Welcome to Pre-Algebra Monday: Week 17

1. Review Slope2. “Redo” Slope Art Project

IntroductionTo Slope

Slope is a measure ofSteepness.

Types of Slope

PositiveNegative

Zero

Undefinedor

No Slope

Slope is sometimesreferred to as the“rate of change”

between 2 points.

If given 2 points on a line, you may findthe slope using theformula m = y2 – y1

x2 – x1

The formula may sometimes be written

as m =∆y . ∆x

What is ∆ ?

Find the slope of the line through the

points (3,7) and (5, 19).x1 y1 x2 y2

m = 19 – 7

5 – 3 m = 12 2

m = 6

The End

Welcome to Pre-Algebra Tuesday

1. Please have your journals out– 3.4 Paying Bills and Counting Profits

2. Tonight’s Assignment– Problem 3.4 Follow up

Number Of

Customers

Income Bike Rental Food and Camp Cost

Van Rental

1

2

3

4

5

6

7

8

9

10

Expected Cost and the Resulting Profit:

Do you see any patterns in the above table?

Cost of trip: $350 per rider$30 per person for a bike$125 per person food and camp$700 per tour for van rental

PAYING BILLS AND COUNTING PROFITS

In your group answer the following questions in your spiral notebooks…..

How does the income column change as the number of customers increases?Explain how you can use this relationship to calculate the income for any number of customers

Add and complete a column for “Total Cost” (including bike rental, food and camp costs, and van rental) to your table

How does the total cost change as the number of customers increases?Describe how you can calculate the total cost for any number of

customers.

Add and Complete a column for “Profit” What profit would be earned from a trip with 5 customers? 10 customers? 25 customers?

Warm-up: Wednesday• Determine whether the rate of change are

constant or variable.1.

2.

Fill in the question marks3. Slope =

Weight(lb) 1 2 3

Price ($) 3 6 9

Constant Speed (mi/hr)

10 20 30

Time (h) 3 1.5 1

valuechangeinx

rise

?

?

Welcome to Pre-Algebra Wednesday

1. Please have your homework on your desk and get started on your warm up.

2. Discuss 3.4 Follow up

3. Introduction into Investigation 4

Investigation 4: Patterns and Rules

By using tables and graphs, we have investigated how these variables are related to one another. For example, we explored how the number of customers is related to profit and how the number of hours of riding is related to the distance covered.

By studying how variables are related, we are learning ALGEBRA!!

• Can be described with a simple rule.

• By having a rule we can make predictions for values that are not included in a table or graph.

• We have used words to describe rules and now we will look at using symbols to express rules.

Relationships between two variables

• If the tour operator charges $350 per customer, the rule for calculating the tour income can be expressed as…

Income = 350 x number of customers

• The rule for calculating the circumference of a bike tire(or any circle) can be written as…

Circumference = pi x diameter

Rules are referred to as equations or formulas

Can we write rules in a shorter form??

• Yes!!– Replace the word names for the variables with single

letters.

– Income = 350 x number of customers

– Circumference = pi x diameter

In algebra, when a number is multiplied by a variable, the multiplication sign is often omitted.

Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua.

When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua.

Addition• More than• Increase by• Greater than• Add• Total• Plus• Sum

SubtractionDecreased byDifference betweenTake Away LessSubtractLess than*Subtract from*

MultiplicationProductTimesMultiply OfTwice or doubleTriple

DivisionQuotientDivideDivided bySplit equally

Examples

3 more than x 3 + x

6 less than a number z z - 6

twice the number x 2x

the quotient of 25 and a number b 25 / b

Warm – up: Thursday

Write an algebraic expression1. 6 times the sum of 4 and y2. 6 less than twice x3. The number of years in m months4. How many minutes are in h hours5. Karen buys n raffle tickets for $0.50 each. If

she buys 13 of them, how much will they cost?

Welcome to Pre-Algebra HonorsThursday

1. Please have your homework out Core Workbook p. 19 – 21 stop at 2c and get started on your warm up.

2. Correct homework3. Intro to 4.1

– Heading Home

4. Tonight’s Assignment– Follow up 4.1 and Common Core Workbook

p.218 # 1 - 11

Warm-up: Friday

• A freight train moving at a constant speed travels 15 miles in one hour.

1. Complete the table

2. Write each pair of time and distance values as an ordered pair.

Time (h), x 0 2 4 6

Distance (mi), y

Welcome to Pre-Algebra HonorsFriday

1. Please have your homework( Follow up 4.1and Core Workbook p. 218 # 1 – 11) on your desk and get started on your warm up.

2. Discuss and Correct last night’s assignment

3. Core Workbook p. 219 - 220

4. Turn in Packets