math 2/2/15. monday- test day no bell work tuesday: bell work *show work use notebook paper and...
TRANSCRIPT
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Math
2/2/15
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Monday- Test Day
No Bell Work
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Tuesday: Bell Work *show work
Use notebook paper and create the bell work grid
Date Work Answer
2/3
2/4
2/5
2/6
Problem of the day
1) A triangle has side lengths of 28 inches, 32 inches, and 36
inches. Which list shows the side lengths
of a similar triangle?
F 6 inches, 8 inches, 9 inchesG 14 inches, 16 inches, 18 inchesH 21 inches, 26 inches, 27 inchesJ 54 inches, 64 inches, 72 inches
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Agenda
• 1- bell work• 2- Agenda-
• *Quiz on Tuesday 2/10 over Direct and Inverse Variation
• *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28
• 3- Vocabulary• 4- Objective • 5- lesson *Direct Variation• 6- exit ticket
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21. Slope
What does this word mean to you?
This word actually means…..measure of the steepness of a line on a graph (rise / run).
Examples… Explain how you would use this word in math.
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Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
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What is it?
A set of inputs and outputs with a constant ratio called K
Variable key:X is the inputY is the outputK is the constant
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Equation
A direct variation equation follows this format
y = kxOutput = constant x input
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What are other ways you could write this equation…..
Y= kx
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What are other ways you could write this equation…..
Y= kx
So we can rework it using inverse operations
y/k = x or y/x = k
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Examples
Examples of DV equations: *notice they are 1 step!!
y = 1/5x where k=1/5
y = -2x where k = -2
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Non-Examples
Non-Examples of DV equations: *notice they can’t be 2 step!!
y = 7x + 5
y = 1/2x – 18
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How do you test?
Table: Step 1: Check the direction – both up or both
down Step 2: Divide every y by its x to see if it
matches • *if they all have the same answer then that is the
constant!!!
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TABLES
X Y X Y X Y
2 7 2 7 3 8
4 5 4 11 6 16
8 4 6 15 9 24
12 2 8 19 12 32
10 23 15 40
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GRAPHS
Direct variation lines have 2 requirements!
Linear
Through the origin
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Graph Examples
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Graph Examples
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Graph Non-Examples
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Sum it up
Line when graphed will be straight and go through the origin!
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Lines on Graph can be classified as the following
Linear
Non linear
Direct variation
Inverse variation…. To come later
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Review
You can test for direct variation with equations, tables or graphs.
Equations- 1 step and follows format y=kx
Tables- check for 1) directions of columns *must be same direction 2) find constant--divide y by x
Graphs- linear through the origin (0, 0)
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Exit Ticket
Partner Discussion
Name two additional names for direct variation. Why is it important to know the different names?
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Wednesday: Bell Work *show work
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Agenda
• 1- bell work• 2- Agenda-
• *Quiz on Tuesday 2/10 over Direct and Inverse Variation
• *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28
• 3- Vocabulary• 4- Objective • 5- lesson *Direct Variation• 6- exit ticket
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22. Reciprocal
What does this word mean to you?
This word actually means…..one of two numbers whose product is one: aka as the multiplicative inverse.
Examples… Explain how you would use this word in math.
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Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
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ProportionalDirect Variation
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Take each y value and divide it by its x value.
If the ratio of y divided by x comes out to the same value for EVERY pair of x and y, the function is proportional.
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1) X Y Proportional? 5 10 6 11 7 12 Common ratio? 8 132) X Y Proportional? 5 10 6 12 7 14 Common ratio? 8 16
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Direct Variation is very similar to proportional functions.
For direct variation, first check that X and Y both change in the same direction (both up or both down)
Then check to make sure the ratio of y divided by x matches for all pairs of x and y.
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1) X Y
1 5
2 6
3 7
4 8
2) X Y
1 2
2 4
3 6
4 8
3) X Y
1 10
2 9
3 8
4 7
4) X Y
1 10
2 9.9
3 9.8
4 9.7
31
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1) X Y
1 50
2 100
3 150
4 200
2) X Y
100 500
200 400
300 300
400 200
3) X Y
66 3
55 5
44 2
33 1
4) X Y
1.5 1
3 3
4.5 4
6 6
32
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1) X Y
10 5
20 6
30 7
40 8
2) X Y
10 2
20 10
30 16
40 28
3) X Y
100 10
90 9
80 8
70 7
4) X Y
1 10
2 9
3 8
4 7
33
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1) X Y
10 5
20 10
30
40
2) X Y
60 4
50 3.3333
40
30
3) X Y
100 1
90 .9
80
70
4) X Y
1 8
2 16
3
4
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Problem:
If y = 10 and x = -5, find y when x = 13.Formula y/x
10/-5= -2
Multiply x by the quotient
13( -2) = -26
y = -26
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Exit Ticket
Partner Discussion
What skills were needed for the N2K?
