Independent and Dependent Variables

What are the dependent and independent variables in the pattern problems?

**Independent: Doesn't change
**Dependent: depends on the independent

Independent- n or the figure #
Dependent-net value  (total neg + pos)


What kind of graphs are we going to make?

R-50 Patterns

Draw what the fourth and fifth one would look like.
1. n x 3 + 1 or n+n+n+1

**This is linear because it is going up by a constant rate of 3

2. n x 2 + -1  or n x 2-1

Dark is negative, Grey is positive

**This is linear because it is going up by a constant rate of 2

3. (n x 2) + (n x -2) +-4 or n x 0-4  or n +-n+-4

Dark is negative, grey is positive

**This is linear. It make a straight line and is going up by a constant rate of 0. The x changes, but the y remains -4.

4.even=0
odd=-1

**Not linear

5.(n x n) +1 (for negatives)
(nx-n)+-1 (for positives)

(nx2) + ((nx-n)+-1))

**Not Linear

6.Odds n+-4
Even n+4

nx2+1

**Not linear

Linear Relationships

Walking Experiment Outside-
Students were given a stop watch and meter stick and were expected to record times for walking 10 meters.

Represent your data:
Graphs
Tables
Equations
Unit rates
ratios
Proportions

**Our Best Guesses
Tell us everything you know about Linear Relationships. What generalizations can you make?

-Constant of proportionality in graph/table
-Looks like a table/graphed in a unit rate
-2 numbers in a ratio
-Table/graph should go up by a steady rate
-Graph-straight line
-Dependent and Independent variable
-Should be able to find a constant someplace

Baby and Adult Chimps

Baby Chimps
40% high fiber
60% high protein

Adult Chimps
60% high fiber
40% high protein

Tell us everything you know about this information? How can you represent it?

Tables
Graphs
Proportions
ratios


Equations: Which one works? Come up with a mathematical justification.

P=protein
F=fiber 

Baby Chimps
P/1.5=F     
F x 1.5 =P

Adult Chimps 
P x 1.5=F


L-44 New problem

The zoo keeper is making a batch of baby chimp food. He decides the food will have a total of 125 scoops. How many of those scoops will be high fiber? 
-You must use a proportion to solve the problem.

40 = x 
10    40

125   =  x  
100       40

Does this work?
40  =  50   (40 + 10=1/4 of 40)
60      75  (60 + 15=1/4 of 60)

Proportions

*Something to something else ratio
*Help you compare
*Need three pieces of info.
*Different ways to set one up
*Find a scale factor
*Use them to find a %
*Helps find mystery value

R-39 Percents

Core Math Goal: How can you use proportions to find percentages of a value when you know a certain percentage of the same value?

TMWYK: Percents


-Similar to fractions
-Show a fraction-25%=1/4
-multiply/divide turn % into decimal part of a #
-Out of 100 26/100=26%

Constant of Proportionality
-The other number in a unit rate that is not the 1
-The amount the thing goes up or down by each time
43:1

R-40
Sweater cost $36
7% sales tax

How much will the sweater cost?

Digital Camera
$249.99
4% sales tax

How much does the sweater cost?