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3DUnit 1: 2D SHAPES
Polígono Figura plana Cuadrilátero
= polygon = 2-D shape or plane shape = quadrilateral
Polígono regular Radio Diagonal Apotema
= = = =
Ángulo central Ángulo interior
= central angle = interior angle
Ángulo recto Ángulo agudo Ángulo obtuso
= rightangle = acuteangle = obtuseangle
Linea recta Semirrecta Segmento
= straight line = ray = segment
Rectasparalelas Rectasperpendiculares
= parallellines = perpendicular lines
Circunferencia Diámetro Cuerda Arco
= = = =
Centro (de la circunf.)
= central point
Figuras circulares Círculo Semicírculo
= circular shapes = circle = semicircle
Sector circular Segmento circular
= circular sector = circular segment
Ángulos complementarios
= complementary angles: their measures add up to 90 degrees = supplementary angles: their measures add up to 180 degrees
Ángulos suplementarios
regular polygon radius diagonal apothem
circumference diameter chord arc
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PerĂmetro Diagonal mayor Diagonal menor Base mayor Base menor
=perimeter =major diagonal =minor diagonal = bigger base = shorter base
Lado
= side
VĂŠrtice Eje de simetrĂa Punto medio Longitud Paralelo
= = = = =
Teorema de Thales
= Thales Theorem
Cateto Hipotenusa
= cathetus (pl. catheti) = hypotenuse
1m2 =
Square metre
corner or vertex (pl. vertices) axis of symmetry middlepoint length parallel
Pythagorean Theorem: Example:
Circumference:For English-speaking people, a circumference is the complete distance around a circle. Therefore, what is the length of the circumference for us.This can be a bit confusing. Radius (radii pl.): A straight line from the centre to a point on the circumference. Diameter: A straight line going from a point on the circumference through the centre to the opposite point on the circumference. A diameter is twice the length of a radius.
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Chord: A straight line going from a point on the circumference to another and which does not pass through the centre. Arc: A portion of the circumference. Circular sector: The area enclosed by two radii of a circle, and the enclosed arc. Circular segment: The region between a chord of a circle and its associated arc. Types of Quadrilaterals:
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Centers of a triangle:The main centers of a triangle are: Altura de un triángulo
height oraltitude of a triangle: An altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. The three altitudes intersect in a single point, called the orthocenterof the triangle.
Mediatriz
perpendicular bisector: A line which cuts another line into two equal parts at 90°. The three perpendicular bisectors meet in a single point, the circumcenter.
Bisectriz
angle bisector: The bisector of an angle is the line that divides the angle into two equal parts. The intersection of the angle bisectors is the incenter.
Mediana
median: A median of a triangle is a straight line through a vertex and the midpoint of the opposite side. The intersection of the medians is the centroid.
Area of Plane Shapes Triangle
Area = ½ × b × h b = base h = height
Square
Area = a2 a = length of side
Rectangle
Parallelogram
Area = w × h
Area = b × h
w = width h = height
b = base h = height
Trapezoid (US) Trapezium (UK)
Circle
Area = ½(a+b) × h h = height
Area =
π × r2
Circumference = 2 × r = radius
π×
r
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SOLVING PROBLEMS
1.- A painter is on a top of a 35 ft ladder that is leaning against a house. The base of the ladder is 21 ft from the base of the house. If the painter were to fall, how far down would his fall be? Give the result in centimetres. NOTE:1 ft (feet) = 30.48 centimetres
2.- John wants to put his TV for sale on craigslist. The problem is that John forgot the inches of his TV. TVs are advertised by the inches of the diagonal. John knows the width of the TV is 45in and the height is 28in. How many inches should John advertise his TV as?
3.- In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch?
4.- Two joggers run 8 miles north and then 5 miles west. What is the shortest distance they must travel to return to their starting point? Give the result in kilometres. NOTE: 1 mile = 1.6 kilometres.
5.- Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point? Give the result in centimetres.
