TEACHER S GUIDE: ORDER OF OPERATIONS


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1 TEACHER S GUIDE: ORDER OF OPERATIONS LEARNING OBJECTIVES Students will learn the order of operations (PEMDAS). Students will solve simple expressions by following the order of operations. Students will learn that calculating in the wrong order can result in a wrong answer. Estimated Viewing Time: Completing the entire episode will take approximately minutes. A breakdown of time by segment follows: WATCH: TRY: APPLY: 56 minutes 35 minutes 46 minutes SYNOPSIS OF THE WATCH SEGMENT Nermal is excited about his new magic box. He borrows Otto s Pet Force comic book so he can make it disappear. Unfortunately, once he puts the comic book in the box and locks it, he can t get it back open. Nermal then reads the box s instructions, which explain that he must solve three long mathematical equations to find the correct code to unlock the box. Otto and Nermal are confused about the long equations because they have lots of different mathematical symbols. Dr. Nova pops up on the hotline to help the two friends learn about the Order of Operations using the mnemonic device PEMDAS. BUILD BACKGROUND Put students into two groups (count off by 1 s and 2 s, or have them move physically into the two groups). Ask one group to shout out mathematical operations while the other group shouts out numbers under 10 in random order. Write these on a chalkboard or whiteboard in a long string of numbers. Then, add a few exponents and sets of parentheses at various places in this long numerical expression. SAY: Does anyone know what this is? (Get students to volunteer a numerical expression or a mathematical equation. ) It s rather long, isn t it? How should we go about finding out what the answer is? (Someone will probably suggest that you just do all the operations one by one.) Okay, so let s try solving this the first person who gets the answer gets to write it on the board! Have students work quickly on the problem, and let the first student who comes up with an answer write it on the board. In the meantime, you should solve the problem correctly and also incorrectly. Did anyone get a different answer? (If no students volunteer, you can show them your answer the correct one if the student got the answer incorrect and the incorrect one if the student got it correct.) Well, there is a problem with our problem! We seem to have different answers for it. Does anyone know how that could be? (Solicit various ideas from the students.) You know, we re not the only people to have this problem. A long time ago, mathematicians realized that this was a problem, so they made a rule for everyone to follow. That rule is called the Order of Operations.
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 smallsized number on the upper right side of a regularsized 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
5 QUIZ: ORDER OF OPERATIONS NAME DATE Multiple Choice Answer each question with the best response. 1. The Order of Operations in a mathematics problem means that. a. if there are parentheses, exponents, multiplication, division, addition, or subtraction signs in the same mathematical problem, follow this specific order to solve the problem. b. if there are addition signs and minus signs in the same mathematical problem, always start with the minus sign. c. if there are parentheses and exponents in the same mathematical problem, always do the problem backwards. d. if there are parentheses, exponents, multiplication, division, addition, or subtraction signs in the same mathematical problem, do all of the operations from right to left. 2. In the following mathematical problem, should you add or subtract first? a. Subtract first because if addition and subtraction are in the same problem, you should work from left to right. b. Add first because you always add before you subtract. c. Neither you should add and subtract at the same time. 3. In the following mathematical problem, should you multiply or divide first? 12 / (6 x 1) a. Divide first because if multiplication and division are in the same problem, you should work from left to right. b. Multiply first because 6 x 1 is inside the parentheses numbers inside parentheses always come first. c. Divide first because 12 is the highest number. Solve for the Correct Answer (2 x 3) = (5 x 2) + 3 = x 2 + (8 4) = (4 2) x 2 =
6 NAME DATE = 9. (2 2 x 3) = x 8 4 x (5 + 1) =
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