Day 4
Week ONE … almost done
Bell Ringer
Simplify the following expression.
1)
2)
3)
9/5
Homework Questions ?
Identify the terms of each expression and the coefficient of each term.
1) 7x + 8y
2
2) a – b
terms: 7x and 8y
coefficient: 7 and 8
3) 3m – 6n
2
terms: 3m and -6n
coefficient: 3 and -6
terms: a and -b
coefficient: 1 and -1
Evaluate each expression for a = 2, b = 3, c = -6
4) 7a – 5b + 4
2
5) b (c + 4)
3
6) 8 – 2ab
-4
-18
2
2
7) a + b – c
2
-23
Evaluate each expression for a = 2, b = 3, c = -6
8) (a – c)(c + 5)
-8
10) a + (b – c)
83
9) 12 – 2(a – b)
10
2
11) (a + b) – ab
-1
2
Evaluate each expression for a = 2, b = 3, c = -6
2
2
12) 5a + bc
128
EXAMPLE
Evaluating Real-World Expressions
a) Sheila is participating in a multi-day bike
trip. On the first day, she rode 100 miles in
𝒅
8 hours. Use the expression where d is
𝒕
the distance traveled and t is the travel
time to find her average rate of travel.
Include units when evaluating the
expression.
𝒅
=
𝒕
100 miles
8 hours
=
12.5 miles per hours
EXAMPLE
Evaluating Real-World Expressions
b) If Sheila continues riding at her average
rate for the first day, then the expression
100 + 12.5t gives the total distance that
she has traveled after riding for t hours on
the second day. Evaluate this expression
when t = 7, and include units.
100 + 12.5t = 100 miles + 12.5
·
Miles per hour
=
b) If Sheila continues riding at her average rate for
the first day, then the expression 100 + 12.5t gives
the total distance that she has traveled after
riding for t hours on the second day. Evaluate this
expression when t = 7, and include units.
100 + 12.5t
= 100 miles + 12.5 Miles per hour ·
=
187.5 miles
7 hours
REFLECT
3a. What are the terms in the
expression 100 + 12.5t ? What
does each term represent in the
context of Sheila’s bike trip?
100 – distance in miles Sheila traveled on the 1st day
12.5t – distance in miles she traveled on the 2nd day
3b. What is the coefficient of the
term 12.5t? What does it
represent in the context of Sheila’s
bike trip?
The coefficient 12.5 represents Sheila’s
average rate of travel in miles per hour
3c. If you write only the units for
the expression 100 + 12.5t, you get
𝒎𝒊𝒍𝒆𝒔
miles + 𝒉𝒐𝒖𝒓𝒔 · hours. Explain what
the following unit analysis shows:
mi +
𝒎𝒊
·
𝒉
h = mi + mi = mi
When you multiply miles per hour by
hours you get miles, and when you add
miles to miles you get miles.
3d. How can you modify the
expression 100 + 12.5t so that the
units are feet when the expression
is evaluated?
Sample Answer  5280(100 + 12.5t)
13)
a) Can you multiply 25 and 15 to find the difference
Henry traveled to the library?
b) Show how to find the distance from Henry’s house
to the lirbary.
14)
a) What are the units of the fraction?
b) Rewrite the expression substituting the given
values for p and t. What are the units of each term of
your new expression? Explain.
c) Evaluate your expression for s = 5. Include units.
Summary / Essential question
1) How do you interpret and
evaluate algebraic expressions
that model real-world situation?
Exit Slip …….
2) On Monday, Giselle drives 242 miles in 4
𝒅
hours. Use the expression 𝒕 where d is the
distance traveled and t is the travel time to
find her average rate of travel. Include
units.
3) If Giselle travels at the same rate on
Tuesday, then the expression 242 + 60.5t
gives the total distance she has traveled
after t hours on Tuesday. Evaluate this
expression when t = 9. Include units.