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# New week 7

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### New week 7

1. 1. Welcome to Pre-Algebra Monday: Week 17 1. Review Slope 2. “Redo” Slope Art Project
2. 2. Introduction To Slope
3. 3. Slope is a measure of Steepness.
4. 4. Types of Slope Zero Negative Positive Undefined or No Slope
5. 5. Slope is sometimes referred to as the “rate of change” between 2 points.
6. 6. If given 2 points on a line, you may find the slope using the formula m = y2 – y1 x2 – x1
7. 7. The formula may sometimes be written as m =∆y . ∆x What is ∆ ?
8. 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. 9. The End
10. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
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