Transcript IMP 1 - Shope-Math

IMP 1- 10/21 (P), 10/22 (W)
• Warm up- do back side of “Percent
Review” – look in your folders! 
exit quiz- debrief (P)
• let A = # apples
B = # bananas
D = cost for a piece of fruit
Write an algebraic expression for each
summary phrase:
1) total # of pieces of fruit
2) cost for bananas
3) cost for apples
4) total cost for apples and bananas
DUE TODAY
Pg. 184 Haybaler POW
first DRAFT
Submit in left side of group folder
Due Next Class
pg. 267 Substitute, Substitute
Start by writing the problem on your paper.
Show your substitutions and your steps.
Remember if x = -1, then –x = - (-1) = +1
(remove cold = add hot)
study for quiz on summary phrases, like
variables, and substitution next class
Objective
- Students will be able to write
verbal descriptions for algebraic
expressions
Agenda
Warm Up/ Announcements
More Summary Phrases, pg. 270
If I Could See This thing, pg. 202 – 203
Wagon Train Sketched and Situations. pg. 205- 206
Quiz – summary phrases
Algebraic Expressions
and Summary Phrases
• Situation
- total number of trees on a street
• THINK- #’s…. Say 2 trees per yard, 20
yards on a street, WHAT operation would
you do to find the total # of trees on a
street?
Arithmetic (numbers)
• 2 (20) = 40 trees on a street
• What if there are 3 trees per yard and 50
yards on a street?
• 5 trees per yard and 100 yards per street?
• 2 trees per yard and 30 yards per street?
what pattern do you see?
•
•
•
•
2 (20) = 40
3 (50) = 150
5 (100) = 500
2 (30) = 60
What did we do? what do 40, 150, 500 and
60 represent?
Now algebra (generalization w/ variables)
• Let ____ = avg. # of trees per yard
• Let ____ = # yards on a street
• ____ _____ = # trees on a street
NOT- # trees per yard times number of
yards on a street….
• NOTICE--- no “yard” in summary phrase -- UNITS cancel!!
SUMMARY PHRASE
• the WORDS that describe the situation
in general
The summary phrase is
“the number of trees on a street”
Algebraic expression
 summary phrase
1) Read to see what the variables represent
2) Think of a numerical example
3) Write a concise phrase to describe what
the expression represents
Classroom Expressions,
pg. 270
Find a summary phrase for the following
algebraic expressions:
1) B + G
2) G PG
3) BM + BHM
4) LS
VARIABLES are defined on pg. 270!!
Percent Review
• All of something = 100%
• Percent means “per cent” or “divide by 100”
100% = 100/100 = 1.0
50% = 50/100 = 0.50
10% = 10/100 = 0.10
5% = 5/100 = .05
If 90% see movie, ____% DON’t see movie?
If I could see this thing, pg. 202+
• READ pg. 202 together
SUMMARIZE what we read
1)
WANT?
KNOW?
Pg. 202, #1
• Chose a population for 1492.
• How much is 90% of that population?
What happened to 90% of the population?
• How many people are left in 1900?
• How would you write this using variables?
• What equation describes the situation?
Make sure you define your variables!
Pg. 202, # 2
2)
Want?
Know?
NOTE– how many adults and how many
children are in our wagon train?
Pg. 202, #2
• 2c-- describe what you did to get your
numeric results in 2a and 2b.
• Look for arithmetic patterns
• Define your variables
• Use variables to write an equation that
describes the situation
If I could see this thing- debrief
• Does it make sense for the output to be a
decimal number?
• How can you resolve this?
Add vocabulary to handout add visual
constant rate
rate of change stays the
same; Δy/Δx is a number;
graph is a straight line
linear
data forms a line when
graphed
data is not connected
data is connected
discrete
continuous
independent
variable
dependent
variable
the changing quantity
represented by the “in”;
plotted on the x-axis
the “out”; the quantity
that changes as a result of
changes in the “in”;
plotted on the y-axis
pg. 205- 206
• read pg. 205 together
• Who can summarize what we read?
Note- these graphs are different than
frequency bar graphs. We will use a
horizontal (x-axis) and vertical (y-axis)
In this activity:
want? ____________________
Know? given a graph with labels but no
numbers– describe in general terms! 
what story does the “shoes or boots versus
people” tell?
• beginning?
• middle? how is it changing?
is it increasing or decreasing? by how much?
is it linear?
is the change at a constant rate?
• end?
each student needs to record their ideas
for each graph on the activity handout
- to be submitted
BE READY TO PRESENT YOUR WORK!!
pg. 205 – 206 debrief
1. Note change in coffee consumption is at a
constant rate
– the graph goes down the same amt every
day
- they drink the same amt of coffee every day!
2. What might be happening at point A? B? C?
pg. 205-206 debrief
3. Where is the graph the steepest? What is
does that tell about the speed of travel?
What might cause the wagon train’s speed
to change?
What would the graph sketch look like if the
wagon train had covered the distance at a
constant rate?
pg. 205- 206 debrief
4. Why are there points instead of a line?
Discrete= broken graph
Continuous= non-broken graph
pg. 206
• Do # 5 – 7 in your CW
BE READY TO PRESENT TO THE CLASS
• independent variable- plot on the x-axis or
horizontal axis
• dependent variable- plot on the y-axis or
vertical axis
pg. 207- handout
• Do # 1 – 4
WANT?
Each student needs to write their ideas on
the handout- to be submitted
BE READY TO PRESENT TO CLASS!
DO PART II on index card- trade with
someone in your group
pg. 207 debrief
2. Discrete graph- broken graph
why can’t it be continuous?
3. “step function”- the graph jumps from one
horizontal segment to the next
continuous independent variable but a
discrete dependent variable!!
Which are linear? non-linear? how do you
know??
Exit QUIZ
Find a summary phrase for each
expression:
Let C = # of classes in a hall 10 classes
B = # of boys in a class
15 boys
G = # of girls in a class
12 girls
1) B + G
2) CB
3) CG
4) C (B + G)