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Thursday: Bell Work *show work 3) The graph shows five points of a relation. Which equation best represents this relation?
F y = 3x + 6 G y = 3x - 6 H y = 2x - 3 J
13
1 xy
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Agenda
• 1- bell work• 2- Agenda-*
• *Quiz on Tuesday 2/10 over Direct and Inverse Variation
• *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28
• 3- Vocabulary• 4- Objective • 5- lesson – N2K and Inverse Variation• 6- exit ticket
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23. Inverse
What does this word mean to you?
This word actually means…..operations that undo each other: (addition/subtraction or multiplication/division).
Examples… Explain how you would use this word in math.
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Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
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Inverse VariationAKA:
Inversely Proportional
Or just plain
Not-Proportional
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Need 2 Know 3-5
Critical Thinking: Answer the question Justify in words and work your answer
Constructed Response: Make a function table then graph the answers **label your axis correctly
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What is it?
A set of inputs and outputs with a constant product called K
Variable key:X is the inputY is the outputK is the constant *k cannot be 0
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Equation
A inverse variation equation follows this format
y = k/xOutput = constant divided input
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What are other ways you could write this equation…..
Y= k/x
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What are other ways you could write this equation…..
Y= k/x
So we can rework it using inverse operations
k/y = x or yx = k
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Examples
Examples of IV equations: *notice they are 1 step!!
y = 5/x where k=5
y = -4/x where k = -4
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Non-Examples
Non-Examples of IV equations: *notice they can’t be 2 step and that it must be k/x!!
y = x/6
y = x/-3
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Tables
Input (x) Output (y)
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How do you test?
Table: Step 1: Check the direction – going in opposite
directions *1 least to greatest and 1 greatest to least
Step 2: Multiply every y by its x to see if it matches (yx = k)
• *if they all have the same answer then that is the constant!!!
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TABLES
X Y X Y X Y
2 7 2 7 4 30
4 5 4 11 6 20
8 4 6 15 8 15
12 2 8 19 10 12
10 23 12 10
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GRAPHS
Inverse variation lines have 2 requirements!
Non-Linear *curved lines!!!
It is actually 2 curved lines in 2 opposite quadrants
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Graph Examples
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Graph Examples
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Graph Non-Examples
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Sum it up
Line when graphed will be 2 curved lines in opposite quadrants! Be careful because some graphs are only in the 1st quadrant and when graphed you don’t see the 2nd line.
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Review
You can test for inverse variation with equations, tables or graphs.
Equations- 1 step and follows format y=k/x
Tables- check for 1) directions of columns *must be opposite direction 2) find constant--multiply y by x
Graphs- 2 non linear lines in opposite quadrants
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Lines on Graph can be classified as the following
Linear
Non linear
Direct variation
Inverse variation
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Exit Ticket
Partner Discussion
What are two distinguishing features of a direct variation line?
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Friday: Bell Work *show work Reminder – bell work is due today!! Complete it quickly!
1) A recipe for making 12 cups of soup requires 5 cups of water. At this rate, how many cups of water are required to make 6 cups of soup?
A 2 1/2 cups B 10 cups C 7 cups D 1 cup
2) A recipe for making 14 cups of soup requires 4 cups of water. At this rate, how many cups of water are required to make 7 cups of soup?
A 3 cups B 1 1/2 cups C 10 cups D 2 cups
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Agenda
• 1- bell work• 2- Agenda-
• *Quiz on Tuesday 2/10 over Direct and Inverse Variation
• *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28
• 3- Vocabulary• 4- Objective • 5- lesson *Inverse Variation• 6- exit ticket
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24. Equation
What does this word mean to you?
This word actually means…..math sentence that shows two equivalent expressions.
Examples… Explain how you would use this word in math.
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Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
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Finish Thursday’s notes
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Exit Ticket
Partner Discussion
What is the difference between a direct and inverse variation equations?