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PYTHAGOREAN THEOREM RAP (Watch it on YouTubehttp://www.youtube.com/watch?v=lb115CBDJew)
In a right triangle this is always true Square the shorter legs, add that’s all you do And, what do they equal? We’ll tell you now: The longer side squared, hypotenuse, wow! Chorus: So “a” times itself, “a” squared “b” times itself, “b” squared And “c” times itself, “c” squared “a” squared plus “b” squared equals “c” squared. A long time ago, your in Ancient Greeks A man named Pythagoras, he added a piece, A little piece of history we still use today, The Pyghagorean Theorem, and this is what we say What he found out, a pattern he saw, In a right triangle there was a law, That 2 squares form on the shorter sides, Piece them together, this is what he decides: They equal the square of the longer side line, Named hypotenuse it works every time, So for example, we’ll tell what now, 3 squared plus 4 squared equals 5 squared, pow! How many squares sounds like a three? Nine is what we get, we’ll solve a simple lead 4 times itself, 16’s what we get, The sum of the squares, 25 is what we get.
In a right triangle this is always true Name the legs squared, add that’s all you do. And, what do they equal? We’ll tell you now: Now, the longer side squared, hypotenuse, wow! Chorus What if I know the longer side’s length and the shorter leg? I’ll use my math strengths with the hypotenuse subtract the leg squared, square root the difference if you dare. Another example, we’ll give you some The longest leg 10, 8 the shorter one, 100 minus 64, 36 we get Root the 36, 6 we’ll bet. Chorus In a right triangle this is always true Square the shorter legs, add that’s all you do And, what do they equal? We’ll tell you now: The longer side squared, hypotenuse, wow! Chorus (Repeat twice)
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Unit 2: 3D SHAPES Cuerpogeométrico
= 3D shape
Poliedro
= polyhedron
Poliedro regular
= platonicsolid
Prisma
= prism
Prisma triangular
= triangular prism
Prisma cuadrangular
= squareprism
Pirámide
= pyramid
Apotema de la pirámide
= slantlenght
Esfera
= sphere
Cilindro
= cylinder
Cono
= cone
Generatriz del cono
= slant height or lateral height
Altura del cono
= altitudeor vertical height
Arista básica
= basic edge
Anchura
= width
Profundidad
= depth
Altura
= height
Área lateral
= lateral area/ side area
Área de la base
= base area / area of the base
Metro cúbico
= cubic metre
1 m3
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ACTIVITIES: 1) Translate into English (you can find them in our vocabulary: Edmodo, blog …); Poliedro = Arista = Cara = Prisma pentagonal = Ortoedro = Pirámide cuadrangular = Cono = Metro cuadrado =
Generatriz del cono= Arista básica = Prisma = Prisma hexagonal = Pirámide = Cilindro = Esfera = Metro cúbico =
Now you have to answer different questions. In order to do so, we are going to visit: http://www.mathsisfun.com/geometry/index.html 2) Define Polyhedron:
3) The five Platonic Solids: Name
Number of faces
Faces (name of the polygons)
4) Prisms: a) What is a cross section?
b) What polygon is the cross section of a pentagonal prism? c) If the cross section were a circle, it wouldn’t be a prism. What would it be?
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5) Pyramids: a) Draw a square pyramid and name its different parts: base, apex, slant height, height, edge, basic edge.
b) What is an irregular pyramid?
6) Non-polyhedra: a) Write three properties of the sphere: 1.2.3.-
b) Name three objects that are cone shaped:
c) Name threecylindrical objects.
d) Draw a cone and name the height, the radius and the side length.
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Unit 3: TRANSFORMATIONS Transformations are the changes in the position or size of a shape.
Types of transformations: Translation (traslación) Reflection (simetría) Rotation (giro)
We get congruent shapes
Enlargement (semejanza)
We get similar shapes
If two shapes are similar: They have the same shape All the corresponding angles are equal All the corresponding lengths are in the same ratio. A tessellation is an arrangement of a shape or set of shapes on a flat surface so that all the space is filled, with no gaps and no overlaps.
module Vector direction (English people don´t speak about “sentido”in mathematical terms)
UTENSILS /ju:’tensils/: Ruler (regla) Protractor (transportador de ángulos) Compass (compás. Se usa mucho en plural: compasses) Note that we can say: - Set your compasses to (a radius of) 4 cm - Place your protractor over point P - Mark a point at 100º and join it to P with a line Go to: www.youtube.com/watch?v=0Z1aUhGCZs0 and SING!
