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?