Download Accelerated Math Unit 3 - Youngstown City Schools

YOUNGSTOWN CITY SCHOOLS
MATH: GRADE 7
UNIT # 3: EXPRESSIONS AND EQUATIONS– (2 WEEKS)
Synopsis: In this unit, students work with order of operations and properties in conjunction with writing algebraic
expressions for given situations. Students learn to use variables in writing expressions. Students also learn how to
simplify expressions and write equivalent expressions.
STANDARDS
7. EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational
coefficients.
7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how
the quantities in it are related (e.g., a + 0.05a = 1.05a means that “increase by 5% is the same as multiply by 1.05).
MATH PRACTICES
1. Make sense of problems and persevere in solving them.
2.
3.
4.
5.
6.
7.
8.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning
LITERACY STANDARDS
L.1 Learn to read mathematical text (including textbooks, articles, problems, problem explanations)
L.2 Communicate using correct mathematical terminology
L.5 Justify orally and in writing mathematical reasoning
MOTIVATION
TEACHER NOTES
1. Teacher does Fun with Calendars activity from Math Playground. Explain to students that we
are going to be working with expressions, and equivalent expressions where the expressions
look different, but the values are the same (e.g., n + n+1+n+7+n+8 = 4n +16 or 4a +4b = 4(a+b) )
http://math.rice.edu/~lanius/Lessons/calen.html
2. Students establish academic and personal goals for the unit.
3. Teacher previews the Authentic Assessment for the end of the unit.
TEACHING-LEARNING
1. Teacher begins by reviewing the properties: Commutative, Associative, Distributive, Identity, Zero
with numerical expressions (e.g., 3+2 = 2+3; (2+3)+5 = 2+(3+5); 5(2 + 7) = 10 + 35; etc.). Have
students write samples for each property. Have students connect a story with real world focus to
each situation. Samples for the properties are in the Glencoe Pre-Algebra book pages 23-27 for
both numeric and variables. Make sure students understand that a numerical expression names a
number. (7.EE.1)
TEACHER NOTES
Teachers: key vocabulary
terms are bold and
underlined in the text of
the Unit.
2. Next the teacher moves to doing the properties with variables in algebraic expressions (e.g., 1+a =
a+1, etc.); Students should recognize that these are different from the numerical expressions in that
they contain a variable (e.g., 3x +2, or 3(4x -2), etc. Have students practice with the following
problem: You want to build a doghouse and the cost will be $50/hour for labor and $125 for
materials. (125 + 50h) (7.EE.1) (L.1, L.5)
3. Give several examples for students to translate words into algebraic expressions (see examples
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TEACHING-LEARNING
TEACHER NOTES
on page 4 of Unit Plan); have students use wipe-off boards to have a quick check or play “Travel”
with these examples. Next challenge students to generate other examples by creating a situation and
the corresponding algebraic equation. Students may work individually, in pairs or in small groups.
Teachers may want to use the Millionaire Game for matching expressions to words found at the
following website:
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html
(7.EE.1) (L.1, L.5)
4. Teacher gives students problems to practice writing expressions and also gives expressions and
students write the words to describe the expressions (reference: Glencoe Pre-Algebra Section 1.3:
pages 17-21 and Addison –Wesley Book 2 pages 78-81; also, Addison Wesley Book 3: pages 130132. (7.EE.1) (L.1, L.2, L.5) (several attached on page 5-6). Suggested activity for writing
expressions – http://www.youtube.com/watch?v=L7soJdOhKZM
Students can write expressions for the exchange of money between Theo and his dad. You can
show the entire video once, then repeat, pausing at each part and asking students to write an
expression for the situation.
5. Show students how to simplify expressions by following order of operations and combining like
terms (refer back to the calendar activity in the Motivation) - - 4(n+4) = 4n+16. Suggested activity
for order of operations: Students hold cards with parts of an expression. Have the student whose
part should go first, step forward: then the one whose part would be solved next steps forward, and
so on.