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Unit 4:RATIONAL NUMBERS INTEGERS: The opposite of a is -a. The opposite of -
ais a.
Really we can! We knowINTEGERS!
POWERS AND ROOTS:
42 ď€ ď€ ď€ ď€ four squared. 7 3 ď€ ď€ ď€ ď€ seven cubed 154 ď€ ď€ ď€ ď€ fifteento the power of four/ to the fourth 65289 ď€ ď€ ď€ ď€ sixty ď€ five to the power of two hundredand eightyď€ nine To square a number is to multiply it by itself. Write as a single power57 ∙ 56 : 54 đ?‘šđ?‘’đ?‘Žđ?‘›đ?‘ đ?‘Śđ?‘œđ?‘˘ â„Žđ?‘Žđ?‘Łđ?‘’ đ?‘Ąđ?‘œ đ?‘¤đ?‘&#x;đ?‘–đ?‘Ąđ?‘’ đ?‘–đ?‘Ą đ?‘Žđ?‘ 59
ďƒŹthe square root of twenty ď€ five is five 25  5 ď€ ď€ ď€ ďƒ ďƒŽTwenty ď€ five square root is five
5
243  3 ď€ ď€ ď€ ď€ the fifth root of two hundred and forty ď€ three is three
6
32  2
ď€ ď€ ď€ ď€ the sixth root of thirty ď€ two is two
DIVISIBILITY: 
12 is divisible by 4and12 is multiple of 4and 4 is a factor of 12
 
prime numbersare: 2, 3, 5, 7, 11, 13, 17 ‌ compound numbers are: 4, 6, 8, 9, 10‌

9 and 16, 34 and 25 are prime numbers between them. Write 36 in prime factor formmeans we write 36 = 22 ∙ 32

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FRACTIONS: o Properfraction: numerator is less thandenominator o Improper fraction: numerator is greater thandenominator
Equivalent fractions: fractions that represent the same number. Amplify (a fraction) Simplify (a fraction): we can simplify a fraction if the numerator and denominator have a common factor. A fraction is in its simplest form when it cannot be simplified any more.
Reading of fractions:
3 = three fourths/three quarters 4 5 = five halves 2 7 = seven ninths 9 2 = two over sixty-five 65
DECIMAL NUMBERS:
Approximating a decimal number: o by rounding o by truncating.
Percentages: Calculate how many percent… 65%… sixty-five percent of …
Displace the decimal point
to the left or to the right
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TYPES OF DECIMAL NUMBERS THAT WE CAN GET FROM A FRACTION:
Pure recurring decimal Mixed recurring decimal
Reading of decimal numbers: o 1.827
= one point eight two seven
o 35.15
= thirty-five point one five
o 3. 1414… = three point one four repeating o 3.14343… = three point one fourthree with four three repeating o 3.01111… = Three point zero one with one repeating
Order or hierarchy of the operations: Remember!!
P
Parenthesesfirst
E
Exponents (ie Powers and Roots)
MD Multiplication and Division (left-to-right) AS Addition and Subtraction (left-to-right)
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FINALLY IN THIS UNIT‌. ‌.The different sets of numbers that we are studying:
Set of numbers that can be written as a quotient of two integers: Q
Set of whole numbers and their opposites: Z
Set of natural numbers and the number 0 Set of numbers starting with 1 and counting up by ones: N
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Activities: RATIONAL NUMBERS. I) 1)
Fill in the gaps. Numbers 0, 1, 2, 3, 4, 5, … are ______________ numbers.
2) All positive and negative whole numbers are _____________________
3) The number 3 is the ____________ of the number -3. 4) The __________ ____________ of 5 and -5 is 5. 5) Two times twenty-eight is ____________ 6) Two hundred and eighty-five divided ___ three is ninety-five. 7) 2, 3, 5, 7, 11, 13, 17 … are _________ numbers; 1, 3, 5, 7, 9…..are ____________ numbers and 2, 4, 6, 8, 10, 12,,,are __________numbers 8) A ____________ is a number that is expressed in the form p/q where p and q are integers and q is not equal to zero. 9) In a fraction, the____________is the number of parts the whole is divided into. 10) A ___________ numberis a number that can be written as a fraction. 11)
1 is in its _______________ _________, because it cannot be simplified any more. 4
12) 6.333… is a _________ ____________ decimal. 13) 0.25555… is a ___________ ___________ decimal number.
