You want me to Excuse your Dear Aunt
Who for What?!
Activities to Enhance the
Order of Operations
Grade Level: 710, with some modifications for primary students.
Introduction: This packet/lesson has been created to help teachers teach the order of
operations. In this packet, you will find the guided notes and practice for students
as well as four activities to enhance their understanding as well as get away from
the traditional teaching style. Please feel free to change the material to suit the
grade level that is being served.
Standards: New York State MST Standard #3
-Operations: 3. Students use mathematical operations and relationships among them to understand mathematics.
Students:
• add, subtract, multiply, and divide whole numbers.
• develop strategies for selecting the appropriate computational and operational method in problem
solving situations.
• know single digit addition, subtraction, multiplication, and division facts.
Objectives: After this “lesson,” students should be able to perform the order of operations
on given sets of numbers and in given mathematical statements and equations
Instructional Protocol: The guided notes are basically there to show students how
problems are to be done and give teachers handouts to use when teaching PEMDAS. Do
not plan on doing all of these activities in a single block class. This packet is meant for
you to choose an activity to do on a certain day. None of the following activities will
take a full class period to complete. Use the Internet links to find websites that I find
helpful to my students. This is not the end all lesson for the order of operations. Please
modify it and use it when and if you need it.
Chris Anderson
Pat Kirell
Lesson:
Order of Operations
Guided Notes
Order of
Please
Excuse
My
Always go from Left to Right
Examples:
Simplify: 80 – 4(7-5)
Simplify: 6(4 + 1)2 + (8 – 5)3
Simplify: 28 ÷ 4 – 2(8 – 7)2 + 5 x 3
Simplify:
48
15 3
Dear
Aunt
Sally
Guided Practice: Work on the following problems in groups of 2 or 3. Ask questions when
you have something that is confusing to you.
11 + (2 + 5)
50(6)2 - 75
8(5 + 4)
(18-9)2
48
53
1200 – 3(6-1)3
20 – (25 ÷ 5)
[7 – (2 + 3)]3
22 – 3(7 – 5)
(4 + 10)2
Activities
Bowl A Fact
Need: 4 dice
Set of plastic bowling pins
Rules: Students are given 3 dice. Plastic bowling pins will be set up labeled 1-10. One
student rolls all three dice and uses those three numbers* using any operations to reach one
of the pin numbers. If a number is reached, the pin is knocked down. Students knock
down as many pins as possible with the first three numbers and are allowed a 2nd roll if all
the pins are not knocked down.
Object: Knock as many pins down as possible.
Ex. Dice are rolled and 3, 1, 6, and 4 come up
Need to obtain all number from 1 to 10.
3*4–6+1=7
3*461=5
3/1 * 4 6 = 6
3 + 4/1 6 = 1
3 + 4 + 1 6 = 2 and so on until all 10 numbers have been taken away. If all ten cannot be taken
away, then the student rolls a second time to try and pick up the spare.
Scoring
(http://www.bowlingindex.com/instruction/scoring.htm)
Here are three examples of scoring for bowling
EXAMPLE 1
Frame 1 2 3 4 5 6 7 8 9 10
John 9-0 3-5 6-1 3-6 8-1 5-3 2-5 8-0 7-1 8-1
Score 9 17 24 33 42 50 57 65 73 82
In Example 1 we omitted strikes and spares for simplicity. Each frame is totaled and
added to the cumulative score.
EXAMPLE 2
Frame 1 2 3 4 5 6 7 8 9 10
Mary 9-0 3/ 6-1 3/ 8-1 5/ 0/ 8-0 7/ 8/8
Score 9 25 32 50 59 69 87 95 113 131
In Example 2 we learn how to score spares and open frames together. A spare is scored as
10, plus the pinfall of the next ball rolled. This total is added to the cumulative score.
Frame 1) Count 9 pins
Frame 2) Spare (10), plus next ball (6) added to score = 25
Frame 3) Count 7 pins and add to score = 32
Frame 4) Spare (10), plus next ball (8) added to score = 50
Frame 5) Count 9 pins and add to score = 59
Frame 6) Spare (10), plus next ball (0) added to score = 69
Frame 7) Spare (10), plus next ball (8) added to score = 87
Frame 8) Count 8 pins and add to score = 95
Frame 9) Spare (10), plus next ball (8) added to score = 113
Frame 10) Add (10), plus 8 to score = 131
Example 3
Frame 1 2 3 4 5 6 7 8 9 10
Kim
X 3/ 6-1 X X X 2/ 9-0 7/ XXX
Score 20 36 43 73 95 115 134 143 163 193
In Example 2 we learn how to score strikes, spares and open frames together. As
previously demonstrated, a spare is scored as 10, plus the pinfall of the next ball rolled. A
strike is scored as 10, plus the pinfall of the next 2 balls rolled. This total is added to the
cumulative score.
