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Pre-Algebra

Work in groups to research and track the abilities of three baseball players. Learn about divisibility, prime and composite numbers, greatest common factor, factoring, least common multiple, and scientific notation.

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Pre-Algebra

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  1. Pre-Algebra Chapter 3: Number Theory

  2. Chapter Project – 50 points • You will work in groups of 2. • You will research on the internet 3 baseball players. You will track their abilities, using a provided worksheet. • Due at the end of the chapter: _____NOV 24th __

  3. Schedule of Events

  4. Goals for Learning • To identify divisible numbers • To tell prime numbers from composite numbers • To find the greatest common divisor • To use the distributive property to multiply or factor expressions • To find the least common multiple • To use scientific notation for large and small numbers

  5. Lesson 1 – Divisibility Rules • Vocabulary – • Divisible – able to be divided by a whole number with no remainder • Rules: • Divisibility by 2: if the last digit is an even number:0,2,4,6,8 • Divisibility by 3: the sum of the digits is divisible by 3. • Divisibility by 4: last 2 digits divisible by 4. • Divisibility by 5: the last digit is 0 or 5. • Divisibility by 6: if its divisible by 2 or 3. • Divisibility by 8: last 3 digits divisible by 8. • Divisibility by 9: the sum of the digits is divisible by 9. • Divisibility by 10: last digit is 0.

  6. Practice In the textbook, you will notice that they write the statements just like below. 2|12 - this is asking….is 12 divisible by 2?

  7. Homework • Lesson 1 cont. • Homework: Pg 63 #1-20

  8. Lesson 2 – Prime and Composite Numbers • Vocabulary – • Prime – a whole number greater than one that has only 1 and itself as factors • Composite – a whole number that is not a prime number, or who has more than 2 factors.

  9. More Information… • The numbers 0 and 1 are neither prime nor composite. • All even numbers are divisible by two and so all even numbers greater than two are composite numbers. • All numbers that end in five are divisible by five. Therefore all numbers that end with five and are greater than five are composite numbers.

  10. Finding Prime/Composite Numbers: Using a 1-50 chart.

  11. Finding Prime/Composite Numbers: Using Prime Factorization

  12. Homework • Lesson 2 – Prime and Composite Numbers • Homework: Worksheet 24

  13. Lesson 3 – Greatest Common Factor • Vocabulary – • Common Factor – a number that will divide each of two or more number with no remainder • Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) – the largest factor of two or more numbers or terms

  14. Finding the GCD/GCF • Step 1: Find all of the factors. • Step 2: Circle all of the common factors. • Step 3: Choose the GREATEST common factor. • Example: (9,24) • Example 2: (12x, 60x) • Example 3: (18y, 36)

  15. Homework: • Lesson 3: Greatest Common Factor • Homework: Pg. 67 #1-15

  16. Lesson 4 – Factoring • Vocabulary – • Distributive Property – numbers within parenthesis that can be multiplied by the same factor • Examples: • 2(9+2) = • 4r(2-1) = • 3(a+3b-4c)=

  17. Few more examples: • 2(4+3)= • 2(x+5)= • 8(4m+4)=

  18. Factoring Terms • Step 1: List the factors, and find the GCF. • Step 2: Write the GCF outside the parenthesis. • Step 3: Determine what factors will make the original statement true. • Factor: 4x+6. • Factor: 3x+3y. • Factor: ab+ac. • Factor: 4x+7y.

  19. Few more examples: • 9c+3 = • 12y+20= • 6h+36 = • 14m+28k= • 5s+20 = 5(s+__________) • 2c+22d = _____(c+11d) • 7p+28 = 7(_________+4)

  20. Homework: • Lesson 4: More on Factoring • Pg. 70-71 #2-30 even

  21. Lesson 5 – Least Common Multiple • Vocabulary – • Least Common Multiple (LCM) – the smallest number divisible by all numbers in a group. • Multiples are like counting by numbers… • For Example: 2 - M2 – 2,4,6,8,10,12,14,16,18,20, etc. • What are the M5? • M10? • What is the common multiple of (4,9)?

  22. Cont. • LCM of (3,63) • LCM of (9,6) • LCM of (54,120)

  23. Vocabulary Cont… • Prime Factorization – an expression showing the prime factors of a number • Step 1: Construct a factor tree. (54,120) • Step 2: Identify the greatest power of each prime number. • Step 3: Multiply the greatest primes.

  24. More Examples: • LCM (18, 55, 125)

  25. Cont. • LCM (16, 21, 32)

  26. Homework: • Lesson 5 – Least Common Multiple • Pg. 74 #1-12

  27. Lesson 6 – Scientific Notation • Vocabulary – • Scientific Notation – a number written as the product of a number between 1 and 10 and a power of 10. • What is power of 10? Does anyone remember? • What about exponents?

  28. Rules: • When changing a WHOLE NUMBER to a number between 1 and 10, place the decimal point behind the last digit and move the decimal point to the LEFT. • When changing a DECIMAL NUMBER to a number between 1 and 10, move the decimal point to the RIGHT. • 3,500 • 0.073 • 83,000 • 0.00065 • 0.0078 • 768,000

  29. Writing in Scientific Notation • Step 1: Change you number to a number between 1 and 10. • Step 2: Add the power of 10. • If you added a decimal point, your exponent will be positive. • If you moved a decimal point already present, your exponent will be NEGATIVE. • 24,000 • 606,000,000 • 0.00347 • 517,000,000,000 • 0.000438 • 84,000,000,000 • 0.0000947 • 0.000000346

  30. Homework: • Lesson 6 – Scientific Notation • Pg. 77 #1-25

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