying

- Divide both numerator and denominator by a common factor.

- Write out num/denom with prime factorizations. Cancel out common factors.

Multiplying

- Integer x Num/Denom

- Num x Num/Denom x Denom

- Cross cancel if you can.

Example.

48 people are coming to a dinner. The cook need 2/3 lb. salmon for each couple. How many lbs of salmon are needed?

Find area of a tiny kite. 20 inches long, 15 inches wide, widest part is 5 inches from the end. Area of a Triangle A = ½ b h (2 triangles, right?)

Find the area of the front of a house. Walls are 10 feet tall, 30 feet wide. Top of roof is 15 feet tall. Area of a Rectangle A = L W (a triangle and a rectangle, right?)

Area units are always squared.

Length units are not.

Assignment: Section 3.6 Exercises 1 – 20, 45, 49, 50, 53, 57, 61, 67, OR Exercises 1 – 40, and 67, pages 216 – 220.

October 26, 2007

Bellwork: Overhead Problems

Times Tables 3’s.

1. 8x - -9 + 2x = -11

2. 23 + X/-3 - 15 = 6

3. Prime Factorization of 68.

4. A number is divisible by 6 if it _____________.

5. 2x - -4 + 3x = -6

6. 12 + X/-2 - 13 = 7

7. Prime Factorization of 48.

8. A number is divisible by 9 if it _____________.

9. Find the area of a triangle b = 12 h= 5 A = 1/2bh

10. 4/7 / 8/21

Summary and Review, Exercises 1 – 59, pages 235 – 237.

Notes: None (prepare for test)

Assignment: Chapter 3 Test

Chapter Three Test A

Do not write on this test. Simplify all answers, but improper fractions are ok.

If you have to add, subtract, multiply, or divide, you must show all work.

1. 3x + 12 = -12

2. x/-4 – 7 = -15

3. 12084 Divisible by 2, 3, 5, 6, 9, 10? List all.

4. List three prime numbers less than 20.

5. Simplify

a. 0/-4

b. 6/24

c. -8A/1

d. 15/0

6. Find the reciprocal of each.

a. 2/5

b. -5

c. 3x

7. Greater, Less, or Equal?

a. 7/12 ___ 5/8

b. 4/5 ____ 20/25

8. Simplify

a. 2/9 ● 7/5

b. 3A ● 2/5

9. Simplify

a. 21 ÷ 7/2a

b. 21/30 ÷ 14/15

10. A=½BH

October 29, 2007

Bellwork: Overhead Problems

Times Tables 3’s

1. 8 + 7x = -13

2. 3 = 5 + m/-4

3. 5/6 ● 3/10

4. 4/7 ÷ 16/21

Page 251, Problems 49 - 53

Notes: Least Common Multiples

- Multiple is the product of a # and any other number

Multiples of 10 are 0, 10, 20, 30, 40, …

- The smallest number that is a multiple of two natural numbers

- Method 1: Listing – list multiples of each number until you have one in common

o Ok for smaller numbers Ex. 6 and 8.

o Check to see if one of the numbers is a multiple of the other. If so, the LCM is the larger number.

- Method 2: Prime Factorizations – After finding the prime factorization of each number (could be more than 2 numbers, could contain variables), list each factor the greatest number of times that it appears in any factorization, then multiply them.

Assignment: 4.1 Exercises 1 – 43, odd (45 and 46 for extra credit) Must show work! Pages 250 – 251.

October 30, 2007

Bellwork: Overhead Problems

Times Tables 6”s

1. 4x + 13 = -11

2. w/-5 + -18 = -9

3. 2/7 ● 7/10 =

4. 3/8 ÷ ¼ =

5. Simplify

a. 0/4 =

b. 5a/1 =

c. -8/0 =

6. Find the reciprocal

a. 4/5

b. -2

c. 7m

7. Find the LCM of 12 and 20.

Notes: Adding and Ordering Fractions

- Adding Fractions with like denominators

o Add numerators while keeping same denominator.

o Simplify if possible.

o 2/9 + 5/9 = 7/9

- Adding Fractions with unlike denominators

o Find least common denominator (LCD)

o This is the LCM of the denominators.

§ Remind the students what LCM is.

o Find equivalent fractions using the LCD.

o Add numerators while keeping same denominator.

o Simplify if possible.

o 3/5 + ¼ …. 12/20 + 5/20 = 17/20

- Ordering Fractions

o Find equivalent fractions using LCD.

o Use >, <, or put in order.

Assignment: 4.2 Exercises 1 – 20 all, 21- 72 every third problem, do # 65 instead of 66, Must show work! Pages 259 – 262.

October 31, 2007

Bellwork: Overhead Problems

Times Tables 7’s

1. 9x + -10 = 17

2. 3456 Divisible by 2, 3, 5, 6, 9, 10? List all.

