# TEACHER S GUIDE: ORDER OF OPERATIONS

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2 INTRODUCE VOCABULARY Write and discuss the definition of each keyword. Pause after each definition to answer questions and provide examples. Use each keyword in a sample sentence to show students how each is used in context. order of operations mnemonic device parentheses exponent multiplication division addition subtraction progression the correct order in which you solve the different parts of a long numerical expression something to help us remember things often, it is a short word or phrase symbols that come in pairs in numerical expressions, this part of the expression is completed before other parts a small-sized number on the upper right side of a regular-sized number, which is called the base number ; it tells you how many times you should multiply the base number by itself for example, 4 2 means to multiply 4 x 4 and 4 5 means to multiply 4 x 4 x 4 x 4 x 4. a mathematical operation where you add a number to itself a number of times to find a product for example, 2 x 4 means and 6 x 3 means a mathematical operation that determines how many times one number contains another number; the answer is known as a quotient for example, 10 contains 5 of the number 2 (or, said mathematically, 10 / 2 = 5, or 10 2 = 5) a mathematical operation that puts numbers together to make a total or a sum for example, 2 birds added to 5 birds equals 7 birds (or, said mathematically, = 7) to take numbers away from another number, making a lesser number; the total is called the difference. For example, 4 grapes subtracted from 10 grapes equals 6 grapes (or, said mathematically, 10 4 = 6) moving forward; in Order of Operations, it means solving a problem from left to right and using PEMDAS rules to solve a problem in the correct sequence GUIDE THE VIEWING OF ORDER OF OPERATIONS SAY: To learn about the Order of Operations, let s discover how Nermal and Otto learn the same thing!

3 TRY Answer Key Officer Bob asks the students to determine which parts of long numerical expressions should be solved in a certain order. 1. Which part is solved first: (4 x 2) (4 x 2) 2. Which part is solved first: 16 / 4 x / 4 3. Which part is solved next: 16 / 4 x x 2 4. Which part is solved last: 16 / 4 x Which part is solved first: 3 x (3 + 4) / 4 (3 + 4) 6. Which part is solved next: 3 x (3 + 4) / Which part is solved next: 3 x (3 + 4) / 4 3 x 8. Which part is solved last: 3 x (3 + 4) / 4 - APPLY Answer Key Solve the equations using the Order of Operations (PEMDAS) (4 x 2) / 4 x (3 + 4) MONITOR COMPREHENSION After students complete the interactive lesson, have them come back together. ASK: Why didn t the magic box open when Nermal said his magic words? (It had a lock that needed a special code for it to open.) How did Nermal and Otto figure out the code? (They solved three long numerical expressions.)

4 What did Dr. Nova mean by Order of Operations? (She was talking about a set of rules that mathematicians came up with to solve long, complicated numerical expressions.) What is a good mnemonic device for remembering the Order of Operations? (PEMDAS) What do the letters PEMDAS stand for? (parentheses, exponents, multiplication, division, addition, subtraction) In which direction do you solve a problem when you are using PEMDAS? (from left to right) SAY: Now that you know how to solve a problem using the Order of Operations, I bet we can solve the problem we created earlier! CONSOLIDATE LEARNING Have the students suggest which parts to do first, and make sure everyone agrees. Continue to ask questions about why they chose a particular part to solve before others, and make sure they all understand how the Order of Operations and PEMDAS work. Finish solving the problem, and write the answer with a big flourish! EVALUATE Assign students to six groups, each of which is in charge of one particular mathematical operation (subtraction, exponents, etc.). Set up the blackboard or whiteboard with four different sections and a written in each section at the left side. Have students from each group take turns going up to the board and writing down their operation and a number under 10 (such as +3, /4, 3, etc. those with parentheses can only put them around two numbers connected by an operation which are already on the board). Students are only allowed to write in one section but it can be any section. When they are done, have the students solve all the equations on their own to turn into you for checking. QUIZ ANSWER KEY 1. a 2. a 3. b

6 NAME DATE = 9. (2 2 x 3) = x 8 4 x (5 + 1) =

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