Vocabulary 2nd by José Antonio Tarifa Garzón

MATHS VOCABULARY AND ACTIVITIES nd

CSE

Bilingual Program

Unit 0: REMEMBER! NATURAL NUMBERS

Cardinal Numbers a=b aâ&#x2030; b

a is equal to b / a equals b a is not equal to b

a<b a>b

a is smaller/less than b a is bigger/greater than b

aâ&#x2030;&#x2C6;b

a is approximately equal to b

0 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

zero one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen twenty twenty-one twenty-two twenty-three twenty-four twenty-five

26 twenty-six 27 twenty-seven 28 twenty-eight 29 twenty-nine 30 thirty 40 forty 50 fifty 60 sixty 70 seventy 80 eighty 90 ninety 100 a/one hundred 101 a hundred and one 110 a hundred and ten 120 a hundred and twenty 200 two hundred 1,000 a/one thousand 1,001 a thousand and one 1,010 a thousand and ten 2,000 two thousand 10,000 ten thousand 11,000 eleven thousand 100,000 a/one hundred thousand 1,000,000 a/one million 2,000,000 two million 1,000,000,000 a/one billion

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Exercises: 1.- Write how we read the following cardinal numbers: Examples: 7,482 476,985 10, 956, 407

seven thousand, four hundred and eighty-two four hundred seventy-six thousand, nine hundred and eighty-five ten million, nine hundred fifty-six thousand, four hundred and seven Check your answers here: http://www.mathcats.com/explore/reallybignumbers.html

915 4,329 70,001 145,012 86,374 14,896,327

2.- Write the following roman numerals in the decimal system:

Bilingual Program 3.- Write how we read the following ordinal numbers: 12th 29th 31st 102nd 15th 53rd

SUMA

ADDITION

RESTA

SUBTRACTION

Plus (sign)

Minus (sign)

Sumar

To Add (verb)

Restar

To Subtract (verb)

La suma

The Sum (The result)

La diferencia

The difference (The result)

MULTIPLICACIÓN

MULTIPLICATION

DIVISIÓN

DIVISION

Times (sign)

/ or :

Divided by (sign)

Multiplicar

To Multiply (verb)

Dividir

To Divide (verb)

El producto

The Product (The result)

Dividend

divisor Quotient

Remainder

Reading operations:    



3+5 = 8 12 – 3 = 9 8 x 4 = 32 28 : 4 = 7 Réstale X a Y

three plus five equals eight twelve minus three equals nine eight times four equals thirty-two (or eight multiplied by four equals thirty-two) twenty-eight divided by four equals seven (or twenty-eight divided into four equals seven) Subtract X from Y

i.e. Subtract 3 from 8

Bilingual Program

Unit 1: INTEGERS AND DIVISIBILITY

INTEGERS     

    

integer positive number negative number absolute value opposite of a number

sign rule distance to zero degrees below zero symmetrical with respect to numerical value

POWERS AND ROOTS

8 2     eight squared . 7 3     seven cubed 15 4     fifteen to the power of four/ to the fourth 65289     sixty  five to the power of two hundred and eighty  nine To square a number is to multiply it by itself. Write as a single power

the square root of twenty  five is five 25  5     Twenty  five square root is five 3

27  3     the cube root of twenty  seven is three



Tienes que sacar raiz cuadrada de … --- You have to calculate the square root of ...



Saca la raiz cúbica de…

---

Calculate the cube root of… or Take the cube root of…

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DIVISIBILITY 

divisible (by) 12 is divisible by 4 and 12 is multiple of 4 and 4 is a factor of 12



prime number 2, 3, 5, 7, 11 are prime numbers



composite number or compound number 12, 38, 70 are compound numbers



write a number in prime factor form 36 written in prime factor form is



prime numbers between them 9 and 16 are prime numbers between them



highest common factor (HCF) or greatest common factor (GCF) 6 is the HCF of 12, 30



lowest common multiple (LCM) or least common multiple (LCM)

24 is the LCM of 6 and 8 DEFINITIONS:

The multiples of an integer are found by multiplying the integer by another.

The divisors of an integer (or factors) are those numbers that divide the number without leaving a remainder.

