The week of October 30th – November 3rd

Monday, October 30, 2017 Today I am learning my strengths and weaknesses with proportions and percents because this is an important step before the test tomorrow Agenda: Lemonade Question: Warm-up Review Study Guide Answers Unit 2 jeopardy Game How are you going to study tonight? Homework: Study for Unit exam starting tomorrow

Monday’s – Warm UP Jenna and Diana make 3 gallons of lemonade for their lemonade stand. If there are 16 cups in a gallon, how many cups of lemonade can they sell? Show your work and explain your answer using a sentence.

HOW ARE YOU GOING TO STUDY TONIGHT???

Tuesday, October 31, 2017 Today I am proving that I have mastered the standards for Unit 2 because this is an important step before moving on to Unit 3. Agenda: Any last minute questions Unit 2 exam Homework: Study for Unit exam Work on Unit 3 vocabulary in MSG

Wednesday, November 1, 2017 Today I am proving that I have mastered the standards for Unit 2 because this is an important step before moving on to Unit 3. Agenda: Finish Unit 2 Summative Set up MSG unit 3 Work on unit 3 Vocabulary Homework: Make flash cards unit 3 vocabulary

Thursday, November 2, 2017 Today I am learning it is helpful to write numbers in different ways because this will save me time. Agenda: Exponents: Brain Pop video MSG notes on exponents Roll the Dice MSG task Quiz: put in MSG Homework: p. 350 #3, 5; P. 351 # 5, 7, 9; p. 352 #11

What is another way to write this? Thursday – Warm UP JUST THINK ABOUT YOUR ANSWER NO NEED TO WRITE ANYTHING DOWN. What is another way to write this? 3 x 3 x 3 x 3 x 3 x 3 x 3

https://www.brainpop.com/math/numbersandoperations/exponents/

How can I write 2 + 2 + 2 + 2 using multiplication? Prior Knowledge Years ago you learned that multiplication is an easier way to show repeated addition. Example: How can I write 2 + 2 + 2 + 2 using multiplication? 2 x 4

How can I write 2 x 2 x 2 x 2 using exponents? Exponential Form Writing numbers in exponential form is just an easier way to show repeated multiplication. Example: How can I write 2 x 2 x 2 x 2 using exponents? 2 x 2 x 2 x 2 = How many twos are shown? 24 1 2 3 4

32 means 3 is multiplied by itself 2 times Vocabulary baseexponent An exponent tells how many times a number (called the base) is multiplied by itself. exponent 3² base 32 means 3 is multiplied by itself 2 times

4 is multiplied by itself 3 times So… 43 4 is multiplied by itself 3 times 43 = 4 x 4 x 4 = 64 43 ≠ 4 x 3

There are two specially-named powers: Reading Exponents 46 is read “4 to the sixth power.” 51 is read “5 to the first power.” 38 is read “3 to the eighth power.” And so on… There are two specially-named powers: 32 is read “3 to the second power” or “3 squared.” 43 is read “4 to the third power” or “4 cubed.”

Write each in exponential form and find the value. 2 x 2 x 2 x 2 7 x 7 1 x 1 x 1 x 1 5 x 5 x 5 6 24 = 16 72 = 49 14 = 1 53 = 125

Write each as repeated multiplication and find the value. 32 33 101 25 3 x 3 = 9 3 x 3 x 3 = 27 10 2 x 2 x 2 x 2 x 2 = 32

Friday, November 3, 2017 Today I am learning how to simplify numerical expressions because it is helpful to write numbers in different ways. Agenda: ALL #s raised to the zero power? Warm up ? Brain pop on order of operations MSG notes on O.O.O. 5 ? Quiz in MSG PEMDAS Homework: NONE

What is the value of all numbers raised to the zero power? Friday – Warm UP What is the value of all numbers raised to the zero power? Be ready to discuss

What about a number raised to the power of ZERO? Example: What is 30 ? Complete the table below. See if YOU and your partner can see the pattern to figure it out…. 34 3x3x3x3 = 81 33 32 31 30

What about a number raised to the power of ZERO? Example: What is 30 ? Did you find that dividing by 3 gives you the next value? 34 3x3x3x3= 81 33 3x3x3 =27 32 3x3 =9 31 3 30 1

What about a number raised to the power of ZERO? FACT: All positive numbers raised to the power of zero are equal to 1. 20 = 1 40 = 1 1,000,0000 = 1

What is the value of the following expression: 4 + 3 · 7

BRAINPOP! http://www.brainpop.com/math/numbersandoperations/orderofoperations/

That is why mathematicians have agreed upon the order of operations. Does order matter?... When you get ready for school, you put on your socks before you put on your shoes. In mathematics, as in life, some tasks must be done in a certain order. A numerical expression is made up of numbers and operations. When simplifying a numerical expression, rules must be followed so that everyone gets the same answer. That is why mathematicians have agreed upon the order of operations.

Parenthesis Exponents Multiply Divide Add Subtract Left to right

ORDER OF OPERATIONS 1. Perform operations within grouping symbols. 2. Evaluate exponents. 3. Multiply and/or divide in order from left to right. 4. Add and/or subtract in order from left to right.

When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set and work in the PEMDAS order within the grouping symbols. Helpful Hint

Let’s practice… 3 + 15 ÷ 5 Divide. 3 + 3 Add. 6 Simplify the expression. 3 + 15 ÷ 5 3 + 15 ÷ 5 Divide. 3 + 3 Add. 6

Now you try with your table partner… Simplify the expression. 44 – 14 ÷ 2 · 4 + 6

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

Now you try again with your table partner… Simplify the expression. 3 + 23 · 5

Simplify the expression. 3 + 23 · 5 3 + 23 · 5 Evaluate the power. 3 + 8 · 5 Multiply. 3 + 40 Add. 43

Now you try on your own… Simplify the expression. 28 – 21 ÷ 3 · 4 + 5

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

Practice makes perfect! Try again on your own… Simplify the expression. 42 – (3 · 4) ÷ 6

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

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

Stand up. Find someone you have not spoken with today and discuss how you would answer this question. SOLVE and Return to your seat. Simplify the expression. [(32 – 4 · 4) + 2]2

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

Simplify the expression. 9 + 6 (8-5)

Simplify the expression. 3 + 6(5 + 4) ÷ 3 - 7

Let’s review. It’s time to show me what you know.

Which operation should be performed first in the expression : 9 + 5 × (6 - 1) A. addition B. subtraction C. multiplication D. division B

Which operation should be performed first in the expression : 6 + 2 × 7 - 4 A. addition B. subtraction C. multiplication D. division B

5 + 1 × 8 - 2 = Is this an expression? Why or why not? 16

Which operation should be performed first in the expression: 4 + 8 ÷ 2 × 3 – 10 A. addition B. subtraction C. multiplication D. division D

Which operation should be performed first in the expression: 3(4 - 2) + 8 × 2 A. addition B. subtraction C. multiplication D. division D

Which operation should be performed first in the expression: 32 - 6 × 2 ÷ 3 + 1 A. addition B. subtraction C. exponent D. division D

Extra Practice if you want Simplify (solve) 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