9/23/13 Mon

9/23/13 Mon

A photo measuring 5 inches in width by 4 inches in length is enlarged to produce a photo with a length of 16 inches.1) What is the width of

the enlargement? _________2) What scale factor

was used to make the enlargement? _________

Boot-Up 9.23.13 / 6 min.

Find p 154: Methods & Meanings

1) What is a “Ratio”?

2) How can a ratio be expressed?

3) What is a “Ratio of Similarity”?

4) What Ratio of Similarity is being used for the 2 s in the textbook?

5) What is a Zoom Factor (or Scale Factor)?

→ means 6 units of length on one hypotenuse compared to 10 units on the other hypotenuse

Where did the 3/5 come from?

Find Lesson 3.1.3

Today’s To-Do List:

3-24 3-27 3-25 3-28 3-26

Team Expectations

Facilitators: Remember, there is usually > 1 way to solve a problem. Make sure everyone’s ideas are heard.

Task Mgrs: Make sure each person justifies their ideas.

Recorder/Reporters: Make sure each person is writing.

Recorder/Reporters: Get resources as needed, including Teacher, but Make sure your team is “Asking 3 before me.”

3-24

Tracing Paper?

72

621

Does this remind you of anything we did in class?

3-24

3-24


Stretch Point (Point of Dilation)

3-24

3-24

Figure Height BaseSmall 2 6Large 7 21

27

621=

Side Small LargeHeight 2 7Base 6 21

26

721=

3-24

Figure

Height Base

Small 6 2Large x 4

6x

24=

Figure H1 H2

Small 3 6Large 4 x

34

6x=

Figure H1 H2

Small x 3Large 21 ?

3-26

3-26

Zoom Factor: 3/2 = 1.5

812

6 9

8

12

2 2

3 3

6 6

9 9

23

Graph Paper

3-27

Similar (~) figures: s are congruent (), but Sides are not. (The sides are proportional.)

3-28

Similar (~) figures:

Perimeters (& side lengths) are found by multiplying by the zoom (scale) factor.

Areas are found by multiplying by the square of the zoom (scale) factor.

Areas

Ratios: A comparison of 2 #s.Ex: 1 dog : 2 cats 1

2

Proportions: A comparison of 2 ratios.1 = 22 4

Lesson 3.1.3pgs 158 – 159#s 3-29 – 3-34

9/124/13 Tue

Boot-Up 9.24.13 / 6 min.

1) What is the relationship between the s shown below?

A) Congruent B) Complementary C) Supplementary

2x + 3

4x - 9

2) Solve for x2x + 3

4x - 9

0

10

20

30

40

50

60

70

80

90

100

7774

80 8272

Block 1 Test Performance: Class Averages / Term 1

1st Time 2nd Time

A B C D F0

1

2

3

4

5

6

7

6 (30%)

1 (5%)

5 (25%)

6 (30%)

2 (10%)

Chapter 2 End-Unit Test 9/18/13 1a

0

10

20

30

40

50

60

70

80

90

100

7470

78 8272

Block 2 Test Performance: Class Averages / Term 1

1st Time 2nd Time

A B C D F0

1

2

3

4

5

6

7

8

9

10

5 (19%)

9 (33%)

2 (7%)

4 (15%)

7 (26%)

Chapter 2 End-Unit Test 9/18/13 2a

1) What do we know about these s?

2) What do we know about the red s?

3) What do we know about the green s?

Alternate Interiors

Alternate Interiors

Supplementary = 180

2-38

2-46

Same Side Interiors Supplementary

Rianna says something’s wrong with this picture. Do you agree?

What is the sum of s x & y?

2-47

2-48

Based on the degree measurements shown, must lines FG & HI be parallel? If so, complete this sentence:Theorem:

If ______________ angles are supplementary, then the lines intersected by a ___________ are ________.

2-48

Theorem: If same-side interior angles are supplementary, then the lines intersected by a transversal are parallel.

Similar (~): Figures that are the same shape but not necessarily the same size.

x°

x° y°

x°

x° y°

Honey, I shrunk the Polygons! (They still

look the same, though.)

~ ~

Similar (~) figures: Their orientation (position in space) does not matter!

~~

Honey, I shrunk the Polygons! (They still

look the same, though.)

Similar (~) figures: Angles are congruent, but Sides are not. (The sides are proportional.)

x°

z°

y°

z°

y° x°

Proportional: The lengths of corresponding sides of similar figures form equivalent fractions.

8”

6”

4”

3”

What other fractions that are equivalent to 3/4?

x°

z°

y° y° x°

z°

y°

10

12

x

18

A) 10 B) 12 C) 15 D) 180

The following diagram shows similar figures.What is the value of side x?

15 ft.9

ft.

10 ft.

6 ft

.

Similar (~) figures: Angles are congruent (), but Sides are proportional.

50° 50°

80°

3.2

in. 3.2 in.

4.1 in.