Frame 1) Strike (10), plus next 2 balls (3)(7) = 20
Frame 2) Spare (10), plus next ball (6) added to score = 36
Frame 3) Count 7 pins and add to score = 43
Frame 4) Strike (10), plus next 2 balls (10)(10) add to score = 73
Frame 5) Strike (10), plus next 2 balls (10)(2) add to score = 95
Frame 6) Strike (10), plus next 2 balls (2)(8) add to score = 115
Frame 7) Spare (10), plus next ball (9) added to score = 134
Frame 8) Count 9 pins and add to score = 143
Frame 9) Spare (10), plus next ball (10) added to score = 163
Frame 10) Strike (10), Strike (10), Strike (10) = 193
This game can be played over a ten day period (1 frame per day) or can be used as a math warm-up
or filler activity.
*primary students get to pick 2 numbers instead of 3
Target Number and Number Squeeze(everyday math game)
Target Number
$$All numbers cannot be solved for exactly$$
Need: 5 dice
Level: Any level after talking about order of operations
Object: To make a number as close to a given number as possible
Procedure:
1.
You need 5 dice
2.
Roll two of the dice and choose the number you want(ex. If a 3 and 5
come up you can use 35 or 53(target number)).
3.
Roll all 5 dice
4.
The students have to use the 4 numbers that come up and perform math
operations to try to get as close as they can to the target number. They
are only allowed to use each number once. They are to use any operation
including squares and square roots.
5.
Give the kids one minute to work. When time is up, whoever is closest gets a
point. If more than two kids are the closest, then both get a point but the students
must have the
work written down to get credit. If a student should get the target number while
working, he must yell out TARGET indicating that he/she got it. If they did the
work correctly, then they get 2 points and you start all over.
An example
Target number: 45
Numbers Rolled: 1, 3, 5, 6
(6+3) * 5/1 = 45
If a student uses an exponent, it must be one of the numbers, which would
make two numbers gone.
Another way to play this game is to use playing cards instead of dice.
In Primary instead of dice, to select target number teacher will have pre-made target numbers to
control level of difficulty (goal will be closest to number).
Number Squeeze
Need: 2 yardsticks or tongue depressors per pair of students
2 large graphics of your choice (hands) per pair of students
number line (large for a group, small for individual)
Make two hands (or graphics of your choice). Attach them to the end of yardstick or tongue
depressors.
Pick a secret number on the number line. One student covers up a number that comes before your
number and another student covers a number that comes after your number.
Ex. Magic #9
Student #1: Is you number bigger than 6?
- Yes, they put their left hand (BOLT) on the 6.
-----|------|------|------|------|------|-------|------|-----------
5
6
7 8
9
10
11 12
Student #2: Is your number bigger than 11?
- No, they put their right hand (BOLT) on 11.
-----|------|------|------|------|------|-------|------|-----------
5
6
7 8
9
10
11 12
Continue this process until the only number left is 9.
Smadness**
Need: 4 dice
Object: Create the numbers 1–10 using four numbers rolled
Procedure:
1. Students are separated into 2 or more teams and a team leader is selected.
2. All 4 dice are rolled simultaneously, giving us 4 distinct numbers
3. Teams use the four numbers rolled and the order of operations to create the numbers
from 110
4. When a team has found all of the digits, the leader stands and yells SMADNESS
5. The team leader shows the rest of the class the proper way to find each number.
6. A second team can challenge the first team’s findings. If the first team is wrong, the
second team takes the point away from the first team.
Ex. The roll consisted of 1, 2, 5, and 5.
(2-1)(5/5) = 1
(2-1) + (5/5) = 2
5-5+1+2 = 3
(5+5)/2-1 = 4
(5+5)/2*1 = 5
(5+5)/2+1 = 6
5+5-2-1 = 7
5+5-2*1 = 8
5+5-2+1 = 9
5*(2+1)-5 = 10
**(from Volume 56, Number 1, 2006 version of Mathematics’ Teacher Journal)
Online version of Smadness
http://www.theproblemsite.com/games/onetoten.asp
Computer Based Learning (great resource if you have computer lab access)
http://classroom.jc-schools.net/basic/math-order.html
Matchmaker Matchmaker Make Me a Match
See rules at:
http://regentsprep.org/Regents/math/orderop/Torder.htm
Solution Key for Matchmaker Matchmaker Make Me a Match
Procedure: Raise your hand if you have a question
1. Cut out all squares
2. Perform the necessary calculations
3. Match the calculations the correct answer
4. Raise your hand when you are finished
HANDOUTS HANDOUTS HANDOUTS HANDOUTS HANDOUTS HANDOUTS
Bowl A Fact
Plastic bowling pins will be set up labeled 1-10 in a triangular shape.
