MS After School Intervention
Unit: Powers, Square Roots, & Order of Operations
Day 4 Lesson
Objective
Students will solve problems using the order of operations.
Common Core Standards:
6.EE.1 Write and evaluate numerical expressions involving whole-number
exponents.
Materials
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“Integer and Operation Cards” resource sheet (cut into square cards before start of
the lesson)
“Grab Bag Cards” resource sheet (one per pair, cut into square cards before start
of the lesson)
Grab bags (one per pair)
Number cubes
Document camera or overhead projector
White boards and markers
“Exit Ticket” resource sheet (one per student)
“Traffic Lights” resource sheet (one half sheet per student)
Warm-Up: The Tip Problem (15 minutes)
Separate the class into two groups and read the following scenario:
“Mark and his brother John are at a restaurant and are arguing over the tip. Mark wants
to tip 20% on the total before taxes, but John wants to leave the 20% on the total after
taxes. The bill total is $50, and taxes are an additional $2.50.”
Have one group discuss Mark’s proposal and the other group discuss John’s proposal.
Each group should come up with the tip cost, the total amount they will pay after tip, and
the order of operations that will lead to their solution. (Solution: Mark’s method: tip is
$10.00 and $62.50 is total with tip, John’s method: tip is $10.50 and $63.00 is total with
tip.)
Have each group present their answers. Have groups discuss which option is “more
appropriate” and why. (Answers will vary.)
Fill in the Operations (20 minutes)
Separate the class into small groups. Open a set of integer and operation cards. Choose
five integer cards and place them under the document camera or on the overhead,
grouping four together and the last integer by itself. Explain that the students must use
their operations and the first four integers in order to arrive at the fifth integer as their
solution. For instance, place the integers 1, 2, 3 and 4 in a group with the result being 6.
Students will arrange their own cards to set up the problem. A possible solution would
be 2  4 1  3  6 . Discuss the solution and place it on the document camera or
overhead. Explain that you are going to use the same integers and operations, but in a
different order to arrive at the number 7 instead. The solution would be
2  (4  1)  3  7 . Discuss, as a class, how to represent adding 4 + 1 first. Use the
integer and operation cards to go through a few more examples, while discussing order of
operations.
Moving with Math (20 minutes)
Lead students through the Introductory Activity on page 14 of Moving with Math:
Number Sense, Reasoning and Data (MH1). Students should practice moving from a
statement to physical representation, to the symbolic representation with correct grouping
symbols. Using the example from the Introductory Activity on page 15, have students
explain how to group 2  5  4 to get a solution of 18. Have students explain why their
method does not produce a solution of 14. Give additional examples from the exercises
on the top of page 15, having students include grouping symbols to generate a desired
solution. Make
sure students explain their reasoning.
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Grab Bag (20 minutes)
Assign each student a partner. Each set of partners should have a grab bag filled with the
grab bag cards and a number cube. One partner should roll the number cube and pick
three cards from the grab bag. The number on the cube represents the starting value, and
the three operations from the grab bag are to be applied, in the order in which they are
pulled. The partners should work out the problem on their paper, determining how to
correctly write the problem with parentheses, exponents, etc.
Once they have worked out the solution, the partners should write the problem on a white
board and switch with another set of partners, who will evaluate the problem and explain
the steps. Partners should continue to set up, switch, and solve problems until the time
limit has been reached, replacing the grab bag cards as they go.
Exit Ticket (10 minutes)
Have students complete the exit ticket and turn in. Check for accuracy to see how well
students mastered the lesson.
Exit Ticket: Evaluate each problem. Show work and/or explain what you did to find the
answer.
1. 32  5  (2  4)
Solution: 8
2. 2  5  4  2 2
Solution: 11
3. 8  2  3  23
Solution: 10
4. 9  (5  2) 2
Solution: 0
5. 8  2  (4  1)  3
Solution: 1
Closure – Traffic Light (5 minutes)
Hand each student a traffic light. Ask the following questions, and have the students
point to green if they are “good to go,” yellow if they “need to slow” or red if they “need
to stop and review.”
1. How do you feel about combining multiplication and division with addition and
subtraction to evaluate a single problem?
2. How do you feel when you must evaluate a problem involving exponents?
3. How do you feel when you must evaluate a problem involving parentheses?
4. How do you feel about the order of operations overall?
Integer and Operation Cards
1
2
3
4
5
6
7
8
9
10
+
+
–
–
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
(
)
=
Grab Bag Cards
Divide by 2
Add 3
Subtract 9
Multiply by 4
Raise to the second
power
Subtract 1
Add 8
Multiply by 2
Divide by 3
Raise to the third
power
Add 5
Subtract 7
Add 10
Subtract 4
Multiply by 5
Multiply by 10
Subtract 10
Add 12
Divide by 4
Add 1
Subtract 2
Exit Ticket
Exit Ticket: Evaluate each problem. Show work and/or explain what you did to find the
answer.
1. 32  5  (2  4)
2. 2  5  4  2 2
3. 8  2  3  23
4. 9  (5  2) 2
5. 8  2  (4  1)  3
Traffic Lights