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A pattern of shapes that fit perfectly together!
A Tessellation (or Tiling) is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.
Examples:
 |  |  | ||
Rectangles | Octagons and Squares | Different Pentagons |
Regular Tessellations
A regular tessellation is a pattern made by repeating a regular polygon.
There are only 3 regular tessellations:
 |  |  | ||
Triangles | Squares | Hexagons | ||
3.3.3.3.3.3 | 4.4.4.4 | 6.6.6 |
Look at a Vertex ...
| ||
| ||
For a regular tessellation, the pattern is identical at each vertex! |
Semi-regular Tessellations
A semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same!
There are only 8 semi-regular tessellations:
 |  |  | ||
| 3.3.3.3.6 | 3.3.3.4.4 | 3.3.4.3.4 | ||
 |  |  | ||
| 3.4.6.4 | 3.6.3.6 | 3.12.12 | ||
 |  | |||
| 4.6.12 | 4.8.8 | |||
 | To name a tessellation, go around a vertex and write down how many sides each polygon has, in order ... like "3.12.12". |
| And always start at the polygon with the least number of sides, so "3.12.12", not "12.3.12" |
 | Question 1: For the tessellations above, is the pattern the same at each vertex? |
| Question 2: One of those patterns becomes different when you make a mirror-image of it ... which one? |
Other Tessellations
There are also "demiregular" tessellations, but mathematicians disagree on what they actually are!
And some people allow curved shapes (not just polygons) so you can have tessellations like these:
 |  |  | ||
Curvy Shapes | Circles | Eagles? |
Tessellation Artist
All these images were made using Tessellation Artist, (with some color added using a paint program).
You can try it too - maybe you will invent a new tessellation!
Definition of Tessellation | Tessellation | Definisi Tessellation
ROMANCE MATHEMATICS
Smart man + smart woman = romance
Smart man + dumb woman = affair
Dumb man + smart woman = marriage
Dumb man + dumb woman = pregnancy
OFFICE ARITHMETIC
Smart boss + smart employee = profit
Smart boss + dumb employee = production
Dumb boss + smart employee = promotion
Dumb boss + dumb employee = overtime
SHOPPING MATH
A man will pay $2 for a $1 item he needs.
A woman will pay $1 for a $2 item that she doesn't need.
GENERAL EQUATIONS & STATISTICS
A woman worries about the future until she gets a husband.
A man never worries about the future until he gets a wife
A successful man is one who makes more money than his wife can spend.
A successful woman is one who can find such a man.
HAPPINESS
To be happy with a man, you must understand him a lot and love him a little.
To be happy with a woman, you must love her a lot and not try to understand her at all.
LONGEVITY
Married men live longer than single men do, but married men are a lot more willing to die.
PROPENSITY TO CHANGE
A woman marries a man expecting he will change, but he doesn't.
A man marries a woman expecting that she won't change, and she does.
DISCUSSION TECHNIQUE
A woman has the last word in any argument.
Anything a man says after that is the beginning of a new argument.
The beauty of math
Apa yang dapat melebihi 100%?
Apakah pernah terpikir oleh anda untuk memberi lebih dari 100%?
Adakah dalam hidup ini yang dapat memberi lebih dari 100%?
Mungkin skema berikut akan sedikit membantu anda...
Jika,
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Mewakili,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26
Maka,
H-A-R-D-W-O-R-K
8+1+18+4+23+15+18+11 = 98%
K-N-O-W-L-E-D-G-E
11+14+15+23+12+5+4+7+5 = 96%
A-T-T-I-T-U-D-E
1+20+20+9+20+21+4+5 = 100%
Sekarang lihatlah bagaimana Tuhan memberi anda 101%...
L-O-V-E-O-F-G-O-D
12+15+22+5+15+6+7+15+4 = 101%
"While Hard Work and Knowledge will get you close, and Attitude will get you there, it’s the Love of God that will put you over the top!"
http://hermawayne.blogspot.com/
Roda yang diameternya 1 meter yang diukur kelilingnya dengan cara melekatkan seutas tali pada sekeliling roda tersebut, maka panjang tali yang dibutuhkan adalah sekitar 3.14159 meter. Nilai perbandingan antara keliling dan diameter lingkaran ini selalu konstan untuk setiap lingkaran yaitu 3.14159. Pi juga biasanya diartikan sebagai 1 putaran penuh lingkaran atau 1pi = 180derajat.
