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Good Afternoon!

Good Afternoon!. Our objective today will be to review all of the material we have covered in Unit 1. WARM-UP: . Can you use mental math to solve these problems? Don't use your pencil!. = 70 = 310 = 1,000 = 490. 1.) 58 + 12 2.) 638 - 328 3.) 594 + 406 4.) 702 - 212. 12. 3. 4.

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Good Afternoon!

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  1. Good Afternoon! Our objective today will be to review all of the material we have covered in Unit 1. WARM-UP: Can you use mental math to solve these problems? Don't use your pencil! = 70 = 310 = 1,000 = 490 1.) 58 + 12 2.) 638 - 328 3.) 594 + 406 4.) 702 - 212

  2. 12 3 4 1 19 A whole number is DIVISIBLE by another number if the remainder is 0. 2 5 14 18 A whole number is EVEN if it is divisible by 2. 7 A whole number is ODD if it is not divisible by 2. 8 9 15 6

  3. DIVISIBILITY RULES Can you give me some examples?? A whole number is divisible by: 2 if the ones digit is divisible by 2 3 if the sum of the digits is divisible by 3 5 if the ones digit is 0 or 5 10 if the ones digit is 0

  4. DIVISIBILITY RULES The rules for 4, 6, and 9 are related to the rules for 2 and 3. Examples: A whole number is divisible by: 4 if the number formed by the last two digits is divisible by 4 6 if the number is divisible by 2 AND 3 9 if the sum of the digits is divisible by 9

  5. Let's practice some Long Division. 122 8 976 8 976 -8 Check 17 -16 16 -16 0

  6. Remember that when two or more numbers are multiplied, each number is called a FACTOR of the product*. 1 x 6 = 6 and 2 x 3 = 6 1, 6, 2, and 3 are the factors of 6 * Remember that "product" is the answer to a multiplication problem.

  7. How to identify COMPOSITE NUMBERS and PRIME NUMBERS COMPOSITE NUMBER - A number greater than 1 with more than two factors Can you think of a number that we would classify as COMPOSITE? What are its factors?

  8. PRIME NUMBERS A Prime Number is a whole number that has exactly two factors.....1 and itself Can you think of a number like that?

  9. A factor tree can be used to find the PRIME FACTORIZATION of a number. Write the number being factored at the top. 54 54 Choose any pair of whole number factors. x 2 x 18 27 3 Continue to factor any number that is not prime. x x 9 3 2 x 9 x 3 2 Except for the order, the prime factors are the same. 3 x x 3 x 3 x 2 3 x 2 3 x 3 THE PRIME FACTORIZATION OF 54 IS 2 x 3 x 3 x 3

  10. Numbers expressed using Exponents are called Powers

  11. Let's Practice... If we write 3 x 3 x 3 x 3 using an exponent, the base is 3 AND the exponent is 4 . . . 3 3 3 3 = 34 = 81

  12. We can also refer to writing 45 as a PRODUCT OF THE SAME FACTOR (Remember that a "Product" is the answer to a multiplication problem.) The Base is 4. The Exponent is 5. So 4 is a Factor 5 times. 45 = 4 x 4 x 4 x 4 x 4 = 1,024

  13. Exponents can be used to write the Prime Factorization of a number. 24 Example: x 2 12 x x 2 2 6 OR x x 2 2 2 x 3 23 x 3 (Start with the smallest prime factor)

  14. 5 2 4 1 6 3 ANumerical Expressionis a combination of numbers and operations. Examples: 4 + 3 * 5 22 + 6 ÷ 2 (10 * 8) - 7

  15. OrderofOperations Simplifying the expressions inside grouping symbols examples: (3+5) or (4*6) P 1. Parentheses Find the value of all powers examples: 23 or 42 E 2. Exponents M Perform multiplication or division in the order in which it occurs when reading the expression from left to right. 3. Multiplication Division D Perform addition or subtraction in the order in which it occurs when reading the expression from left to right. A 4. Addition Subtraction S

  16. We can remember the OrderofOperations as PEMDAS S P D E A M ddition ivision xponents ubtraction arentheses ultiplication "Please Excuse My Dear Aunt Sally"

  17. "Please Excuse My Dear Aunt Sally" whichever comes first whichever comes first P D S A M E ddition ivision ultiplication xponents ubtraction arentheses 20 ÷ 4 + 17 * (9 - 6) = Do the operations in Parentheses first. There are no Exponents. 20 ÷ 4 + 17 * 3 = Perform Multiplication or Division in the order in which they occur. The Division should be done first. Then perform the Multiplication. 5 + 17 * 3 = Finally perform the Addition. 5 + 51 = 56 =

  18. 3 + n is an "ALGEBRAIC EXPRESSION" Numbers Variables Operations Algebraic Expressions consist of Numbers, Operations, and Variables.

