Things you are expected to know so far in this unit:

  1. How to write a ratio comparing two things (order matters!)
  2. How to compare two different amounts by using ratios (part-to-part or part-to-whole)

[orange concentrate problem, pizza sharing problem]

  1. How to write and use a proportion to find missing quantities
  2. Write proportion in words first
  3. Substitute in known amounts to appropriate places
  4. Use cross-multiplication and/or scale factor to solve
  5. How to find a constant of proportionality (aka unit rate) when given a table, graph, or equation
  6. How to determine if a relationship is proportional by looking at a table, graph, or equation
  7. How to create a rate table when given a description [Howdy’s/Royal problem]
  8. How to graph a relationship from a rate table and/or equation [Howdy’s/Royal problem]
  9. How to write an equation relating two variables, when given a situation [Howdy’s/Royal problem]
How to tell if a relationship is proportional from a graph
Proportional relationships:
1)Have constant rates of change (straight lines) AND
2)Pass through the origin [the coordinate (0,0)]
SKETCH A PROPORTIONAL GRAPH HERE: / Example
How to tell if a relationship is proportional from a table
  1. Use cross-multiplication to see if cross products make equivalent ratios
  2. Simplify all ratios to look for equivalent amounts
  3. Use scaling to check for equivalent ratios
Notes: / Example Proportional or Non-Proportional?
a / 2 / 3 / 7
b / 10 / 15 / 35
Proportional or Non-Proportional?
n / 0 / 1 / 2
p / 6 / 9 / 12
Practice:After your respond to the questions above, create some of your own examples.
How to tell if a relationship is proportional from an equation
  1. If the equation is in y=kx form, the relationship is proportional
  2. If the equation is y = kx + # OR y = kx - #, then the relationship is non-proportional.
Notes: / Example
Proportional / Non-Proportional
C = 6x / C = 6x + 2 OR C = 6x - 1
P = ½n / P = ½n + 2.5 ORP = ½n - 7
Y = 3x / Y = 3x + 7 OR Y = 3x - 9
Practice: Create more examples in the table above.
Finding the constant of proportionality (unit rate) when given a graph
  1. Determine that the relationship is proportional first (straight line through the origin)
  2. Pick a coordinate and divide the dependent variable by the independent variable ( )
Note: / Example:

Practice: Graph a proportional relationship on a piece of graph paper. Practice finding the constant of proportionality.
Finding the constant of proportionality (unit rate) when given a table
  1. Determine that the relationship is proportional first
  2. Divide the dependent variable by the independent variable
Tip:
If the table is horizontal, divide the bottom number by the top number.
If the table is vertical, divide the right number by the left number. / Example:
h / 0 / 4 / 9
S / 0 / 32 / 72
Constant of proportionality ______
p / C
12 / 4
18 / 6
30 / 10
33 / 11
Constant of proportionality ______
Writing an equation from a table
  1. Determine that the relationship is proportional first
  2. Divide the dependent variable by the independent variable to find the constant of proportionality.
  3. Write the equation in the form y = kx, where k is the constant of proportionality, y is the dependent variable, and x is the independent variable.
Notes: / Example:
h / 0 / 3 / 9
S / 0 / 21 / 63
Constant of proportionality ______
Equation:______
p / C
16 / 4
24 / 6
40 / 10
44 / 11
Constant of proportionality ______
Equation:______
Practice: Create your own examples on a separate sheet of paper.
How to create a rate table from an equation:
  1. Determine the independent variable.
  2. Pick different values and substitute them into the equation to find the value of the dependent variable.
  3. MAKE SURE TO INCLUDE 0 AS ONE OF THE VALUES THAT YOU PICK.
Notes: / Example:
Y = 6x
x
y
S =
j / S
How to graph from a rate table:
  1. Set up a coordinate plane in which the independent variable is on the x-axis, and the dependent variable is on the y-axis.
  2. Make sure to use consistent scaling between numbers. If the scaling is wrong, the graph will automatically be wrong.
  3. Plot the coordinates. Use a straight edge to connect the coordinates.
  4. If the graph produces a straight line through the origin, then it is proportional.
Notes: / Example:
Graph
h / 0 / 4 / 9
S / 0 / 32 / 72

How to solve a proportional problem
  1. Write the proportion in words
  2. Substitute in known values.
  3. Use cross multiplication and/or scale factor to find the missing quantity.
Notes: / Example:
Ms. Graves gave her class 12 minutes to read. Carrie read 5 pages in that time. At what rate, in pages per hour, did Carrie read?


12x = 330
12 12
X = 27.5 pages
Practice: Create your own problems.