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6 th Grade Review

6 th Grade Review. Racing Review. Race!. Whole Number Operations. Addition. 1 . 4137 + 739. 2 . 567 +139. 3 . 5602 +8835. 4 . 65391 + 87. 5 . 941372 + 128343. Solutions:. 4,876 706 14,437 65,478 1,069,715. Whole Number Operations. Subtraction. Right or Wrong?.

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6 th Grade Review

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  1. 6th Grade Review

  2. Racing Review

  3. Race! Whole Number Operations Addition 1. 4137 + 739 2. 567 +139 3. 5602 +8835 4. 65391 + 87 5. 941372 + 128343

  4. Solutions: • 4,876 • 706 • 14,437 • 65,478 • 1,069,715

  5. Whole Number Operations Subtraction Right or Wrong? Can you find the mistake? • 345 • - 278 • 57 2. 9864 - 671 9193 3. 149856 - 51743 97113 • 4. 7548362 • 969457 • 6678905

  6. Whole Number Operations Multiplication Learning Partners • Create 3 multiplication problems (do not use more than 3 digits) • Switch with a neighbor • Check your partner’s work

  7. Whole Number Operations Division RACE! • 9954 ÷ 63 • 87 ÷ 3 • 48026 ÷ 37 • 73080 ÷ 20 • 850 ÷ 5 6. 210 ÷ 7 7. 54 ÷ 6 8. 2571 ÷ 3 9. 2992 ÷ 4 10. 63 ÷ 9

  8. 1. 1582. 293. 12984. 36545. 1706. 307. 98. 8579. 74810. 7 Solutions

  9. EQ: How do I solve numerical expressions?

  10. Launch • Draw a real world example of an event that must be done in a certain order Order is important!

  11. Vocabulary Term EXAMPLE Expression – a collection of numbers and operations 11 – 14 ÷ 2 + 6

  12. P - parentheses E - exponents M - multiply D - divide A – add S - subtract Vocabulary PEMDAS EXAMPLE 11 – 14 ÷ 2 + 6 Order of Operations – the rules we follow when simplifying a numerical expression

  13. Order of Operations Which student evaluated the arithmetic expression correctly? Susie!

  14. Using the Order of Operations Example 1 Simplify the expression. 3 + 15 ÷ 5 Divide. 3 + 15 ÷ 5 3 + 3 Add. 6

  15. Using the Order of Operations Example 2 Simplify the expression. 44 – 14 ÷ 2 · 4 + 6 44 –14 ÷ 2 · 4 + 6 Divide and multiply from left to right. 44 –7 · 4 + 6 44 – 28 + 6 Subtract and add from left to right. 16 + 6 22

  16. Using the Order of Operations Example 3 Simplify the expression. 3 + 23 · 5 Evaluate the power. 3 + 23 · 5 Multiply. 3 + 8 · 5 3 + 40 Add. 43

  17. Using the Order of Operations Example 4 Simplify the expression. 28 – 21 ÷ 3 · 4 + 5 28 –21 ÷ 3 · 4 + 5 Divide and multiply from left to right. 28 –7 · 4 + 5 Subtract and add from left to right. 28 – 28 + 5 0 + 5 5

  18. Helpful Hint When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set. Grouping Symbols [ ] ( ) { }

  19. Using the Order of Operations with Grouping Symbols Example 5 Simplify the expression. 42 – (3 · 4) ÷ 6 Perform the operation inside the parentheses. 42 –(3 · 4) ÷ 6 42 –12 ÷ 6 Divide. 42 – 2 Subtract. 40

  20. Using the Order of Operations with Grouping Symbols Example 6 Simplify the expression. A. 24 – (4 · 5) ÷ 4 Perform the operation inside the parentheses. 24 – (4 · 5) ÷ 4 24 –20 ÷ 4 Divide. 24 – 5 Subtract. 19

  21. Using the Order of Operations with Grouping Symbols Example 7 Simplify the expression. [(26 – 4 · 5) + 6]2 The parentheses are inside the brackets, so perform the operations inside the parentheses first. [(26 –4 · 5) + 6]2 [(26 –20) + 6]2 [6 + 6]2 122 144

  22. Using the Order of Operations with Grouping Symbols Example 8 Simplify the expression. [(32 – 4 · 4) + 2]2 The parentheses are inside the brackets, so perform the operations inside the parentheses first. [(32 –4 · 4) + 2]2 [(32 –16) + 2]2 [16 + 2]2 182 324

