Numerical Expressions 6.2 p. 441

Real World Link ItemPrice Popcorn$2 Juice or Soda$1 Hot Dog$4 Let’s look at the pictures and tie this idea back into translating expressions. Obviously, someone bought 3 popcorns and 4 hot dogs. Using p as the variable, what expressions could give us the total cost? 3p is the multiplication expression…. p + p + p would be the addition expression. 3(2) = $6 and = $6 Using d as the variable, what expressions could give us the total cost? 4d is the multiplication, d + d + d + d is the addition. 4(4) = $16 and = $16 Can you write an expression with two multiplication terms and one addition sign to find the cost of 3 popcorns and 4 hot dogs? 3p + 4 d = 3(2) + 4(4) = = $22

Our Objective? We will properly use the order of to findn the value of numerical expressions. * The order of operations is a set of accepted rules that outlines the order in which calculations are to be performed.

Learn the Correct Terms p. 442 Grouping Symbols Powers (Exponents) Multiply or Divide as you work from left to right Add or Subtract as you work from left to right As you work through your problems, each line MUST be equal in value to the line above it!! We will add notations to the examples in your notes. ( ) { } | | ________

Learn the Process!! You will notice that almost all problems will have the same shape! Each line in an expression MUST be equal in value to the line above it. This means ALL values MUST be carried to the next line until they are evaluated!!

10 – Please notice we will set ours up a little differently. Work down Bring down the values you haven’t used. Notice what must be done first. 16 Finish the problem with your solution · 5 Look at the problem. Notice what must be done first Bring down the values you haven’t used. 19 Finish the problem with your solution. Please use the space to the right of your sample problems to work these out vertically. At this point, you may not see the need for this. You will as the problems become more complex. Your homework will completed in the form that we practice.

x 15 Please notice we will set ours up a little differently. Work down Bring down the values you haven’t used. Notice what must be done first. 40 Finish the problem with your solution. 16 ÷ 2 · 4 Look at the problem. Notice what must be done first. 8 · 4 Bring down the values you haven’t used. 32 Finish the problem with your solution. Work the practice problems UNDER the problems in vertical form. Got it???

You can do the division and parentheses at the same time when they are separated by a + or - Parentheses and Exponents p ÷ x (9 – 6) = 20 ÷ x (9 – 6) = x (9 – 6) x 3 3 · (64 – 2) x x x

25 x 3 ÷ ÷ ÷ ( 8 + 4) 24 ÷ 12 2 Got it??? ? Writing Expressions and Evaluating using Order of Operations p. 444 COSTS Item:LotionCandleLip Balm Cost ($)572 Study the example given. We will then write our own. 5 lotions, 2 candles, 4 lip balms = ?? 5(5) + 2(7) + 4(2) = = $47 COSTS Item:PretzelSauceDrink Cost ($)412 Write and evaluate the expression that would give us the total cost if Alexis and three friends each buys a pretzel, sauce, and a drink. 4(4) + 4(1) + 4(2) = = $28 Does anyone see another way?????

Guided Practice p. 444 SHOW ALL STEPS! WORK VERTICALLY! x – ÷ Tickets to a play cost $10 for members and $24 for non members. Write and correctly evaluate an expression to find the total cost of tickets for 4 non members and 2 members. Grouping symbols help you to identify ____________________________ 4(24) + 2(10) = = $116 The operations that must be done first are easier to identify.

Please make sure you add these notes to your folder.

Up for a Challenge???? Why all this attention to detail???? ÷ x ( 3 – 1) 1.What would you do first? ( 3 -1) 2.What would you do next? Next? Divide 14 by 2 4. The fourth step? Multiply 6 x 9 Now that all signs are + or -, how will you finish? 5.Add Subtract 2

The Solution.... When written correctly, your problem would look like this: ÷ x ( 3 – 1) ÷ ∙ (2) ÷ ∙ 9 - (2) ∙ 9 - (2) = 67 When written correctly, your problem would look like this: ÷ x ( 3 – 1) ÷ ∙ (2) ÷ ∙ 9 - (2) ∙ 9 - (2) = 67

Did We Meet the Objective? We properly used the order of operations in problem solving. We correctly wrote and evaluated expressions that required several steps, using exponents and grouping symbols. There are many more types of grouping symbols. Practice these and the new ones will be easy!!