A prime number is a natural number that has only two divisors, itself and one. (1 is not a prime/compound number)

A number is a compound number (or composite number) when it is not a prime number.

The lowest common multiple (LCM) of two or more numbers is the smallest of the multiples common to all of them.

The highest common factor (HCF) of two or more numbers is the largest of the divisors common to all of them.

Bilingual Program

The Divisibility Rules These rules let you test if one number is divisible by another, without having to do too much calculation! A number is divisible by:

If:

Example:

The last digit is even (0,2,4,6,8)

128 is 129 is not

The sum of the digits is divisible by 3

381 (3+8+1=12, and 12÷3 = 4) Yes

The last 2 digits are divisible by 4

The last digit is 0 or 5

1312 is (12÷4=3) 7019 is not

175 is 809 is not 114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes

The number is divisible by both 2 and 3 308 No If you double the last digit and subtract it from the rest of the number and the answer is: 672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes

 

0, or divisible by 7

905 No

(Note: you can apply this rule to that answer again if you want)

The sum of the digits is divisible by 9

1629 (1+6+2+9=18, and again, 1+8=9)Yes

(Note: you can apply this rule to that answer again if you want)

2013 (2+0+1+3=6) No

The number ends in 0

If you sum every second digit and then subtract all other digits

220 is 221 is not

1364 ((3+4) - (1+6) = 0) Yes

and the answer is: 3729 ((7+9) - (3+2) = 11) Yes

 

0, or divisible by 11

25176 ((5+7) - (2+1+6) = 3) No

Bilingual Program EXERCISES: 1)

READING MATHS. Write in English how we read the following expressions:

14 + 67 = 81

346 – 125 = 221

45 x 3 = 135

128 : 4 = 32

√

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2) Find the three first multiples of the following numbers: 7 15 11 3) Which of the following numbers are prime numbers? 18, 11, 27, 19 4) Given the number 2381N, in order for this number to be divisible by 3, 6 and 9, N must be 4, 5, 0, 6 or 9?

5) Name two numbers whose HCF is 1. 6) Name three numbers whose LCM is 36.

7) Put the right sign, <, >, = into each sentence: a) -9

b) 5

-3

c) -3 -7

d) -5

-8

8) Complete the following sentences. Choose the right word: opposite       

- subtract - natural - absolute value

- integers - times - divided by

The _____________ of a number is its distance from zero on the number line. The _______________ of an integer is obtained by changing its sign. The numbers that we use for counting are ___________ numbers. The _____________can be positive o negative. If we ____________seven from nine we get two. Eight ____________five is forty. Thirty-two _______________eight is four.

9) Put the right sign, <, >, = into each sentence: a) 7

7

e) Op (8)  6

b) 2

Op(6)

f) Op (  2 )

c)  1

7

g)   5

d)  8

 8

 9

10) Alice wants to buy a bicycle with the money she earns from her after-school job. The bicycle costs $150. If she can save $21 a week, how much money will he have after six weeks? How many weeks does she need work to save enough money to buy the bicycle?

Bilingual Program 11) Fill in the gaps with the right word:

origin opposite left

opposite below zero

absolute value positive sign greater than

less than distance right

above negative sign

• We use positive integers to indicate temperatures ______zero or height above sea level. • For temperatures below zero or height ______sea level, we use negative integers. • On the Integer Line, positive integers are found to the ______ of zero, while negative integers are found to the ______ of zero. • Zero is called the ___________, and it’s neither negative nor positive. • For every positive integer, there’s a negative integer at the same distance from the origin. Two integers that lie the same distance from the origin in opposite directions are called _________ numbers • The integers 4 and -4 are called ______ integers, since they are the same distance away from zero. • The ______________________of a number is its distance away from zero. • The symbol for absolute value is two vertical lines. Since opposites are the same _________from the origin, they have the same absolute value. • The absolute value of zero is ______. • -1 is to the right of -4 on the number line; therefore -1 is __________ - 4. We write -1 >-4 to represent it. • -4 is ___________ 1 because -4 lies to the left of 1 • We don’t have to include a _________________ (+) when we write positive numbers. However, we do have to include the __________________ (-) when we write negative numbers.

Bilingual Program Unit 2: FRACTIONS    

Fraction. To divide. Numerator or top. Denominator or bottom.  

