Lesson1_1Part3

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Transcript Lesson1_1Part3

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) a b terms: 7x and 8y

coefficient: 7 and 8

3) 3m 2 – 6n terms: 3m 2 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 5) b 2 (c + 4)

3 -18

6) 8 – 2ab

-4

7) a 2 + b 2 – c 2

-23

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

8) (a c)(c + 5) 9) 12 – 2(a – b) 2

-8 10

10) a + (b c) 2 11) (a + b) – ab

83 -1

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

12) 5a 2 + bc 2

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 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 + 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

= 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 1 st day 12.5t – distance in miles she traveled on the 2 nd 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 + · hours. Explain what 𝒉𝒐𝒖𝒓𝒔 the following unit analysis shows: 𝒎𝒊

mi + · h = mi + mi = mi

𝒉

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 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.