55° 55°

70°

2.9

in. 2.9 in.

3.5 in.

15 ft.9

ft.

10 ft.

6 ft

.

So, look at the angles 1st! If the angles are not , then the figures are not ~

50° 50°

80°

3.2

in. 3.2 in.

4.1 in.

55° 55°

70°

2.9

in. 2.9 in.

3.5 in.

What is this question asking you to find?

How can you use similarity to solve this problem?

Is there something in this room that you can use to compare to the monument?

What parts do you need to compare?

Do you have any math tools that can help you gather information?

3-35

3-35

3-35

5 cm20 cm

n ft.60 ft.=

20 n =

=

60 5

20n 300

=n 15

3-36

ACAB

DFDE

=

9/25/13 Wed

Ant-Man is 4 inches tall, and his shoulders are 2.5 inches wide. After taking a Pym Particle, he has grown to 28 inches tall.

1) How wide are his shoulders when he grows to 28 inches tall? _______________

2) What is the zoom (scale) factor of the Pym Particle he took?

A) 2.5 B) 4 C) 7 D) 28

4 28

2.5 w

=

4 w =

=

28 2.5

4w 70

=n 17.5

Figure Height WidthSmall 4 2.5Large 28 w

10

12

x

18

The following diagram shows a dilation. How can we solve for x?

Figure Height WidthSmallLarge

10

12

x

18

The following diagram shows a dilation. How can we solve for x?

Figure Height WidthSmallLarge

Small Hypotenuse BaseLarge Hypotenuse Base=

=GI PR GH PQ

3-37

3-38

3-38

3-39

3-40

8 min.

Lesson 3.1.4pgs 164 – 165#s 3-41 – 3-46

9/26/13 Thu

If BD = 6, DA = 2, and BC = 15, which proportion would you use to find BE?

Boot-Up 9.25.13 / 6 min.

Put HW & HW log on you desk for teacher to check.

Boot-Up 9.25.13 / 6 min.

6 x

156

2


Stretch Point (Point of Dilation)

3-24

3-24

3-49 a.

87 + 68 + ? = 180

87 + 25 + ? = 180

AA Triangle Similarity (AA):When 2 pairs of corresponding s are , the 2 s must be . If 2 pairs of s are , the 3rd pair must also be .

ACAB

DFDE

=

M&M

3-50 b.

3-50 b.

SAS Triangle Similarity (SAS):When 2 pairs of corresponding sides are proportional, & the s between those sides are , then the other correspondings must also be , & the remaining pair of sides must be proportional.

3 46 8

3-51 a.

3-51 a.

3-51 b.

3-51 b.

3-52

9/27/13 Fri

The following diagram shows a dilation.Which proportion could be used to determine the length of side x?

h’

h

b’

b

Boot-Up 9.27.13 / 6 min.

3-59a 3-59b

3-60

C R

CAT PGI

SAS What do you notice about the order of the letters?

3-60

Facts

ConclusionSimilarity Condition

3-61

3-61

A G C P

CAT PGI

3-61

3-62

3-63

Lesson 3.2.3

3-71

3-71

3-72

3-73

3-74

Which statement is true about ABC and JKL? A) The triangles are congruent.B) The triangles are similar.C) The ratio of the lengths

of corresponding sides is not constant.

D) Corresponding angles are not congruent.

Mastering the MCT2, Grade 6, p11,3c, P

3 mins1/30/13 DO NOW

Released 2009MCT2, Grade 6, Test 2; 4d

Which proportion could be used to determine the length of side x?

52. The following diagram shows a dilation.

a’

a

b’b

12

6

8 x

TTW Lead-in to Exit Ticket:

10

12

x

18

A) C)

B) D)

The following diagram shows a dilation.Which proportion can be used to find the value of side x?

6 2

5

15

Draw a dilation of a figure using a Scale Factor of 3.

Draw a dilation of a figure using a Scale Factor of 1/2.

6 3

14

7

My Turn:What is the Scale factor to go from the smaller figure to the larger figure?

4 12

3

9

3 12

2

8

Your Turn:What is the Scale factor to go from the smaller figure to the larger figure?

4 12

3

9

My Turn:What is the Scale factor to go from the Larger figure to the smaller figure?

3 12

2

8

My Turn:What is the Scale factor to go from the Larger figure to the smaller figure?

An original photograph of Kimberly is 3.5 inches wide by 5 inches long.She wants to get an enlargement measuring 28 inches wide by 40 long.What is the scale factor of the enlargement?A. 3.5 B. 5 C. 8 D. 28

Released 2009MCT2, Grade 6, Test 2; 4d

The following diagram shows a dilation.

What is the scale factor to go from:

1) the smaller figure to the larger figure?

a’

a

b’b

2) the larger figure to the smaller figure?

TTW:

TSW:

49. Triangle PQR has been dilated to create triangle P′Q′R′.

Based on the figure at right, which of the following statements is true?

