Patterns & Proportions Unit 1 - Science

Simple Proportions If Y is directly proportional to X then… …If X doubles, Y will __________. Double

Directly Proportional Equation: k X

How do I solve for K? Graph Y vs. X & the slope = k (k is called the proportionality constant).

Natural Graph vs. Linearized Graph Don’t Need Y X

Let’s Try An Example: You are curious if there is a relationship between the height of a child and its weight. You collect the following data by measuring all the children on your street…

Here is the data you collect: Height (in) Weight (lbs.) 25 31 29 35 33 44 41 51 45 54

Graph the information on the graph grid in your notes.

Your graph should look similar to this: Height and Weight Relationship of Babies Weight (lbs) Height (in)

Next Steps: Write the EQUATION FORM: Y= kx Circle your cross points. Solve for K. K = (50-0)/(40-0) = 50/40 = 1.25

So our real world equation is: 1.25 h Where W is the weight & h is the height.

Summing it up! Answer: 65 lbs Based on the shape of your graph, the weight of a child is directly proportional to height. This means if a child is THREE times as tall it will weigh 3 times as much! Use your real world equation to predict how much a child would weigh if she was 52 inches tall. Answer: 65 lbs

Now try it on your own! Go back to your turtle graph and determine the real world equation. K = 0.6 and real world equation is d=0.6t

Now let’s do a real world application Now let’s do a real world application. Follow the instructions for the Spring Lab found below.

Simple Proportions If Y is inversely proportional to X then… …If X doubles, Y will __________. Half

Inversely Proportional Equation: k __ X

How do I solve for K? Graph Y= 1 __ X & the slope = k

Natural Graph vs. Linearized Graph Y Y X 1/x

Inversely Proportional Example: You are curious if there is a relationship between the time you study for a test and the number of points you miss. You keep track of your test scores for the year…

Here is the data you collect: Time (min) Missed (pts.) 5 10 25 2 40 1 50

Graph the information on the first graph grid in your notes.

Your graph should look similar to this: How study time affects my grade Missed (pts.) Time (min)

Now we need to linearize the graph: To do this we will graph 1/x and Y. First we need to change our data table.

Our new data table will look like this: 1/x Y 1/5 = .2 10 1/10 = .1 5 1/25 =.04 2 1/40 = .025 1 1/50 = .02

Graph the information on the second graph grid in your notes.

Your graph should look similar to this: 1/x

Next Steps: Write the EQUATION FORM: Y= k/x Circle your cross points. Solve for K. K = (4-3)/(.08-.06) = 1/.02 = 50

So our real world equation is: P = 50 __ t Where P is the points & t is the study time.

Summing it up! Based on the shape of your graph, the points lost on a test are Inversely proportional to Study time. This means if you study FIVE times you will loose 1/5 as many points! (See studying helps!) Use your real world equation to predict how many points you would miss if you only studied for 2 minutes. Answer: 25 points

Now try it on your own! Go back to your medication graph from the basic graphs lab and determine the real world equation.

Now let’s do a real world application Now let’s do a real world application. Follow the instructions for the Mass Lab found on the next page.