Coordinate Graphs

Core Math Goal: How can you determine if a relationship is linear or not?? How can you see this linear relationship in a model, table, graph, and equation?

TMWYK: Coordinate Graphs

*Neg and pos
*plot points to represent data
*x-axis shows a value
*x axis is independent variable, y axis the dependent variable
*Look for patterns

Patterns

TMWYK: How can you make rules from patterns
-observations
-predict
-see what it goes up by
-more/different rules
-Must work for everything
-Identify what each part of the equation does
-compare all scenarios



Pattern Rules-

1. (n*3)+1  n=figure #

2. Dark is negative, Grey is positive

(n*3)-1  n=figure #
(the minus 1 is from the middle square)

3. Dark is negative, grey is positive

(n*2)-((n*2)+4)  n=figure

**Class discovered that every figure is equal to -4.
Different Equation: 0-4   (The n*2-n*2 cancels out or zeroates)

4.0=-1   0=odd
   E=0    E=even

5.

6.

Chimp Problem

2 different ways to write ratio

part to part
part to whole

Fiber
2/5

Protein
3/5

Baby Chimps Part to Part ratios
2amounts fiber
3 amounts protein

40 amounts fiber
60 amounts protein

4 amounts fiber
6 amounts protein

3 amounts protein
2 amounts finber          (This one was flipped around 

R-41 Proportions

R-41 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: About creating a proportion

-set it up as a fraction (2 equivalent fractions)
-use scale factor
-two=fractions w/change between them (discount or raise in price)

100 =  200
123      X

R-41

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

TMWYK: About using proportions to solve problems


$22,500

Markup 10%

Original price=??

Strategy:

Delany's Idea

10+100=110 (full price + mark up price)

10         2050
110  =   22550 (price of the car)   

***Flynn's Idea: Maybe they need to be equivalent fractions. We   can check it with that. Scale factor is 205. This means that they are equal fractions and are in proportion.
Proportional Strategy

*We should divide by 11. 10 is the mark up price 
110
10   =   11

10% of 110=11



New Problem: 

22,770=resale price
Original proce=19,800

What is the markup?

Miles Driven and Gallons used

 

Rules/equation

gallons x 30=miles

miles/30=gallons 

Gallons of gas           Distance 

 1                                   30

 2                                   60

 3                                   90

Unit rate

1 gallon to 30 miles

1 mile to .03 gallons

R-24

What is the relationship between two similar figures? (Reptiles)

Scale Factor- Number I multiply side length or perimeter by to get similar figure

Side Length- in proportion smaller side length x scale factor= bigger side length

Perimeter- small perimeter x scale factor= bigger perimeter

Area- bigger shape side lengths are a multiple of smaller shape side lengths



If my original area is 3 and my scale factor is 2 (twice as big), how can I figure out what that new area is?



If my original area is 6 and I have a scale factor of 3(3 times as big), how can I figure 

 Rule: original area x (scale factor)^2 = bigger area

(scale factor)^2= scale factor x scale factor