MS After School Intervention
Unit: Simplifying Expressions
Theme: Entertainment
Day 3 Lesson
Objective
Students will write and evaluate algebraic expressions to represent unknown quantities.
Common Core Standards:
6.NS.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.NS.2a Write expressions that record operations with numbers and with letters
standing for numbers. For example, express the calculation “Subtract y from 5” as
5y
6.NS.2b Identify parts of an expression, using mathematical terms (sum, term,
product, factor, quotient, coefficient); view one or more parts of an expression
2(8  7) as a product of two factors; (8  7) as both a single entity and a sum of two
terms.
6.NS.2c Evaluate expressions at specific values of their variables. Include
expressions that arise from formulas used in real-world problems. Perform
arithmetic operations, including those involving whole-number exponents, in the
conventional order when there are no parentheses to specify a particular order
(Order of Operations). For example, use the formula V  s 3 and A  6s 2 to find the
volume and surface area of a cube with sides of length s = 1/2.
Materials
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Overhead projector or document camera
Computer with speakers
LCD projector
Chart paper
Tape
Markers
Moving with Math: Algebra (MH5)
QuietShape algebra tiles
“Wicked” resource sheet
“Problem Solving Using Multiple Representations” resource sheets (one per
student)
“Expressions Cards” resource sheets (one per group – cut out prior to lesson)
“Calendar Math” resource sheets (one per group)
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“Window Washing Student Sheet” resource sheets (one per student)
“Raffle Ticket” resource sheets (one per student)
“Wicked” Tickets (20 minutes)
Post the “Wicked” scenario through the document camera and have a student read the
scenario shown: “A local high school is selling tickets to their upcoming musical
‘Wicked.’ They have boxed the tickets in groups of 25 before they are routed to the
middle schools in the county.”
Distribute the “Problem Solving Using Multiple Representations” resource sheet to each
student. Find a way to determine how many tickets have been distributed when various
numbers of boxes have been routed to the middle schools using at least three of the
representations.
Post five pieces of large chart paper around the room, each one labeled with a
representation. (Possible examples: Graph, Table, etc.)
After students have represented their solutions on the “Problem Solving Using Multiple
Representations” resource sheet, have them pick one of their representations and go to the
chart paper. Along with the other students at the chart paper, work together to represent
the expression on the chart paper. Next, have students walk around the room to view the
multiple representations.
Answers:
Algebraic Expression Answer: Let n = the number of boxes
25n
Other multiple representation answers may vary.
Comparing Expressions (15 minutes)
Arrange students in groups of three or four. Distribute a set of expression cards to each
group. Have groups order these values from least to greatest.
Students may need prompting to consider negative numbers or fractions. If they are
struggling, encourage them to use a variety of strategies such as graphing or substitution
to order their values.
Once groups have arranged the cards, pose the following questions:
 Suppose n = 0. Would your ordering change?
 How do you know that 3n < 3n + 1 no matter what value n has?
Representing Algebraic Expressions with Algebra Tiles (20 minutes)
Complete the Introductory Activities on page 36 of Moving with Math: Algebra (MH5).
Once completed, write two additional examples on the board and have students use the
QuietShape algebra tiles to solve.
Note: It may be helpful to create a large set of algebra tiles using colored paper to
display on the board.
Calendar Math (20 minutes)
Show students the short video clip on the invention of the calendar, available on
Discovery Education Streaming:
http://player.discoveryeducation.com/index.cfm?guidAssetId=4C8792D2-57E4-4E4A8F68-2FE8AAE59275&blnFromSearch=1&productcode=US
Calendar Magic Trick:
Arrange students in groups of three or four. Distribute a “Calendar Math” resource sheet
to each group.
Ask one of the students in the classroom to pick out two days in a row (ex. the 14th and
15th) without telling the teacher. Have him or her secretly share the dates with a
neighbor. Have them add up the dates together and give the teacher the sum.
