Download order of operations - Infinite Learning Lab

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 12-17
minutes. A breakdown of time by segment follows:
• WATCH:
• TRY:
• APPLY:
5-6 minutes
3-5 minutes
4-6 minutes
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.
SYNOPSIS OF THE WATCH SEGMENT
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.
© 2012 Virginia Department of Education
© PAWS all rights reserved
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, 42 means to
multiply 4 x 4 and 45 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 2 + 2 + 2 + 2 and 6 x 3
means 6 + 6 + 6.
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, 2 + 5 = 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
SAY:
To learn about the Order of Operations, let’s discover how Nermal and Otto learn the same thing!
GUIDE THE VIEWING OF ORDER OF OPERATIONS
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© PAWS all rights reserved
TRY Answer Key
Officer Bob asks the students to determine which parts of long numerical expressions should
be solved in a certain order.
1.
2.
3.
4.
5.
6.
7.
8.
Which part is solved first: 32 + (4 x 2)
(4 x 2)
Which part is solved first: 16 / 4 x 2 + 3
16 / 4
Which part is solved next: 16 / 4 x 2 + 3
x2
Which part is solved last: 16 / 4 x 2 + 3
+3
Which part is solved first: 3 x (3 + 4) - 22 / 4
(3 + 4)
Which part is solved next: 3 x (3 + 4) - 22 / 4
22
Which part is solved next: 3 x (3 + 4) - 22 / 4
3x
Which part is solved last: 3 x (3 + 4) - 22 / 4
-
APPLY Answer Key
Solve the equations using the Order of Operations (PEMDAS).
1.
2.
3.
32 + (4 x 2)
17
16 / 4 x 2 + 3
11
9 – 6 + (3 + 4) + 22
14
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.)
© 2012 Virginia Department of Education
© PAWS all rights reserved
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 “10 + 4” 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
a
a
b
2
9
22
4
11
27
31
© 2012 Virginia Department of Education
© PAWS all rights reserved
QUIZ:
ORDER OF OPERATIONS
NAME
Multiple Choice
Answer each question with the best response.
DATE
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? 5 – 3 + 2
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
4. 12 ÷ (2 x 3) = _______
5. 42 – (5 x 2) + 3 = _______
6. 32 x 2 + (8 – 4) = _______
7. 22 ÷ (4 ÷ 2) x 2 = _______
© 2012 Virginia Department of Education
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NAME
8. 12 – 8 ÷ 2 + 3 = _______
9. (22 x 3) + 52 – 10 = _______
10. 7 – 4 + 6 + 2 x 8 ÷ 4 x 22 + (5 + 1) = _______
© 2012 Virginia Department of Education
© PAWS all rights reserved
DATE