Proper fraction: numerator is less than denominator Improper fraction: numerator is greater than or equal to denominator

    

Mixed number: it contains a whole number part and a fractional part smaller than 1. Equivalent fractions: fractions that represent the same number Parts (of an all) Unit Common denominator.

 

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. The reciprocal. Ex: ¼ is called the reciprocal of 4.



Reading of fractions:

1 2

= a half

3 4

= three fourths / three quarters

9 8

= nine eighths

17 2

= seventeen halves

21 = twenty-one over two hundred and sixty-five 265

Bilingual Program

Fractions: Label the Fractions:

Label the fractions using the given words below.

one third three quarters two thirds denominator one half one quarter one sixth numerator one eighth

Simplest Form: Pass through the fractions in simplest form and find out the message. STAR T 2 3

3 8

5 6

1 4

6 9

2 12

Â´

3 6

4 16

10 15

2 9

5 9

4 7

8 15

2 5

5 12

4 6

4 12

1 10

11 20

4 8

3 4

9 20

1 9

3 5

2 3

1 3

2 12

9 3

2 30

3 15

2 6

5 3

2 15

1 3

4 5

9 13

E XI T

Bilingual Program READING AND WRITING TRACTIONS

1. Write each fraction in words. a.

2. Write each fraction in numbers. a. a half

f. five ninths

b. two quarters

g. one quarter

c. three fifths

_____

h. five sixths

d. seven tenths

i. one third

e. an eighth

j. five sevenths

3. Read the extract below from a news story. How many fractions can you find in words and numbers? A survey of dog owners by ‘My Friends’ dog food has found that over half of them let their dog sleep in their bedroom.

Two thirds admit letting their ‘best friend’ sleep on the bed, with a third of these people letting the dog sleep on the bedroom floor. However, 1/10 of all those surveyed said they had to leave their dog in the kitchen overnight, because the dog’s snores kept them awake! A spokesman said, “This survey shows how dogs are treated as one of the family, with three out of five of owners allowing them in the bedroom”.

Decide if the survey claims that most people let their dogs sleep on the bed.

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MORE PROBLEMS: Solve the problems below using your knowledge of fractions: 1) Kathy, Karen, and Richey ordered a pizza to share. By the time Richey came to the table, Kathy had eaten

7 5 of the pizza and Karen had eaten of it. How much pizza was left for Richey? 12 12

2) Mr. El bought a bag of two dozen Mounds candies. He immediately ate 11 of the candies. What fraction of the bag was left uneaten?

3) What fraction of a day is 3 hours?

4) How many minutes are in five sixths of an hour?

5) Sam gave Jesse

1 2 of her chocolate bar and Jesse gave Abbey of his piece. What fraction of 4 3

the original chocolate bar did Abbey get?

6) Jeremy gave one half of his candy bar to 4 friends. If his friends shared the piece equally, then what fraction of the original candy bar did each one get?

7) Coach A's team won 7 out of every 8 games, and Coach B's team won 9 out of every 16 games. Determine which coach has a better record.

8) In basketball, John scored a point in 5 out of 7 tries, Joe scored a point in 5 out of 6 tries, and Tim scored a point in 5 out of 8 tries. Order these players from least to greatest mark.

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Unit 3: DECIMAL NUMBERS  

Decimal number. Decimal point.

     

Tenth Hundredth Thousandth Ten thousandth A hundred thousandth Millionth

    

Exact decimal Recurring decimal: It is a decimal which has repeating digits or a repeating pattern of digits. Pure recurring decimal. Mixed recurring decimal Arc (to write recurrent numbers in an abbreviated form)

  

Approximation. Rounding, to round. Truncating, to truncate.

   

To displace the decimal point % = Percent (Ex: 6 % de … = sixty-five percent of …) Percentage Calculate how many percent.

= décima = centésima = milésima = diezmilésima = cienmilésima = millonésima

Note: In English we write 1,000 (one thousand) and 1,000,000 (one million). 1.827 is a decimal number in English. 

Reading of decimal numbers: o

1.827

= one point eight two seven

35.15

= thirty-five point one five

…= three point one four repeating

….= three point one four three with four three repeating

… = Three point zero one with one repeating

Bilingual Program

DECIMAL NUMBERS The zero and the counting numbers (1,2,3,...) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a clever symbol called the decimal point. As you move right from the decimal point, each place value is divided by 10.