Note: You will be able to tell the students which dates the student picked out by
completing the following equation:
1st Day
+
2nd Day
= Sum of Days
n
+
(n + 1)
= n + (n + 1)
ex. Using the 14th and 15th 2n + 1 = 29; n = 14
So if the first day is the 14th, the next day must be the 15th.
Reveal to students that you were able to know the dates by first writing an expression to
represent the dates. Have them guide you through how they can designate the first date
as n and then coming up with an expression to represent the second date (n + 1).
As a class go through a second example by representing what any Monday and
Wednesday could be. Ex. n + (n + 2).
Working within their groups, have students write expressions for the following Calendar
Problems:
- Represent three days in a row
Answer: n + (n + 1) + (n + 2)
- Represent a block (2 by 2) of dates
Answer: n + (n + 1) + (n + 7) + (n + 8)
- Represent two consecutive Thursdays Answer: n + (n + 7)
(Note: Encourage students to use Algebra Tiles to help them represent and combine like
terms.)
“Window Washing” High Five (10 minutes)
Read the following to students: “Over the summer Nick is constantly complaining about
being bored, so his father suggested he do some chores around the neighborhood. Nick
decided to set up a window washing service within his neighborhood. He charges an $8
flat fee plus $2 per window to wash windows.”
Distribute a “Window Washing” resource sheet to each student. Have students complete
the following steps:
1. Answer question #1 and #2 on your paper.
2. Once completed, stand up and hold up your hand. Find someone else in the
classroom with their hand up and high five.
3. Compare your answer to #1 and strategies used to solve the problem.
4. Repeat the high five process for question #2.
Answers:
1. One possible solution strategy:
32 windows would cost 8 + 2(32) = 72 dollars
21 windows would cost 8 + 2(21) = 50 dollars
Thus someone would pay 22 more dollars to have 32 windows washed rather than
21 windows.
2. There is not a possibility for someone to pay $41 since you are beginning at an
even number (8) and then adding by increments of an even number (2).
Closure: “Raffle Ticket” (5 minutes)
Pass out a “Raffle Ticket” resource sheet to each student. Have students put their name
on the resource sheet and answer the question. Collect all papers and draw desired
amount of winners – students must attain the correct answer in order to receive a “prize.”
(Prizes could consist of a pencil, choosing their own seat one day, etc.)
Answers:
Nick’s Fees: 8 + 2w
# of Windows
Cost to Customer ($)
1
10
Nick and Chris’ Fees: 5 + 4w
# of Windows
1
2
12
2
3
14
3
4
16
4
5
18
5
Cost to Customer ($) 9
13
17
21
25
The better deal depends on how many windows the customer is having washed. If they
are having more than one window washed, then it would be cheaper for the customer to
have just Nick wash the windows.
A local high school is selling tickets to their
upcoming musical “Wicked.” They have boxed the
tickets in groups of 25 before they are routed to the
middle schools in the county. Find a way to
determine how many tickets have been distributed
when various numbers of boxes have been routed to
the middle schools.
http://www.brescia.edu/alumni/news/uploaded_images/wicked-logo-732362.jpg
Expression Cards
n
2

3n
n•n
3n + 1
10 – n
Calendar Math
http://www.rocketcalendar.com/preview/2011-03.png
Window Washing Student Sheet
Nick decided to set up a window washing service within his neighborhood.
He charges an $8 flat fee plus $2 per window to wash windows.
1. How much more would someone pay to have 32 windows washed
than 21? Explain.
2. Is there a possibility for someone to pay $41 to have his/her windows
washed? Explain.
http://www.yesclean.com.au/images/window_cleaning.jpg
Raffle Ticket
Nick’s brother Chris has decided to join Nick
in his window washing business. Together
they charge a $5 flat fee and $4 per window.
Is this a better deal than Nick’s original
charge of an $8 flat fee plus $2 per window?
Justify your answer.
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http://www.raffle-drums.net/images/Tickets/Blank-Double-Raffle-Ticket-lg.gif