MCT2, Grade 6, 3e

RELEASED 2008- TEST 1

CHALLENGE QUESTION!!!

4. What are the coordinates of the dilation image of triangle ABC with a scale factor of 2?A A‘ (-4, -4), B‘ (2, -2), C‘ ( 0, 4)B A‘ ( 0, 4), B‘ (2, -2), C‘ (-4, -4)C A‘ (-4, -2), B‘ (3, -1), C‘ ( 0, 4)D A‘ (-2, -4), B‘ (1, -3), C‘ ( 0, 0)

34 Mastering the MCT2, Grade 6

Students work in pairs to solve the following:

DO NOW 2/16/116B Start here Wed 2/16

Released 2009 MCT2, Grade 6, Test 2; 3e

28. The following diagram shows the image and pre-image in a 200% dilation.

4) Identify corresponding parts (sides & angles) of similar polygons

Corresponding angles of similar figures are Congruent!

50. Lubresha performed a 50% dilation on figure KLMN as shown below.

MCT 2 – Grade 6, Test 3, 3e

What is the relationship between the length of K'L' and KL?F. The length of K'L' is half the

length of KL.G. The length of K'L' is twice the

length of KL.H. The length of K'L' is the same

as the length of KL.J. The length of K'L' cannot be

compared to the length of KL.

Released 2010

4) Identify corresponding parts (sides & angles) of similar polygons

Corresponding sides of similar figures are proportional!

30. Look at the figure below.


Which statement about the figure is not true?

F. A’B’C’D’E’ is increased to ABCDE by a scale factor of 200%.

G. ABCDE is a reduction of A’B’C’D’E’ by a scale factor of .

H. O'B’ is twice OB, and E 'D’ is twice ED.

J. AB is a reduction of A’B’ by a scale factor 50%.

Released 2010

16”

x”9”

3”

The triangles show below are similar figures. What is the length of “x”?

An 8 inch by 10 inch photo is enlarged to produce a inch by 24 by 30 inch photo.What scale factor was used to make the enlargement?A. 2 B.

3C. 8 D.

10

Exit Ticket: SWBAT correctly answer the following problem by the end of today’s

lesson:

This will be collected & graded as classwork. Put on a separate sheet with heading: Name, Date, Exit Slip: Scale Factors. SHOW ALL WORK! If you do not show step-by-step work as taught today, you will not get credit.

If BD = 6, DA = 2, and BC = 15, which proportion would you use to find BE?A 4 inch by 5 inch photo is

enlarged to produce a 16 inch by 20 inch photo.What scale factor was used to make the enlargement?

Original (Pre-Image)

Copy (Image)

Width

Length

Scale Factor: Image: 16 Pre-Image: 4

4=

w5

4 16

45. Manuel baked a cake. He used 0.75 cup of frosting and 0.5 cup of sugar. How should Manuel write these decimals as fractions? A. 75/100 and 5/10 B. 75/10 and 5/10 C. 75/100 and 5/100 D. 75/10 and 5/100

MCT2, Grade 6, Test 2; 1f

A regular triangle with 5-inch sides undergoes a dilation with scale factor 2.5. What are the side lengths of the image triangle?A. 7.5 in. B. 12.5 in.C. 17.5 in. D. 20 in.

IND is the image of MRE under adilation. What is the scale factor of thedilation?

SWBAT: 1) Determine the scale factor of a given proportion.

3e. Dilations

Explain the relationships between corresponding parts of the pre-image and

image of a dilation. (DOK 2)

48. XYZ is shown below.


If the coordinates of Z’ are (3, 1), which statement describes the transformation of point Z?

F. Point Z was translated 2 units to the right and 3 units down.

G. Point Z was translated 3 units to the right and 2 units down.

H. Point Z was translated 2 units to the left and 3 units up.

J. Point Z was translated 3 units to the left and 2 units up.Released 2010


lesson:


If BD = 6, BA = 8, and BC = 15, which proportion would you use to find BE?A 4 inch by 5 inch photo is


8


lesson:


If BD = 6, DA = 2, and BC = 15, which proportion would you use to find BE?A 4 inch by 5 inch photo is


9/20/13 Fri

Resource Manager: Make sure to get all of the supplies & call the teacher over, if needed. Take shape inventory at beginning & end. Make sure all shapes are returned to bucket.

Facilitator: Make sure that everyone can participate & that no one dominates the process.

Recorder/Reporter: Make sure that everyone can reach & see the Venn diagram & the shapes. Record shape placements / present findings at end of lesson.

Task Manager: Make sure each team member justifies statements & decisions.

y

x

I

IVIII

II

UN # __________Name __________ 8/29/13 Test # 1

11)

8/30/13 Thu

y

x

I

IVIII

IIA B

D C

Translate (Slide) rectangle ABCD so that point A is at the origin.

Tell me -- do I really look like a “Leonard” to you?

A B

D C

Documents

9/23/13 Mon