8 + 4(2x-5) + 3x
8 + 8x – 20 + 3x
11x-12
Also see http://freemathhelp.com/combining-like-terms.html and Glencoe pg. 103-106 “Simplifying
Algebraic Expressions” for activity using Algebra Tiles to combine like terms. Do problems of
the type: 8 + 4(2x-5) + 3x where there are three operations and students must combine like terms
and simplify to 11x – 12. As students become proficient with this type of expressions, give examples
that have exponents (e.g., 1 + 4x + 3x2 – 5x = 3x2 –x +1.) There are other examples at
FreeMathWorksheets.net (this site allows the teacher to select the problems and students solve on
line with immediate feedback, and then additional problems are presented based on student
answers). (7.EE.1) (L.1, L.2, L.5) other problems can be found at:
http://www.hstutorials.net/dialup/distributiveProp.htm for factoring with the distributive property. You
may want to use Algebra tiles for some students who need more concretes.
6. Equivalent Expressions: Use Glencoe: Section 3-2(98-102) and 3-2 (103) for sample problems.
Also, use the Common Core Math Standards with Hands-On Activities book – pages 106-107, where
students write expressions in different forms - - 10% = 0.1 = 1/10 or 150% = 1.5 = 1+1/2 = 3/2 or 52 =
25 = 125/5 = 2x 12 ½ = 2 x 12.5 = 50/2, etc. so that students have lots of practice writing equivalent
expressions. Have students generate expressions for each other to write equivalent expressions,
and then test to be sure they are indeed equivalent. (7.EE.2) (L.1, L.2, L.5)
. Scientific Notation: introduce with You-tube video (Collin Dodds). When doing this, ask students what
is an easier way to write these numbers/
a. The Sun is 93 million miles or 1,636,800, 000,000,000 yards away from Earth. Have students
then write it down and read number (expect students to complain); Make sure that students
realize what the exponent represents - - and that it does not represent the zeroes, but it is the
number of places the decimal moves.
b. The average diameter of a human hair is 0.00067 inches. Read the number aloud to a partner.
What is an easier way to write the number that is a shorter way - - yes, Scientific Notation, but
how does that look? If students have written the numbers in Scientific Notation correctly, move
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TEACHING-LEARNING
TEACHER NOTES
on, and don’t spend time having students write numbers. Use 10 positive and 10 negative
problems that are varied to be sure they have it.
Go to www.kutasoftware.com for lots of problems to be used to practice. www.khanacademy.org
also has practice and teaching videos. (8.EE.3)
7. Calculation with Numbers in Scientific Notation - -- Multiplication and Division: Glencoe-Algebra I (old
book) pages 428-429. (8.EE.4)
For Multiplication: (2.83 x 105) (3.7 x 107) = Use the associative property: (2.83 x 3.7) (105 x 107) =
10.471 x 1012 ask students if this is in scientific notation = 10.471 = 1.0471 x 101 x 1012 = 1.0471 x 101
+12 = 1.047 x 103
Show students that they can multiply the numbers in Scientific Notation and then change it back to
double check their work.
The Cleveland Indians sold out 455 consecutive home games; the stadium holds 43,345 people; in
those 455 games, what is the total number of people at the stadium who watched these games?
Write the number in Scientific Notation.
The Pittsburgh Steelers have sold out every home game since about 1975 with 8 home games
each season (2.96 x 102 games); the capacity of the stadium is 5.503 x 104. What is the total
number of fans to watch a regular season Steelers home game during this time period? Write your
answer in Scientific Notation.
Go to www.kutasoftware.com for lots of problems to be used to practice.
For Division: The U.S. national debt is $1.62 x 1013 . The population of the United States is 3.1375
x 108. What is each citizen’s share of the national debt? On 9/30/01, the National Debt was
approximately 5.807 x 10 ^ 12 and the U.S. population was about 2.8142 x 10^8.
Lil Wayne’s Phantom Drophead Coupe cost him $4.3 x 105. By the time you graduate from high
school (5.2 x 101 months), you want to buy one of these cars. How much money do you need to save
each month? Answer must be in Scientific Notation.
Students will do practice problems for this as well. Go to www.kutasoftware.com for lots of problems
to be used to practice.