Object:
Knock as many pins down as possible.
Procedure:
1.
You are given 3 dice.
2.
One student rolls all three dice and uses those three numbers using any operations to reach
one of the pin numbers. If a number is reached, the pin is knocked down. Students knock
down as many pins as possible with the first three numbers. If you knock down all ten pins,
you get a strike.
3.
You are allowed a 2nd roll if all the pins are not knocked down to try and pick up the spare.
Scoring
(http://www.bowlingindex.com/instruction/scoring.htm)
Here are three examples of scoring for bowling
EXAMPLE 1
Frame 1 2 3 4 5 6 7 8 9 10
John 9-0 3-5 6-1 3-6 8-1 5-3 2-5 8-0 7-1 8-1
Score 9 17 24 33 42 50 57 65 73 82
In Example 1 we omitted strikes and spares for simplicity. Each frame is totaled and
added to the cumulative score.
EXAMPLE 2
Frame 1 2 3 4 5 6 7 8 9 10
Mary 9-0 3/ 6-1 3/ 8-1 5/ 0/ 8-0 7/ 8/8
Score 9 25 32 50 59 69 87 95 113 131
In Example 2 we learn how to score spares and open frames together. A spare is scored as
10, plus the pinfall of the next ball rolled. This total is added to the cumulative score.
Frame 1) Count 9 pins
Frame 2) Spare (10), plus next ball (6) added to score = 25
Frame 3) Count 7 pins and add to score = 32
Frame 4) Spare (10), plus next ball (8) added to score = 50
Frame 5) Count 9 pins and add to score = 59
Frame 6) Spare (10), plus next ball (0) added to score = 69
Frame 7) Spare (10), plus next ball (8) added to score = 87
Frame 8) Count 8 pins and add to score = 95
Frame 9) Spare (10), plus next ball (8) added to score = 113
Frame 10) Add (10), plus 8 to score = 131
Example 3
Frame 1 2
Kim
X 3/
3 4 5 6 7 8 9 10
6-1 X X X 2/ 9-0 7/ XXX
Score
20 36
43
73
95
115 134
143 163
193
In Example 2 we learn how to score strikes, spares and open frames together. As
previously demonstrated, a spare is scored as 10, plus the pinfall of the next ball rolled. A
strike is scored as 10, plus the pinfall of the next 2 balls rolled. This total is added to the
cumulative score.
Frame 1) Strike (10), plus next 2 balls (3)(7) = 20
Frame 2) Spare (10), plus next ball (6) added to score = 36
Frame 3) Count 7 pins and add to score = 43
Frame 4) Strike (10), plus next 2 balls (10)(10) add to score = 73
Frame 5) Strike (10), plus next 2 balls (10)(2) add to score = 95
Frame 6) Strike (10), plus next 2 balls (2)(8) add to score = 115
Frame 7) Spare (10), plus next ball (9) added to score = 134
Frame 8) Count 9 pins and add to score = 143
Frame 9) Spare (10), plus next ball (10) added to score = 163
Frame 10) Strike (10), Strike (10), Strike (10) = 193
Target Number
Object: Reach the Target Number
Procedure:
1.
You need 4 dice
2.
Roll two of the dice and choose the number you want(ex. If a 3 and 5
come up you can use 35 or 53(target number)).
3.
Roll all 4 dice
4.
You have to use the 4 numbers that come up and perform math operations to try
to get as close as you can to the target number. You are only allowed to use each
number once. You can use any operation including squares and square roots.
5.
You have one minute to work. When time is up, whoever is closest gets a point. If more
than two of you are the closest, you both get a point but the students must have the
work written down to get credit. If you should get the target number while working, you
must yell out TARGET indicating that you got it. If you did the work correctly, then you
get 2 points and you start all over.
An example
Target number: 45
Numbers Rolled: 1, 3, 5, 6
(6+3) * 5/1 = 45
Smadness
With your team, create the numbers 110 using the four numbers given by the
teacher once and only once. You may use any mathematical operation you
wish. After your team has all ten numbers, your team leader must stand up
and say “SMADNESS”
Round 1
Round 2
Round 3
1=
1=
1=
2=
2=
2=
3=
3=
3=
4=
4=
4=
5=
5=
5=
6=
6=
6=
7=
7=
7=
8=
8=
8=
9=
9=
9=
10=
10=
10=
Matchmaker Matchmaker Make Me a Match
Procedure: Raise your hand if you have a question
1. Cut out all squares
2. Perform the necessary calculations
3. Match the calculations the correct answer
4. Raise your hand when you are finished