LESSON PLAN 1
School : Junior High School 4 Metro
Subject : Mathematics
Grade/ Semester : VIII / I
Standard of Competence : 1. To know algebraic form, relation, function and equation of straight line
Basic Competence : 1.1 To do algebraic operation
Indicators :
1. Indentifying the term of algebraic form
2. To determine like terms
3. to simplify algebraic form
4. To solve addition, subtraction in the algebraic form
5. To solve multiplication, division and power in the algebraic form
6. To solve addition, subtraction, multiplication, division and power of algebraic form in the real life
Time Allocation : 4 x 40 minutes
1. LEARNING OBJECTIVES
Student are able
1. Indentifying the term of algebraic form
2. determine like terms
3. to simplify algebraic form
4. To solve addition, subtraction in the algebraic form
5. To solve multiplication, division and power in the algebraic form
6. To solve addition, subtraction, multiplication, division and power of algebraic form in the real life
2. CONTENS/ MATERIALS : Algebraic form
3. METHODS/APPROACH : Discussion, direct instruction, questions answer and assignment task.
4. LEARNING ACTIVITIES
First Meeting
a. Introduction
1. Presenting learning objectives ( 1 – 3) and keywords which will be used often during the lesson.
2. The teacher reminds students about the operation concept of algebraic at grade I
.
Motivation : If this material is well posted will assist students at next material
.
b. Main activities
1. Students formed in group which have been specified (4 members)
2. In group each student do study of reference to Indentify the term and to determine like terms and to simplify of algebraic form
3. By grouping students do Worksheet 1 (made [by] teacher) then the teacher monitors students and also give instruction [at] group or instruction for students which still get difficulty.
4. Each group must collect and present of the discussion result. Teacher guides the way presentation and the other group give opinion and then The teacher gives assessment of each group
5. The teacher gives reinforcement and conclusion at this material
6. The teacher gives test to know ability of students
c. Closing activities
Teacher provides some problems and asks students to do it as homework
.
Second Meeting
a. Introduction
1. Presenting learning objectives (4 – 6) and keywords which will be used often during the lesson
2. The teacher and the students discuss the homework
3. The teacher remind students about the lesson at previous meeting,
Motivation : If this material is well posted will assist students at next material
b. Main activities
1. Students formed in group which have been specified (4 members)
2. In group each student do study of reference to solve addition, subtraction and to solve multiplication, division and power and to solve addition, subtraction, multiplication, division and power of algebraic form in the real life
3. By grouping students do Worksheet 2 (made [by] teacher) then the teacher monitors students and also give instruction [at] group or instruction for students which still get difficulty.
4. Each group must collect and present of the discussion result. Teacher guides the way presentation and the other group give opinion and then The teacher gives assessment of each group
5. The teacher gives reinforcement and conclusion at this material
6. The teacher gives test to know ability of students
c. Closing activities
1. the students summarize all the subject matters that have been discussed
2. The teacher gives some exercises taken from the students book as a home work.
5. RESOURCES : students book, environment, worksheet
6. ASSESMENT
Technique : written
Instrument : Test
Approved by Metro, July 2009
The Principal of SMPN 4 Metro Math Teacher
Sri Rahayu, S.Pd Sri Endang Supriyatun, S.Pd
NIP.19571119 198202 2 002 NIP. 19710929 199412 2002
TEST
1. Given the algebraic form 2x, 3y, 2c + 5, 2 + y – 4x, 2a2 + 3a – 5, a, - c, 4y – c.
a. Group which are monomial, binomials and trinomials
b. Mention of the variables, coefficient and constant of each the algebraic form
2. Group like term of the following algebraic forms
a. 8 + 3x − x − 6
b. 2x2 − 3x – x2 + 2x + 5
3. Write each of the following algebraic forms in the simplest form.
a. 5 + 2x − 1
b. 8 + 3x − x − 6
c. 5x2 + 2x − 3
4. Solve the addition operation below
a. 3x2 – 3x and 5x2 + 8x + 3
b. 19y3 + 7y2 and 2y3 + 6y2 + y + 5
5. Solve the subtraction operations below
a. -3x ( 2x + 5y) from 4x(3x – 2y)
6. Calculate the following algebraic form below
a. 5(x + 2) =
b. 2x(x – 1 ) =
7. Calculate the result of the following multiplication below
a. (2x + 3)(x – 4) =
b. ( x + 3 )2 =
c. (2x + 1)3 =
d. (2a + 3b + c)2 =
8. Calculate the result of the following division
a. 8a4b3 : 4a2b =
b. X2 + 9x + 18 divided by x + 6 is ….
