Acceleration to Algebra Unit 1

THURSDAY 8/7

Complete the following: 1.3, 6, 9, 12, __, __, __ 2.0.5, 1.0, 1.5, __, __, __ 3.¼, ½, ¾, __, __, __ ¼1½

Complete the following TABLE What number is missing? How can you figure out what should go there? ? What letters typically go at the top of the table? ?? 4.50 xy

Using Ratios Use a Ratio to determine the missing values: Hour2348 Mile To find the ratio, divide: 50 / 2 = _____ 100 / 4 = _____ 200 / 8 = _____ 25 ?75 What letter would go here? x y y / x

FRIDAY 8/8

NOTES Ratio: an ordered pair of non-negative numbers – a:b, a/b, a per b Rate: a ratio of 2 quantities, typically simplified – 50 miles per 2 hours = 25 miles per hour (25mph) – $3.60 for 4 pens = $0.90 per pen Unit Rate: numerical part of a simplified rate – 25 miles per hour  unit rate = 25 – $0.90 per pen  unit rate = 0.90

PRACTICE Answers: 1 a) Rate = 60 miles / hourUnit Rate = 60 b) Rate = 12 customers / dayUnit Rate = 12 c) Rate = 2.5 meters / secUnit Rate = 2.5 d) Rate = $1.59 / poundUnit Rate = Possible: 9 R to 2 L / 36 R to 8 L / 27 R to 6 L 3 Mr. Rowley: 16 HW to 14 ET Unit Rate = 1.14 Ms. Rivera: 64 HW to 60 ET Unit Rate = 1.07 NOT EQUIVALENT!Rowley is Higher Pg 4 #’s 1 (a-d), 2, & 3

NOTES Proportional Relationship: Quantities are proportional when there is a constant rate between all x and y values y / x = same number or k (constant)

Turn to Page 6 Is example 1 an example of a proportion? ** Remember: y / x YES!! 0.40 is the constant rate  0.40 = k

Turn to Page 8 Using the constant of proportionality, find the missing value for week 7. Answer: $196  How did you get this? What would the value be for 0 weeks? Answer: $0

Turn to Page 11 Practice identifying if the table contains proportional relationships. If yes, identify k (the constant of proportionality).

HOMEWORK: Page problems 1-9

MONDAY 8/11

Turn to Page 16 As a class, we will complete pages 16 & 17

Turn to Page 19 As a class, we will complete pages 19 & 20

NOTES Graphing Proportional Relationships – In Tables: Proportional Relationships always contain ( 0, 0 )!! – In Graphs: Proportional Relationships always pass through the origin!!

HOMEWORK: Page 18 #’s 1 & 2 Page 21 – 22 #’s 1(a,b,c), 2, & 3(a&b)

TUESDAY 8/12

NOTES Independent vs. Dependent Variable x = independent variable Ex: how many things you buy y = dependent variable Ex: how much you spend The dependent variable changes in response from the independent variable.

Turn to page 23 You and your shoulder partner will each get 2 different problems. For each problem: – Figure out which one is the independent (x) and dependent (y) variables. Create a table with this information. – Label your graph with the information from the table. Make sure your scale fits the graph. – Decide if the problem is proportional and explain why or why not. If it is, make sure to identify the constant of proportionality.

HOMEWORK: Page 25

WEDNESDAY 8/13

Turn to page 26 As a class, we will complete pages 26 & 27

Square MilesNumber of Deer What letter goes here? x y If we know the constant of proportionality (k), How can we find y? How can we find x? Multiply by k  9x Divide by k  270/9 ? ? Will this process always work?YES!

NOTES Equations with Proportionality – You can create “equations” with constants of proportionality! Remember, to find y we multiplied! The equation is: y = kx (k is the constant of proportionality)

Turn to page 31 As a class, we will complete pages 31 & 32

HOMEWORK: Page all

THURSDAY 8/14

Turn to page 40 As a class, we will complete problem 2

Turn to page 43 QUESTION: – To begin the table, what is ALWAYS the first (x,y) value? ( 0, 0 )

HOMEWORK: To study for the TEST tomorrow: Pg 40 #1 Pg 42 #3 & 4 Pg 45 #1 Pg 48 all

FRIDAY 8/15