3. List the first 5 prime numbers.

4. Simplify

a. 0/-2

b. 6/42

c. -12R/1

d. 15/0

5. Find the reciprocal of each.

a. 2/3

b. 2

c. 5x

6. Greater, Less, or Equal? 3/11 ___ 7/19

7. Simplify

a. 8/9 ● 9/16

b. 2/3 ● 7A

8. Simplify 9/22 ÷ 3/11

9. A=½BH

Notes: None

Assignment: Redo your chapter 3 test as if your first attempt was a “rough draft” and you are making a “final copy”.

1. All work is neat.

2. All calculations are shown.

3. Answers are circled or underlined.

4. Each answer is a clear communication of

a. What is the problem?

b. How did you determine the solution?

c. The solution.

5. Make this represent the best work you can do.

6. Turn in

a. Test questions

b. First Test (rough draft)

c. Second Test (final draft)

November 1, 2007

Bellwork: Overhead Problems

Make up and solve problems

1. A two step equation.

2. A divisibility rules problem.

3. A prime # problem.

4. A simplifying fractions problem.

5. A multiplying fractions problem.

6. A dividing fractions problem.

7. A >< with fractions problem.

8. A reciprocal problem.

9. An area of a triangle problem.

Notes: None

Assignment: Retake Chapter 3 Test

Make an answer sheet.

Chapter Three Test A

Do not write on this test. Simplify all answers, but improper fractions are ok.

If you have to add, subtract, multiply, or divide, you must show all work.

1. 8x + 12 = -20

2. -11 = x/-5 – 7

3. 765 Divisible by 2, 3, 5, 6, 9, 10? List all.

4. List three prime numbers from 10 to 20.

5. Simplify

a. 0/-9

b. 9/24

c. -2A/1

d. -9/0

6. Find the reciprocal of each.

a. 3/8

b. -6

c. 7x

7. Greater, Less, or Equal?

a. 4/9 ___ 7/15

b. 2/5 ____ 8/25

8. Simplify

a. 4/9 ● 3/12

b. 4M ● 2/5

9. Simplify

a. 28 ÷ 7/2a

b. 15/32 ÷ 5/16

10. A=½BH

November 2, 2007

Bellwork: Overhead Problems

Times Tables 8’s

1. 17 + 5x = -8

2. 16 = 19 + m/-3

3. 4/9 ● 5/12

4. 15/16 ÷ 9/10

Page 271, Problems 73 – 82.

Notes: Subtracting Fractions

- Just like adding fractions…

- Subtracting Fractions with like denominators

o Subtract numerators while keeping same denominator.

o Simplify if possible.

o 5/9 - 2/9 = 7/9

o (Changing minus to a plus and sign of next number is still a good thing – but many times we still must subtract.)

- Subtracting Fractions with unlike denominators

o Find least common denominator (LCD)

o This is the LCM of the denominators.

o Find equivalent fractions using the LCD.

o Subtract numerators while keeping same denominator.

o Simplify if possible.

o 3/5 - ¼ …. 12/20 - 5/20 = 7/20

- Ordering Fractions

o Find equivalent fractions using LCD.

o Use >, <, or put in order.

Assignment: 4.3 Exercises 1 – 20 all, 21 – 70 complete 5 of every 10, Must show work! Pages 268 – 271.

November 5, 2007

Bellwork: Overhead Problems

Times Tables 9’s

1. 3 + 4x = -5

2. 3 = 4 + m/-5

3. 3/10 ● 20/21

4. 6/7 ÷ 3/14

5. 3/5 + 6/7

6. 8/9 – 3/4

Page 278, Problems 43 – 50, omit 47.

Notes: Solving Equations with Fractions

- Review 2 step equations

- With fractions, follow the same exact rules as 2 step equations with integers.

- 3/4x + 1/6 = 3/8

+-1/6 +-1/6

3/4x = 9/24 + -4/24

3/4x = 5/24

x4/3 x 4/3 (now cross cancel)

x = 5/18

- 12 + 5/7x = 9

+-12 +-12

5/7x = -3

x 7/5 x 7/5

x = -21/5

Assignment: 4.4 Exercises 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 21, 22, 25, 26. Must show work! Pages 277 – 278.

Quiz 1

Quiz A

1. 9 + -3x = -12

2. 2/3 ● 15/16

3. 4/5 ÷ 12/25

4. 1/3 + 5/8

5. 8/7 – 4/9

Quiz B

1. 13 = -15 + -4x

2. 5/9 ● 9/10

3. 7/8 ÷ 35/36

4. 3/4 + 5/7

5. 8/5 – 4/3

November 6, 2007

Bellwork: Overhead Problems

Times Tables 11’s

1. 5 + 8x = -9

2. 7 = 8 + m/-9

3. 3/8 Divided by 9/12

Notes: Solving Equations with Fractions (Review)

- Review 2 step equations

- Review 2 step equations w/fractions.