Teacher uses opposites to teach students about 2 and -2 (NRN.1; NRN.2)
TRADITIONAL ASSESSMENT
TEACHER NOTES
1. Multiple-Choice Unit Test
TEACHER-MADE ASSESSMENT
TEACHER NOTES
1. Teacher Classroom Assessments
2. 2- point and 4- point Constructed Response items
AUTHENTIC ASSESSMENT
TEACHER NOTES
1. Have students evaluate their goals and give evidence
2. Students are given scenarios and they write an expression to represent the situation in the scenario.
Students must do two required and pick one additional one to solve.
 Bill has $10 and he does work for his neighbor for $5 per job. ($10 + 5x)
 Jon mows grass for people in his neighborhood for $15 per yard. ($15x)
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 Joe has a job shoveling snow. He charges $10 plus $0.50 for each inch of snow that has fallen.
(10 + .50i)
 Maria is selling candy to raise money for a field trip. She sold 5 more boxes of candy on the second
day than she sold on the first day. How much candy did she sell in all? (x + (x+5))
 An online shopping site is having a special on sweaters. The first sweater ordered is full price, but if
you buy more than one, the additional sweaters are 10% off each. Jan orders three sweaters.
What will she pay not including tax or shipping? (C + .90c + .90c)
 Mark cleaned his bedroom on Monday. On Tuesday Mark wanted to go to the basketball game, so
he hurried up and cleaned his room in half the time. How many total minutes did Mark spend
cleaning his room on the two days? (m + .50m )
 Janine is babysitting to earn extra money for summer camp. She charges a flat fee of $6 an hour
plus $0.25 for each child in her care. How much does Janine charge for babysitting? (6h + .25c)
 Repairman charges $50 to come to the house plus x per hour plus materials. If you pay in cash,
you receive a 10% discount
3. Students create 5 situations and the expressions that would go with the situations.
(Rubric for the authentic assessments attached on page 7 of this unit plan.)
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T-L # 3
Examples of translating words to expressions
Phrases
Expression
Twice a number subtracted from 6
6-2n
Twice the sum of a number and 8
2(n+8)
Twice a number minus 5
2n-5
A number decreased by 3
n-3
Twice the difference between a number and 9
2(n-9)
Number of sides in t triangles
3t
Number of nickels in x dollars
20x
Number of yards in i inches
__i___
36
3600h
Number of seconds in h hours
Tax rate is .675; tax on x dollars
.675x
Total cost with tax for cost of x
.675x + x or 1.675x
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T-L #4
SAMPLES FOR STUDENTS TO CREATE EXPRESSIONS FROM REAL WORLD SITUATIONS
An airplane is carrying 181 passengers. The number of passengers who have economy tickets is 11 more
than the number of passengers who had super-saver tickets. The number of passengers with full-fare
tickers is 7 less than the number of passengers with super-saver tickets.
 Write an expression for the number of passengers with economy tickets. s + 11
 Write an expression for the number of passengers with full-fare tickets. s – 7
At Lake Logan, there are two boat rental companies. Pier Rentals charges a fee of $20 plus an hourly rate
of $5.00 for each additional hour to rent a sailboat. Lakefront Boats charges a fee of $12.50 plus an hourly
rate of $7.50 for each additional hour.
 Write an expression for the rental fees at Pier Rentals.
20 + 5h
 Write an expression for the rental fees at Lakefront Boats. 12.5 + 7.5h
Martina is 6 years older than 2 times the age of her son, Jimmy.
 Write an expression for Martina’s age. 2j + 6
 Write an expression Jimmy’s age.
(m-6) ÷2
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T-L #4
ADDITIONAL PRACTICE:
1. A company aired its 30-second commercial during Super Bowl XXXIX at a cost of
$2.4 million each time. Write an algebraic expression to determine what the cost
would be if the commercial had aired n times. (2.4x)
2. Lou read some books. Kelly read more 4 books than Lou. Write an expression
for the number of books Kelly read. (x+4)
3. Kevin has 6 more baseball cards than Ethan. Write an expression to represent
the number of baseball cards Kevin has. (c + 6)
4. Mario’s family drove three times as many miles on Saturday as they did on
Friday. Write an expression to represent the number of miles driven on
Saturday. (3m)
5. A dolphin can swim d miles per hour. Humans swim one-third as fast as
dolphins. Write an expression that could show how fast humans swim. (d ÷ 3)
6. Joan is buying a sweater that is $10 of the original price. Write an expression to
show the cost. (p - $10)
7. Tami went shopping and bought 2 bottles of nail polish; each cost the same
amount. She also bought a magazine for $5. Write an expression to represent
how much she spent. (2 x d + 5 or 2d + 5)
8. Shawn rushes for a certain number of yards in a football game. Greg rushed for
8 more than twice Shawn’s yardage. Write an expression for this scenario.
