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%

Warm Up - Wednesdaya) Write a positive or a negative number to

represent each situation:a) You owe $25b) A team has a gain of 20 yards in a football gamec) Two floors below ground leveld) 15 degrees above 0⁰Ce) A stock price fell 4.26 points

b) Use the GCF and distributive property to write 18 + 45 as a product. Then check your answer.

Review Homework

• Go write new vocabulary in math notebook – you create examples that include variables

• Then come show me your properties homework

Opening Exercise• As you evaluate these expressions, pay attention

to how you arrive at your answers:1. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 2. 9 + 9 + 9 + 9 + 93. 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?

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 = ?

Discussion

• Exponents = repeated multiplication

• 10⁵ : 10 is the base and 5 is the exponent (superscript)

• 10 to the fifth power

PracticePut repeated multiplication in exponential form

and exponential form into repeated multiplication. Then evaluate.

1) 5 · 5 · 5 · 5 · 5 =2) 2 · 2 · 2 · 2 = 3) 8³ = 4) 10⁶ = 5) g³ =

Practice

• Bases can be in decimal or fraction form1) 3.8⁴2) 2.1²3) 0.75³4) (½)³5) (⅔)²

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?

Discussion

• #s raised to the third power are called cubed• In Geometry, cubes have 3 dimensions:

___________, __________, and ___________• 1 cubed?• 2 cubed?• 3 cubed?

4ⁿ = (4 · 4 ··· 4)

n timesFor any x, x¹ = x

For any x(except 0), x⁰ = 1

If n > 1

What does the x represent?

What does the n represent?

Discussion

• With our definition, how would we represent 4ⁿ?

• How would we represent 4n?

Exercises

Closing Discussion

• Exponents = ___________________• Write exponents as _____________

Homework

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%

Warm Up - Thursdaya) 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?

b) Students at Crestdale have a goal of collecting 1,000 lbs of recycling material each month. Complete the table.

Month Pounds Collected Compared to 1,000January 985 -15February 1010March 995April 1050May 975June 980

Review Homework

• Bring me homework (Exponents and Properties)

• Copy homework into notebook• Complete the Exponents exercise sheet• Talk about why 3⁰ = 1

Opening Exercise

• Evaluate : 3 + 4 · 2

• Without knowing the Order of Operations, how could you evaluate this expression?

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

Discussion

• 3 + 4 · 2

Practice

• Expressions with Only Addition, Subtraction, Multiplication, and Division

1. What operations are evaluated first?2. What operations are always evaluated last?3. 4 ÷ 2 · 74. 36 ÷ 3 · 45. 20 – 5 · 2

Stretch Break

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

Practice• Expressions with 4 Operations and Exponents4 + 9² ÷ 3 · 2 - 21. What operation is evaluated first?2. What operations are evaluated next?3. What operations are always evaluated last?4. What is the final answer?5. 90 – 5² · 36. 4³ + 2 · 8

Discussion

• Parenthesis is a grouping symbol• These tell us we need to evaluate out of the

usual order• Operations inside always go FIRST

•PEMDAS

Practice

1. 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

2. What if each of the family members want a drink? Set up expression and evaluate.

3. 2 + (9² - 4)4. 2 · (13 + 5 – 14 ÷ (3 + 4))