- 3/5x + ¾ = 7/10

- 4 + 7/8x = 1/3

Assignment: 4.4 Exercises 3, 4, 7, 8, 11, 12, 15, 16, 19, 20, 23, 24 (only the ones not done on 7 Nov), Must show work! Pages 277 – 278.

Quiz (Must Show Work! Circle solutions)

A B

1.	4 + 6x = 8	1.	2 + 5m = 8
2.	4 = 6 + x/-8	2.	2 = 5 + m/-9
3.	X + 2/5 = 7/8	3.	M – 4/9 = -3/4
4.	4/3 – 5/6x = 3/2	4.	-3/4 = -5/6 – 1/2x

November 7, 2007

Bellwork: Overhead Problems

Times Tables 12’s

1. 7 + 2x = -14

2. 7 = 2 + m/-3

3. 2/7 Divided by 3/8

Exercises 55 – 60, page 285.

Notes: Mixed Numbers

- Review ADDING FRACTIONS (most are doing it wrong)

- has both an integer and a fraction

- 4 ½ means 4 + ½

- Fraction notation

o 4 ½ = 9/2 (what we’ve done all along so far)

o Integer x denominator + numerator then keep same denominator.

- Convert from fraction notation to mixed number by dividing.

Assignment: 4.5 Exercises 1 – 52, Must show work! Pages 284 – 285.

Quiz 2

A B

1.	7 + -2x = 13	1.	-5 + 4m = 23
2.	X + 2/3 = 4/5	2.	M – 4/5 = -3/4
3.	1/3 – 3/4x = -1/5	3.	-3/4 = -1/6 – 2/3x

November 8, 2007

Bellwork: Overhead Problems

Times tables 9’s

1. 7x – 4 = -39

2. 3 = 15 + m/2

3. 2/9 ● ½ =

4. ½ ÷ 4/7 =

5. 2/5 x + 3/8 = 2/3

Notes: None

Assignment: Page 278, 29 – 42, omit 41

Quiz 3

A B

1.	4 + -2x = 20	1.	-8 + 2m = 28
2.	X + 1/3 = 5/6	2.	M – 2/5 = -3/10
3.	1/4 – 3/5x = -1/8	3.	-3/4 = -5/8 – 1/4x

November 9, 2007

Bellwork: Overhead Problems

1. 6 5/7 to improper

2. 37/7 to mixed #

3. ¾ ● 7/8

4. 4/9 ÷ 2/3

5. x/-2 – 10 = -5

6. 3/5x= 4/7

7. x + 4/5 = 4/7

8. 14 = -6x – 4

Notes: None

Assignment: None (Veteran’s Day Program)

November 12, 2007

Bellwork: Overhead Problems

Times tables 9’s

1. a. 4 ¾ to a improper b. 34/3 to a mixed number.

2. 2/3 ● ½ =

3. ½ ÷ 1/3 =

4. 1/3 + 2/5 =

5. 5x – 7 = -27

6. 2/3 = 3/4 + m/2

Notes: None (Evacuation Procedures drill)

Assignment: None

November 13, 2007

Bellwork: Overhead Problems

Times Tables 12’s

1. x + -2/5 = 3/8

2. 5/8 x = 2/3

3. 2/3x + ½ = -1/3

4. 44/5 to mixed

5. 3 6/7 to improper

Notes: Adding and Subtracting Mixed Numbers

- Adding with like denominators

- Adding with unlike denominators

- Adding when sum of fractions is improper.

- Subtracting with like denominators

- Subtracting with unlike denominators

- Subtracting when you must borrow.

o The trick is to add the numerator to the denominator

Assignment: 4.6 Page 293, Exercises 1 – 28, Must show work! .

Quiz 4

A B

1.	4 + -2x = 20	1.	-8 + 2m = 28
2.	X + 1/3 = 5/6	2.	M – 2/5 = -3/10
3.	– 3/5x = -1/8	3.	-3/4 = – 1/4x
4.	29/4 to a mixed #	4.	3 3/8 to improper

November 14, 2007

Bellwork: Overhead Problems

Times Tables 11’s

1. -4/5 + 3/4x = 2/3

2. 39/7 = ?

3. 3/7 Divided by 15/28

Exercises 69 – 76, page 311.

Notes: Multiplication and Division of Mixed Numbers

- Must convert to improper fractions first.

- Follow rules for multiplying/ dividing fractions

- Simplify answer and convert to mixed number.

o Ex 2 ½ x 3 1/3 (Not 6 1/6)

o 32 divided by 3 1/5 (Careful w/ reciprocal)

o D = RT

§ Speed is 30 mph

§ Time is 1 ¾ hour

§ How far did you drive?

o 4 2/3 Divided by 1 5/6

Assignment: 4.7 Exercises 1 – 36 any 6 problems and 37 – 66 any 6 problems, Must show work! Page 306 - 310.

Quiz 5

A B

12 + x/-3 = 4