(2s +8)
9. Melinda goes bowling on Saturday afternoon. She bowls 3 games and pays
$2.00 to rent shoes. Write an expression for what she spent. (3b +2)
10. If n represents the amount of songs stored on an MP# player, what does each of
the following expressions mean - - n + 7; n – 2, 4n, and n ÷ 2? (7 more songs; 2
fewer songs, 4 times the songs, and half the number of songs)
11. A shirt costs $16 and a pair of pants costs $23. Write an expression to find the
cost of 4 shirts and 3 pairs of pants. (4 x 16 + 3 x 23)
12. Jan is 7 years younger than her sister Annette. Annette is y years old. Write an
expression that describes Jan’s age. (y – 7)
13. Each container in an 8-pack of yogurt contains y ounces. Write an expression
that describes how many ounces in an 8-pack container. (8y)
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RUBRIC FOR AUTHENTIC ASSESSMENT
TASK I
Assigned Scenario #1
Wrote expression for
situation
Simplified expression
0
1
2
3
Did not
attempt
Did not
attempt
Had multiple errors in the
expression created
Made multiple errors in
simplifying the expression
Had a minor error in the
expression created
Had a minor error in
simplifying the expression
Wrote correct expression for
the given scenario
Simplified the expression
with no errors
Did not
attempt
Did not
attempt
Had multiple errors in the
expression created
Made multiple errors in
simplifying the expression
Had minor error in
expression created
Had a minor error in
simplifying the expression
Wrote correct expression for
the given scenario
Simplified the expression
with no errors
Had multiple errors in the
expression created
Made multiple errors in
simplifying the expression
Had minor error in
expression created
Had a minor error in
simplifying the expression
Wrote correct expression for
the given scenario
Simplified the expression
with no errors
Assigned Scenario #2
Wrote expression for
situation
Simplified expression
Student Choice Scenario #3
Wrote expression for
situation
Simplified expression
TASK II
Did not
attempt
Did not
attempt
0
2
4
Wrote Scenario A
Did not
attempt
Did not
attempt
Had error in the scenario
that made writing the
expression difficult
Had a minor error in
simplifying the expression
Wrote scenario that would
yield an expression
Simplified Scenario A
Attempted to write scenario,
but it did not yield an
expression
Made multiple errors in
simplifying the expression
6
Wrote Scenario B
Did not
attempt
Did not
attempt
Had error in the scenario
that made writing the
expression difficult
Had a minor error in
simplifying the expression
Wrote scenario that would
yield an expression
Simplified Scenario B
Attempted to write scenario,
but it did not yield an
expression
Made multiple errors in
simplifying the expression
Wrote Scenario C
Did not
attempt
Did not
attempt
Had error in the scenario
that made writing the
expression difficult
Had a minor error in
simplifying the expression
Wrote scenario that would
yield an expression
Simplified Scenario C
Attempted to write scenario,
but it did not yield an
expression
Made multiple errors in
simplifying the expression
Wrote Scenario D
Did not
attempt
Did not
attempt
Had error in the scenario
that made writing the
expression difficult
Had a minor error in
simplifying the expression
Wrote scenario that would
yield an expression
Simplified Scenario D
Attempted to write scenario,
but it did not yield an
expression
Made multiple errors in
simplifying the expression
Wrote Scenario E
Did not
attempt
Did not
attempt
Had error in the scenario
that made writing the
expression difficult
Had a minor error in
simplifying the expression
Wrote scenario that would
yield an expression
Simplified Scenario E
Attempted to write scenario,
but it did not yield an
expression
Made multiple errors in
simplifying the expression
Simplified the expression
with no errors
Simplified the expression
with no errors
Simplified the expression
with no errors
Simplified the expression
with no errors
Simplified the expression
with no errors
TOTAL POINTS (78)
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