Day 4

Week ONE … almost done

1)

2)

3)

Bell Ringer 9/5Simplify the following expression.

Homework Questions ?

1) 7x + 8y 2) a – b 3) 3m2 – 6n

Identify the terms of each expression and the coefficient of each term.

terms: 7x and 8ycoefficient: 7 and 8

terms: a and -bcoefficient: 1 and -1

terms: 3m2 and -6ncoefficient: 3 and -6

4) 7a – 5b + 4 5) b2(c + 4)

Evaluate each expression for a = 2, b = 3, c = -6

6) 8 – 2ab 7) a2+ b2 – c2

3 -18

-4 -23

8) (a – c)(c + 5) 9) 12 – 2(a – b)2

10) a + (b – c)2 11) (a + b) – ab

Evaluate each expression for a = 2, b = 3, c = -6

-8 10

83 -1

12) 5a2 + bc2

Evaluate each expression for a = 2, b = 3, c = -6

128

EXAMPLE Evaluating Real-World Expressions

Sheila is participating in a multi-day bike trip. On the first day, she rode 100 miles in 8 hours. Use the expression where d is the distance traveled and t is the travel time to find her average rate of travel. Include units when evaluating the expression.

𝒅𝒕

𝒅𝒕 = =

a)

100 miles

8 hours12.5 miles per hours

EXAMPLE Evaluating Real-World Expressions

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.

=

b)

100 + 12.5t 100 + 12.5 ·=

milesMiles per hour

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.

=

b)

100 + 12.5t100 + 12.5 ·

=

miles Miles per hour 7 hours

187.5 miles

REFLECT3a. 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 getmiles + · hours. Explain what the following unit analysis shows:

𝒎𝒊𝒉

𝒎𝒊𝒍𝒆𝒔𝒉𝒐𝒖𝒓𝒔

mi + · h = mi + mi = miWhen 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)

Finish PRACTICE problems # 13 and 14

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 hours. Use the expression where d is the distance traveled and t is the travel time to find her average rate of travel. Include units.

𝒅𝒕

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.

786.5 miles

60.5 miles per hour