Pledge Problems

Plan A- $10 regardless of miles


Plan B- $2 per mile


Plan C-$5 plus $.50 per mile


Which plan is better? Why? Give three justifications (graph, table, equation)


Equations-

Plan A- $10      

Plan B- 2x=n   (x=miles, n=$)

Plan C- Miles x .50= $


What characteristics will be in all linear equations?
 -a constant of proportionality (multiply it by the independent variable)
-An equations that works for everything in the pattern (pos, neg, even, odd)
- Dependent variable = (indep. variable) (constant of proportionality)
-Amount $= (miles walked) x (4)
-unit rate***

Class is not entirely firm on these ideas.

Linear vs. Non-Linear and homework

R-56
Make observations on rules and graphs

Linear vs. No-linear

Linear                          Non-Linear
Straight line                 have two separate rules
Either pos or neg         negatives
up by a constant          doesn't go up by the same amount
have n                          have n















***The pattern of change is the constant of proportionality. How much something is going up by or down by. 


Homework: 7b pg 16 #3-5, 20

Graphing Patterns

Graphing Patterns
-example: x # of figures, y net value
-If it keeps going at the same rate, it will be straight.
-You need points to show where the data is
-You can use the rate to find the distance in between
-x comes first

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)