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Announcements 3/12

Announcements 3/12. Homework Weekly math Corrections Exponents practice Properties Worksheet New late policy for 6 th grade: -1 day late = -10 -after 1 day late = 50%. Warm Up - Wednesday. Write a positive or a negative number to represent each situation: You owe $25

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Announcements 3/12

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  1. Announcements 3/12 • Homework • Weekly math Corrections • Exponents practice • Properties Worksheet New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50%

  2. Warm Up - Wednesday • Write a positive or a negative number to represent each situation: • You owe $25 • A team has a gain of 20 yards in a football game • Two floors below ground level • 15 degrees above 0⁰C • A stock price fell 4.26 points • Use the GCF and distributive property to write 18 + 45 as a product. Then check your answer.

  3. Review Homework • Go write new vocabulary in math notebook – you create examples that include variables • Then come show me your properties homework

  4. Opening Exercise • As you evaluate these expressions, pay attention to how you arrive at your answers: • 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 • 9 + 9 + 9 + 9 + 9 • h + h + h + h What were some methods you used to evaluate these expressions? - addition -multiplication Which is the more efficient way to evaluate them?

  5. Discussion • When we add five groups of 10, we use an abbreviation and a different notation, called multiplication • 10 + 10 + 10 + 10 + 10 + 10 = • If multiplication is a more efficient way to represent addition problems involving the repeated addition of the same addend, do you think there might be a more efficient way to represent the repeated multiplication of the same factor, as in 10 · 10 · 10 · 10 · 10 = ?

  6. Discussion • Exponents = repeated multiplication • 10⁵ : 10 is the base and 5 is the exponent (superscript) • 10 to the fifth power

  7. Practice Put repeated multiplication in exponential form and exponential form into repeated multiplication. Then evaluate. • 5 · 5 · 5 · 5 · 5 = • 2 · 2 · 2 · 2 = • 8³ = • 10⁶ = • g³ =

  8. Practice • Bases can be in decimal or fraction form • 3.8⁴ • 2.1² • 0.75³ • (½)³ • (⅔)²

  9. Discussion • #s raised to the second power are called squared • In Geometry, squares have 2 dimensions: ___________ and ________ • #s raised to the third power are called cubed • 5 squared? • 7 squared? • 8 squared? • 1 squared?

  10. Discussion • #s raised to the third power are called cubed • In Geometry, cubes have 3 dimensions: ___________, __________, and ___________ • 1 cubed? • 2 cubed? • 3 cubed?

  11. If n > 1 4ⁿ = (4 · 4 ··· 4) n times For any x, x¹ = x For any x(except 0), x⁰ = 1 What does the x represent? What does the n represent?

  12. Discussion • With our definition, how would we represent 4ⁿ? • How would we represent 4n?

  13. Exercises

  14. Closing Discussion • Exponents = ___________________ • Write exponents as _____________

  15. Homework

  16. Announcements 3/13 • Homework • Weekly math Corrections • Distributive Property worksheet • Quiz on Friday or Monday over Exponents, Order of Operations, and Properties New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50%

  17. Warm Up - Thursday • Jackson wants to buy the same number of stamps and envelopes. Stamps are sold in packs of 6. Envelopes are sold in packs of 4. What is the least number of stamps and envelopes Jackson will have to buy? How many packs of each? • Students at Crestdale have a goal of collecting 1,000 lbs of recycling material each month. Complete the table.

  18. Review Homework • Bring me homework (Exponents and Properties) • Copy homework into notebook • Complete the Exponents exercise sheet • Talk about why 3⁰ = 1

  19. Opening Exercise • Evaluate : 3 + 4 · 2 • Without knowing the Order of Operations, how could you evaluate this expression?

  20. Discussion • Addition = shortcut to “counting on” • Subtraction = shortcut to “counting back” • Learned 1st because they are the least complicated • Early mathematicians believed the 2 operations were equally powerful and are evaluated from LEFT to RIGHT • Multiplication = repeated _________ • Division = repeated __________ • More powerful than addition and subtraction • Early mathematicians believed multiplication and division are equally powerful and are evaluated from LEFT to RIGHT

  21. Discussion • 3 + 4 · 2

  22. Practice • Expressions with Only Addition, Subtraction, Multiplication, and Division • What operations are evaluated first? • What operations are always evaluated last? • 4 ÷ 2 · 7 • 36 ÷ 3 · 4 • 20 – 5 · 2

  23. Stretch Break

  24. Discussion • Exponents was repeated _____________ • Exponents are considered more powerful than multiplication or division so they will be evaluated before either of those operations • Evaluate : 4 + 6 · 6 ÷ 8 • Now evaluate : 4 + 6² ÷ 8

  25. Practice • Expressions with 4 Operations and Exponents 4 + 9² ÷ 3 · 2 - 2 • What operation is evaluated first? • What operations are evaluated next? • What operations are always evaluated last? • What is the final answer? • 90 – 5² · 3 • 4³ + 2 · 8

  26. Discussion • Parenthesis is a grouping symbol • These tell us we need to evaluate out of the usual order • Operations inside always go FIRST • PEMDAS

  27. Practice • Consider a family of 4 that goes to a soccer game. Tickets are $5.00 each. The mom also buys a soft drink for $2.00. Set up the expression and evaluate • What if each of the family members want a drink? Set up expression and evaluate. • 2 + (9² - 4) • 2 · (13 + 5 – 14 ÷ (3 + 4))

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