  23. Try this one on your own! Example 9 3 + 6 x (5+4) ÷ 3 - 7 Step 1: Parentheses 3 + 6 x (5+4) ÷ 3 – 7 Step 2: Multiply and Divide in order from left to right 3 + 6 x9 ÷ 3 – 7 3 + 54÷ 3 – 7 Step 3: Add and Subtract in order from left to right 3 + 18 - 7 Solution: 14

  24. Try another! Example 10 150 ÷ (6 +3 x 8) - 5 Step 1: Parentheses 150 ÷ (6 +3 x 8) – 5 Step 2: Division 150 ÷30 – 5 Step 3: Subtraction 5– 5 Solution: 0

  25. Challenge! Classify each statement as true or false. If the statement is false, insert parentheses to make it true. ( ) false 1. 4  5 + 6 = 44 2. 24 – 4  2 = 40 ( ) false true 3. 25÷ 5 + 6  3 = 23 4. 14 – 22 ÷ 2 = 12 true

  26. Application Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month. Perform the operations in parentheses first. (5 + 3 · 3) · 4 (5 + 9) · 4 Add. Multiply. 14 · 4 56 Sandy ran 56 miles last month.

  27. Application* Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate how many words will she know at the end of seven weeks. Perform the operations in parentheses first. (3 · 4 · 7) + 30 (12 · 7) + 30 Multiply. Add. 84 + 30 Jill will know 114 words at the end of 7 weeks. 114

  28. Application* Denzel paid a basic fee of $35 per month plus $2 for each phone call beyond his basic plan. Write an expression and simplify to find how much Denzel paid for a month with 8 calls beyond the basic plan. $51

  29. Ticket out the door Simplify each expression. 1. 27 + 56 ÷ 7 2. 9 · 7 – 5 3. (28 – 8) ÷ 4 4. 136 – 102 ÷ 5 5. (9 – 5)3 · (7 + 1)2 ÷ 4 35 58 5 116 1,024

  30. Lesson 2 EQ: How can I perform operations with fractions?

  31. Fraction Action Vocabulary Math Dictionary Example

  32. Math Dictionary Fraction Action Vocabulary Example

  33. Adding Fractions 1. 1/5 + 2/5 2. 7/12 + 1/12 3. 3/26 + 5/26 With Like Denominators!

  34. Adding Fractions With Different Denominators! 1. 2/3 + 1/5 2. 1/15 + 4/21 3. 2/9 + 3/12 • Steps: • Find the LCD • Rename the fractions to have the same LCD • Add the numerators • Simplify the fraction

  35. Subtracting Fractions 1. 3/5 - 2/5 2. 7/10 – 2/10 3. 21/24 – 15/24 With Like Denominators!

  36. Subtracting Fractions With Different Denominators! 1. 2/3 – 4/12 2. 4/6 – 1/15 3. 2/12 – 1/8 • Steps: • Find the LCD • Rename the fractions to have the same LCD • Subtract the numerators • Simplify the fraction

  37. Multiplying Fractions 1. 2/9 x 3/12 2. ½ x 4/8 3. 1/6 x 5/8 • Steps: • Multiply the numerators • Multiply the denominators • Simplify the fraction

  38. Dividing Fractions • Steps: • Keep it, change it, flip it! • Multiply the numerators • Multiply the denominators • Simplify the fraction 1. 2/10 ÷ 2/12 2. 1/8 ÷ 2/10 3. 1/6 ÷ 3/15 Keep it, Change it, Flip it!

  39. Lesson 3 More with fractions

  40. Fraction Action Vocabulary Math Dictionary Example

  41. Changing Improper Fractions to Mixed Numbers • Steps: • Divide • Remember…First come, first serve 1. 55/9 2. 39/4 3. 77/12 Divide!

  42. Changing Mixed Numbers to Improper Fractions • Steps: • Multiply the whole number by the denominator • Add the result to the numerator (that will be your new numerator) • The denominator stays the same 1. 2. 3. Check Mark Method

  43. Operations with Mixed Numbers 1. 2. • Steps: • Convert both mixed numbers to an improper fraction • Follow the necessary steps for the given operation • Simplify

  44. Equivalent Fractions True or False? • 3/8 = 375/1000 • 18/54 = 23/69 • 6/10 = 6000/1000

  45. Solutions: • True • True • False

  46. Fraction BINGO Homework: handout

  47. Lesson 4 EQ: How do I perform operations with decimals?

  48. Decimals Math Dictionary • A way to represent fractions • EX: • Look at the last decimal place…that place value is the denominator of the fraction • 2. The numbers to the right of the decimal are the numerator

  49. Place Value Math Dictionary • The value of a digit based on its position in a number

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