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II)
Complete the text using the given words:
other, whole numbers, zero, add, negative, higher, kinds, numbers, beginning, subtrahend, result, multiply, contains, sign, count, integers, positive, opposite, below. At the _________ people used _________________ to _________ their goods and identify things, and they were able to ________ and _________those numbers (obtaining ________ whole numbers). They could subtract when the minuend was __________ than the_________________. But people created other _________ of _____________ to solve this, as well as to express debts, temperatures __________ zero… These new numbers are called integers. The set of the integers ___________ the natural numbers, the ______ and the _______________of every whole number (expressed by the _________ “-” before it, like – 6). So the ______________of a sum/multiplication/subtraction of two ____________ is another integer, that can be zero (0), a __________ number (2, 6, 152…) or a ______ number (-24, -85, -652…).
III) Reading Numbers Write, in English, how we read:
7 2 5 39 8.75151515 .... 56.77777.... 3 7 932.111111.. 1 4 74.2323
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IV)
Answer the following questions:
a) What is a rational number?
b) When can we simplify a fraction?
c) Write the number four point one three repeating. d) Is three thousand seven hundred and thirty-one an even number? e) Write the number two hundred and two point zero one seven with one seven repeating. f) Define prime number.
g) Is one hundred and eleven a prime number? h) Write three odd numbers bigger than 40. __________________________
V)
Put the words in order and rewrite the sentences.
a) when is less than the is called improper fraction numerator A fraction the an denominator.
b) the unit (one) numerator and denominator are equal, the fraction When the represents.
c) they represent are equivalent when the same number Two fractions
d) obtain equivalent fractions You can numerator and denominator by the same number by multiplying/dividing.
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Unit 5: REAL NUMBERS A real numberis any number on the number line.
Real numbers is the union of the sets of rational numbers and irrational numbers. So,đ?‘š = đ?‘¸ âˆŞ đ?‘° TYPES OF DECIMAL NUMBERS:
RATIONAL NUMBERS
IRRATIONAL NUMBERS: are decimal numbers neither recurring nor terminating.
INTERVALS: An interval is the set of all real numbers between two given numbers. The two numbers on the ends are the endpoints. 
Closed Interval: An interval that contains its endpoints.

Open Interval:An interval that does not contain its endpoints.

Half-Closed Interval or Half-Open Interval: An interval that contains one endpoint but not the other.
Note: Infinite (adjective) / infinity (noun)
For instance: Real numbers is an infinite set. Infinity is one endpoint of the half-open interval (-∞, -1]
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Activities: REAL NUMBERS. I)
Reading Numbers
Write, in English, how we read:
36 417 3
8
98 5
47
27 3 52 5.6666.... 7.898989 .... 7 8 9 2 54 3
93
13 2
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II)
Fill in the gaps.
1) 2 to the power of five is ______________ 2) Nine squared is ____________________ 3) There are other numbers that cannot be written as a fraction, for instance the square root of 2, and because they are not rational they are called ____________ 4) There are some important irrational numbers in mathematics such as π; one of them is the number e and another is (the golden ratio). Look for information and answer:
- Write π using six decimal figures ________________________ - Write eusing six decimal figures________________________________ - Write using six decimal figures ___________________________ 5) The two methods of approximating a decimal number are: ________________ and
_______________ 6) The set of all real numbers between two given numbers is an ____________ 7) The two numbers on the ends of an interval are the ______________ of the interval. 8)
6 and 0´23242526... are ___________________ numbers
9) When I write 18 = 2 32 , it is said that 18 is written in ________ _________form. 10) If I had to answer this question: Write as a ______________ power the following expression: 2 4 2 6 2 2 , I´d write 212 11) The number 2.3x10-5 is in _____________ ________________ or scientific notation. 12) 3.232425…. is an _____________ number. 13) 6, -4,
1 and are _________ numbers. 2