9. The price of a pen is twice of the price of a pencil, if the price of a pencil is Rp500.00 and the price of a book is Rp800.00 more expensive than a pen. What’s the price of 3 pencils, 5 pens and 2 books
School : Junior High School 4 Metro
Subject : Mathematics
Grade/ Semester : VIII / I
Standard of Competence : 1. To know algebraic form, relation, function and equation of straight line
Basic Competence : 1.1 To do algebraic operation
Indicators :
1. Indentifying the term of algebraic form
2. To determine like terms
3. to simplify algebraic form
4. To solve addition, subtraction in the algebraic form
5. To solve multiplication, division and power in the algebraic form
6. To solve addition, subtraction, multiplication, division and power of algebraic form in the real life
Time Allocation : 4 x 40 minutes
1. LEARNING OBJECTIVES
Student are able
1. Indentifying the term of algebraic form
2. determine like terms
3. to simplify algebraic form
4. To solve addition, subtraction in the algebraic form
5. To solve multiplication, division and power in the algebraic form
6. To solve addition, subtraction, multiplication, division and power of algebraic form in the real life
2. CONTENS/ MATERIALS : Algebraic form
3. METHODS/APPROACH : Discussion, direct instruction, questions answer and assignment task.
4. LEARNING ACTIVITIES
First Meeting
a. Introduction
1. Presenting learning objectives ( 1 – 3) and keywords which will be used often during the lesson.
2. The teacher reminds students about the operation concept of algebraic at grade I
.
Motivation : If this material is well posted will assist students at next material
.
b. Main activities
1. Students formed in group which have been specified (4 members)
2. In group each student do study of reference to Indentify the term and to determine like terms and to simplify of algebraic form
3. By grouping students do Worksheet 1 (made [by] teacher) then the teacher monitors students and also give instruction [at] group or instruction for students which still get difficulty.
4. Each group must collect and present of the discussion result. Teacher guides the way presentation and the other group give opinion and then The teacher gives assessment of each group
5. The teacher gives reinforcement and conclusion at this material
6. The teacher gives test to know ability of students
c. Closing activities
Teacher provides some problems and asks students to do it as homework
.
Second Meeting
a. Introduction
1. Presenting learning objectives (4 – 6) and keywords which will be used often during the lesson
2. The teacher and the students discuss the homework
3. The teacher remind students about the lesson at previous meeting,
Motivation : If this material is well posted will assist students at next material
b. Main activities
1. Students formed in group which have been specified (4 members)
2. In group each student do study of reference to solve addition, subtraction and to solve multiplication, division and power and to solve addition, subtraction, multiplication, division and power of algebraic form in the real life
3. By grouping students do Worksheet 2 (made [by] teacher) then the teacher monitors students and also give instruction [at] group or instruction for students which still get difficulty.
4. Each group must collect and present of the discussion result. Teacher guides the way presentation and the other group give opinion and then The teacher gives assessment of each group
5. The teacher gives reinforcement and conclusion at this material
6. The teacher gives test to know ability of students
c. Closing activities
1. the students summarize all the subject matters that have been discussed
2. The teacher gives some exercises taken from the students book as a home work.
5. RESOURCES : students book, environment, worksheet
6. ASSESMENT
Technique : written
Instrument : Test
Approved by Metro, July 2009
The Principal of SMPN 4 Metro Math Teacher
Sri Rahayu, S.Pd Sri Endang Supriyatun, S.Pd
NIP.19571119 198202 2 002 NIP. 19710929 199412 2002
TEST
1. Given the algebraic form 2x, 3y, 2c + 5, 2 + y – 4x, 2a2 + 3a – 5, a, - c, 4y – c.
a. Group which are monomial, binomials and trinomials
b. Mention of the variables, coefficient and constant of each the algebraic form
2. Group like term of the following algebraic forms
a. 8 + 3x − x − 6
b. 2x2 − 3x – x2 + 2x + 5
3. Write each of the following algebraic forms in the simplest form.
a. 5 + 2x − 1
b. 8 + 3x − x − 6
c. 5x2 + 2x − 3
4. Solve the addition operation below
a. 3x2 – 3x and 5x2 + 8x + 3
b. 19y3 + 7y2 and 2y3 + 6y2 + y + 5
5. Solve the subtraction operations below
a. -3x ( 2x + 5y) from 4x(3x – 2y)
6. Calculate the following algebraic form below
a. 5(x + 2) =
b. 2x(x – 1 ) =
7. Calculate the result of the following multiplication below
a. (2x + 3)(x – 4) =
b. ( x + 3 )2 =
c. (2x + 1)3 =
d. (2a + 3b + c)2 =
8. Calculate the result of the following division
a. 8a4b3 : 4a2b =
b. X2 + 9x + 18 divided by x + 6 is ….
9. The price of a pen is twice of the price of a pencil, if the price of a pencil is Rp500.00 and the price of a book is Rp800.00 more expensive than a pen. What’s the price of 3 pencils, 5 pens and 2 books
