IMP 1- 11/9 (P), 11/10 (W)

Warm Up- simplify each expression

1) 2 (x – 3)

2) 2x + 5x + 5y + 6y + 3

3) 2(x + 6)

4) 3x + 4 + 4x – 10

5) 10 – 2(3 + 4)

DUE TODAY pg. 217… Previous Travelers

Please get your work out and place on your desk.

Due Next Classpg. 221 Who Will Make It?

Use graph paper and a ruler to make your graphs

Read carefully. Write KNOW? WANT? for each question

BRING GRAPH PAPER

MISSING ASSIGNMENTS due by Nov. 13

(any assignment on report dated 11/5 or 6)

Objective

- Students will be able to find rules from tables and graphs

AgendaWarm Up/ Announcements

Scatter Plot Pre-test

Debrief Out Numbered, pg. 211- 212

Finish Previous Travelers, pg. 217 – 218

Sublette’s Cutoff, pg. 220

Goals when creating a graph

- graph accurately represents the data

- graph is not misleading

- graph is easy to read

…not cluttered, or too small

-scale is even, accurate and easy to read

- labels (with units) and title are always included

Outnumbered DebriefConstant Rate

• Constant Rate- y value changes the same each time x increases by an even amount

• On a graph,

a constant rate is indicated by a LINE

Outnumbered Debriefb = y-intercept

• y = mx + b

b is the “beginning” or the value of y

when x = 0

b is the “y- intercept” or the place where

the graph of the line touches the y-axis

Finding rules from graphs….notes

1. Where does it begin? “b”

2. Is the middle increasing or decreasing?

3. By how much?

m = rate of change

m = slope

m = how much does it change each time you add one to the x value?

EQUATION y = mx + b (conventional)

OR y = b ± mx

Basic graph terminologyLabel origin, (0, 0), x-axis, y-axis, line, quadrants I, II, III and IV, independent

axis, dependent axis

independent axis

x

y

line

origin

III

III IV

more math code…

We call the set of all points that fit a rule the “graph of the equation”

The process of putting these points together to form an overall picture is called

“graphing the equation”

pg. 213 debrief

How is looking at a graph like looking at an in-out table?

How can you tell from

the table that the graph

is not linear??

IN OUT

3 9

4 16

5 25

6 36

pg. 213 debrief

• Although the inputs are changing by the same amount each step, the outputs are increasing by different amounts

• Take the first differences

• Take the second differences

WHAT DO YOU NOTICE?

pg. 213 debrief

• CONSTANT CHANGE in the first differences with a regular change in the inputs results in a LINEAR GRAPH

• CONSTANT change in the SECOND differences with a regular change in the inputs results in a PARABOLA

pg. 213 debrief

How can you tell from a table whether or not a graph will be a straight line?

How can you tell from a table if a linear graph will go up or down from left to right?

pg. 217 – 218graph the data

How do we set up our graph?

1) decide which variable is the independent variable and which is the dependent

2) consider min/ max values in data

3) read carefully to see what info is required

4) label and scale each axis

5) plot your points

pg. 218

• Now plot the data points

• (x, y) is an ordered pair that gives us “directions” to place a point

Start at the origin.

Go right (+) or left (-) “x” units

Go up (+) or down (-) “y” units

THIS MARKS YOUR SPOT! Make a dot!

pg. 218

What does the upward trend of the data tell you? Is the change uniform?

pg. 218

• Now draw a “line of best fit”

Consider, should you start at the origin?

Does that make sense in the context of your problem?

Zero people need zero pounds of beans? YES!!! Start at (0, 0)

pg. 218

• Based on the line of best fit, how many pounds of beans will EACH of your Overland Trail families need?

Large family- 21 people

Small family- 6 people

Non- family- 7 people

Conglomerate family- 8 people

pg. 218Now find a rule for your LINE OF BEST FIT

1) make a NEW in/out table with points that spread out along the line- chose points that are on the “cross hairs” of the grid

2) write an algebraic rule for your line of best fit…

Where does it begin? (b)

Does the middle increase or decrease?

By how much each time? (± m)

MAKE SURE YOU DEFINE VARIABLES!!

pg. 218

• Predict how many beans you will need for 21 people…

1) from your graph

2) using your equation

pg. 220 Sublette’s Cutoff

1) read the problem carefully

SUMMARIZE the situation

2) write KNOW? WANT?

3) each student do # 1 – 4 on graph paper

REMEMBER steps….

4) be prepared to present your work