Math
2/2/15
Monday- Test Day
No Bell Work
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
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
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.
Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
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
Equation
A direct variation equation follows this format
y = kxOutput = constant x input
What are other ways you could write this equation…..
Y= kx
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
Examples
Examples of DV equations: *notice they are 1 step!!
y = 1/5x where k=1/5
y = -2x where k = -2
Non-Examples
Non-Examples of DV equations: *notice they can’t be 2 step!!
y = 7x + 5
y = 1/2x – 18
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!!!
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
GRAPHS
Direct variation lines have 2 requirements!
Linear
Through the origin
Graph Examples
Graph Examples
Graph Non-Examples
Sum it up
Line when graphed will be straight and go through the origin!
Lines on Graph can be classified as the following
Linear
Non linear
Direct variation
Inverse variation…. To come later
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)
Exit Ticket
Partner Discussion
Name two additional names for direct variation. Why is it important to know the different names?
Wednesday: Bell Work *show work
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
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.
Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
ProportionalDirect Variation
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.
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
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.
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
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
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
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
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
Exit Ticket
Partner Discussion
What skills were needed for the N2K?
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
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
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.
Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
Inverse VariationAKA:
Inversely Proportional
Or just plain
Not-Proportional
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
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
Equation
A inverse variation equation follows this format
y = k/xOutput = constant divided input
What are other ways you could write this equation…..
Y= k/x
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
Examples
Examples of IV equations: *notice they are 1 step!!
y = 5/x where k=5
y = -4/x where k = -4
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
Tables
Input (x) Output (y)
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!!!
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
GRAPHS
Inverse variation lines have 2 requirements!
Non-Linear *curved lines!!!
It is actually 2 curved lines in 2 opposite quadrants
Graph Examples
Graph Examples
Graph Non-Examples
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.
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
Lines on Graph can be classified as the following
Linear
Non linear
Direct variation
Inverse variation
Exit Ticket
Partner Discussion
What are two distinguishing features of a direct variation line?
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
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
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.
Objective
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
Finish Thursday’s notes
Exit Ticket
Partner Discussion
What is the difference between a direct and inverse variation equations?
Top Related