This document provides an overview of a pre-algebra class covering slope, rates of change, writing rules and expressions, and solving word problems algebraically. It includes examples of slope calculations, tables showing relationships between variables, instructions for homework assignments, and introductions to topics like patterns and rules. The key topics covered are representing relationships between variables with algebraic rules and expressions, translating words to algebra, and using tables and graphs to investigate patterns between variables.

1. Welcome to Pre-Algebra
Monday: Week 17
1. Review Slope
2. “Redo” Slope Art Project

2. Introduction
To Slope

3. Slope is a
measure of
Steepness.

4. Types of Slope
Zero
Negative
Positive
Undefined
or
No Slope

5. Slope is sometimes
referred to as the
“rate of change”
between 2 points.

6. If given 2 points on
a line, you may find
the slope using the
formula m = y2 – y1
x2 – x1

7. The formula may
sometimes be written
as m =∆y .
∆x
What is ∆ ?

8. 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

9. The
End

10. 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

11. Expected Cost and the Resulting Profit:
Number
Of
Customers
Income
Bike Rental
Food and Camp
Cost
1
2
3
4
5
6
7
8
9
10
Do you see any patterns in the above table?
Van Rental

12. PAYING BILLS AND
COUNTING PROFITS
Cost of trip: $350 per rider
$30 per person for a bike
$125 per person food and camp
$700 per tour for van rental

13. 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?

14. Warm-up: Wednesday
• Determine whether the rate of change are
constant or variable.
1 2
3
1. Weight(lb)
Price ($)
2.
3
Constant Speed
(mi/hr)
Time (h)
6
9
10
20
30
3
1.5
1
Fill in the question marks
?
3. Slope = rise
?
changeinx value

15. 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

16. 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!!

17. Relationships between
two variables
• 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.

18. • 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

19. 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.

20. Although they are closely
related, a Great Dane weighs
about 40 times as much as a
Chihuahua.
An expression for the weight of the
Great Dane could be 40c, where c is the
weight of the Chihuahua.
When solving real-world problems, you will need
to translate words, or verbal expressions, into
algebraic expressions.

21. Addition
•
•
•
•
•
•
•
More than
Increase by
Greater than
Add
Total
Plus
Sum
Multiplication
Product
Times
Multiply
Of
Twice or double
Triple
Subtraction
Decreased by
Difference between
Take Away
Less
Subtract
Less than*
Subtract from*
Division
Quotient
Divide
Divided by
Split equally

22. 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

23. Warm – up: Thursday
Write an algebraic expression
1. 6 times the sum of 4 and y
2. 6 less than twice x
3. The number of years in m months
4. How many minutes are in h hours
5. Karen buys n raffle tickets for $0.50 each. If
she buys 13 of them, how much will they
cost?

24. Welcome to Pre-Algebra Honors
Thursday
1. Please have your homework out Core Workbook p.
19 – 21 stop at 2c and get started on your warm up.
2. Correct homework
3. Intro to 4.1
– Heading Home
4. Tonight’s Assignment
– Follow up 4.1 and Common Core Workbook
p.218 # 1 - 11

25. Warm-up: Friday
• A freight train moving at a constant speed
travels 15 miles in one hour.
1. Complete the table
Time (h), x
0
2
4
6
Distance (mi),
y
1. Write each pair of time and distance values
as an ordered pair.

26. Welcome to Pre-Algebra
Honors
Friday
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