  19. The VARIABLES in an expression can be replaced with any number. 3 + x If I substitute a 5 for the x ........... I have 3 + 5 or 8 This is how we Evaluate (or find the value of) the Expression

  20. Let's Evaluate the Algebraic Expression 16 + b if b = 25 We replace b with the number 25 16 + b = 16 + 25 = 41 41 The Value of the Algebraic Expression when b = 25 is

  21. When solving math problems, it is often helpful to have an organized problem-solving plan. U nderstand P lan S olve

  22. To U nderstand the problem, we need to -read the problem carefully -identify the facts that we know -identify what we need to know (WHAT IS THE QUESTION?) -determine if we have enough or too much information (Many students find it helpful to highlight or underline the important facts in the problem.)

  23. Next, we must P lan -determine how the facts relate to each other -plan a strategy for solving the problem -estimate your answer Key words play an important role in determining which operations to use. Add Subtract Divide Multiply minus difference less quotient plus sum total in all times product of

  24. And finally, we S olve the problem -use your plan to solve the problem -if your plan does not work, revise it or make a new plan -find the solution -make sure the answer makes sense and is close to your estimate Keep in mind that numbers do NOT always appear in a problem in the order in which they should be used to solve the problem.

  25. Our formula for Area would be Area = length x width width length The Area of this rectangle would be 4 x 3 or 12

  26. The rectangle with an area of 24 width is 3 length is 8 Using the formula, the area of this rectangle is Area = length x width Area = 8 x 4 Area = 32 square units

  27. LET US TAKE A BREAK!!

  28. HOW ABOUT SOME PUZZLES?? In the following line, cross out nine letters such that the remaining letters spell a well known animal. ENILNEEPLETHTAENRST Elephant. Cross out the letters NINE LETTERS.

  29. 2.) Use Long Division. 1.) How can I tell if a number is divisible by a.) 2 b.) 3 c.) 4 d.) 5 e.) 6 f.) 9 g.) 10 Example: 164 246 246 0

  30. 1.) What is a Prime Number? Can you give me some examples? A whole number that has exactly two unique factors, 1 and the number itself, is a prime number. Examples: 3, 5, 7, 11 2.) What is a Composite Number? Can you give me some examples? A number greater than 1 with more than two factors, is a composite number. Examples: 6, 9, 12, 15 3.) Tell whether each number is Prime, Composite, or Neither. a. 12 Composite b. 5 Prime c. 1 Neither d. 41 Prime 4.) Write the number 28 as the product of prime numbers. 60 28 = 2 x 2 x 7 x 2 30 5.) Use a factor tree to find the Prime Factorization of 60. x 2 x 2 15 The Prime Factorization of 60 is 22 x 3 x5 x 3 2 x X 5 2

  31. Let's see how well we know Powers and Exponents! 1. Can you write this product using an exponent? 6 x 6 x 6 x 6 = 64 2. Can you find the value of this product? 4 x 4 x 4 = 43 = 64 3. Can you write this power as a product of the same factor? 36 = 3 x 3 x 3 x 3 x 3 x 3 4. Can you find the value of this power? 24 = 2 x 2 x 2 x 2 x 2 = 32

  32. 1.) Can you give me an example of a "Numerical Expression"? 4 + 3 * 5 2.) What do I mean by "Operations"? We “operate” on the numbers by Adding, Subtracting, Multiplying or Dividing 3.) In what order do I perform the "Operations"? PEMDAS 4.) Find the value of each expression? a.) 5 x 6 - (9 - 4) = 5x6-5 = 30-5 = 25 b.) 16 ÷ 2 + 8 x 3 =8+8x3 = 8+24 = 32 c.) 43 - 24 + 8 = 64-24+8 = 64-16 = 48

  33. 1.) In the Algebraic Expression 14n + 5 - 6m - what are the variables? n, m -what are the numbers? 14, 5, 6 -what are the operations? + , - Evaluate each expression if a = 4, b = 12, and c = 4. 2.) 7c ÷ 4 + 5a = 7 x 4 ÷ 4 + 5 x 4 = 28 ÷ 4 + 20 = 7 + 20 = 27 3.) b2÷ ( 3 X c) = 122÷ (3 x 4) = 122 ÷ 12 = 144 ÷ 12 = 12

  34. Problem Solving 1.) In 1990, the population of Sacramento, CA was 370,000. In 2000, the population was 407,000. How much did the population increase? Increase in population = Population in 2000 – Population in 1990 = 407,000 – 370,000 = 37,000 2.) The Smith family wants to purchase a television set and pay for it in four equal payments of $180. What is the cost of the television set? Cost of TV set = 4 x 180 = $ 720 3.) Complete the pattern: 36 26 31 6, 11, 16, 21, ___, ___, ___

  35. Area Problems 1.) What is the formula we use to find the area of a rectangle? The area A of a rectangle is the product of the length l and width w. A = l x w 2.) How would we find the area of a square? A = l2 3.) Find the area of each rectangle. 27 cm 11 ft 19 ft 6 cm A = 19 x 11 = 209 A = 6 x 27 = 162 4.) Find the width of this rectangle. 84 yd A = l x w 3360 = 84 x w W = 3360/84 = 40 yd ? yd 3360 yd2

  36. Congratulations! You really understand what we have covered in the first unit!

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