Whole part

Decimal part

The decimal point helps us to keep track of where the "ones" place is. It's placed just to the right of the ones place. As we move right from the decimal point, each number place is divided by 10. We can read the decimal number 127.578 as "one hundred twenty seven and five hundred seventyeight thousandths". Hint #1: Remember to read the decimal point as "and" Hint #2: When writing a decimal number that is less than 1, a zero is normally used in the ones place: 0.526 not .526 But in daily life, we'd usually read it as "one hundred twenty seven point five seven eight." PRACTICE NOW! 1.- Write how to read this decimal numbers: a) 45.6 b) 0.897 c) 19.12 d) 2.1234 e) 1,987.33 f) 33.21087 2.- Write as a decimal number: a) Two hundred thirty-six thousand and six hundred ten thousandths b) Three hundred twenty-one and seven tenths c) Five hundred forty-eight thousandths  d) Five hundred and forty-eight thousandths  e) One thousand one hundred fifty three point eight five seven zero nine 

Bilingual Program

3.- Use the digits 0, 4 and 6 and a decimal point to write five different decimals. 4.- a) Write the smallest possible decimal between zero and one that uses the digits 9, 0, 4, 2, 5, and 7 exactly once. b) Write the greatest possible decimal between zero and one that uses the digits 9, 0, 3, 1, 6 and 5 exactly once.

DECIMAL PROBLEMS 1) A computer processes information in nanoseconds. A nanosecond is one billionth of a second. Write this number as a decimal.

2) Five swimmers are entered into a competition. Four of the swimmers have had their turns. Their scores are 9.8 s, 9.75 s, 9.79 s, and 9.81 s. What score must the last swimmer get in order to win the competition?

3) To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm. Will a tire that is 1.4691 cm in diameter work? Explain why or why not.

4) Ellen wanted to buy the following items: A DVD player for $49.95, a DVD holder for $19.95 and a personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90 with her?

5) Melissa purchased $39.46 in groceries at a store. The cashier gave her $1.46 in change from a $50 bill. Melissa gave the cashier an angry look. What did the cashier do wrong?

6) The times for three runners in a 100-yard dash are 9.85 s, 9.6 s, and 9.625 s. What is the winning time?

7) Brandon is training for the 200-meter dash. His best running time so far was 31.25 seconds. If Brandon wants to run the dash in 27 seconds, then about how much time must he cut in order to reach his goal?

8) Patricia has $425.82 in her checking account. How much does she have in her account after she makes a deposit of $120.75 and a withdrawal of $185.90?

9) An electrician earns $18.75 per hour. If he worked 200 hours this month, then how much did he earn?

10) Danica Patrick can travel at 154.67 miles per hour in her race car. How far can she travel in 3 hours?

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Unit 4 : ALGEBRAIC EXPRESSIONS



Lenguaje numérico

= numerical language

Lenguaje algebraico

= algebraic language

Expresión algebraica

= algebraic expression

Igualdad numérica

= numerical equality

Valor numérico

= numerical value

Coeficiente

= coefficient

Término independiente

= constant term

Binomio

= binomial

Polinomio

= polynomial

Eliminar paréntesis

= remove brackets

Sacar factor común

= factorize or factorise

Reducir términos semejantes

= collect like terms

To remove brackets, multiply each term inside the bracket by the term outside.

In the Polynomial: P(x) =



Factorizing is the you write algebraic different form using brackets.

process that lets expressions in a

For instance: 5x 2  15x  5x  ( x  3) We say that 5 and x are common factors so they can be taken outside the bracket.

is called the leading coefficient. is the constant term

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Bilingual Program ACTIVITIES

--- ALGEBRAIC EXPRESSIONS

1.- Write a similar monomial to 3a bc with coefficient – 5 2

2.- Are similar the following pairs of monomials? a)

6 x 2 y and 7 xy 2 3 b) ab and  9ab 5 3.- What is the degree of

4 xy 5 z 3 ?

4.- Remove brackets in the following expression: 7( x  3)  5.- Factorise: 6ab  3a  2

6.- Do the monomials 6ab and 3a2 have any common factors? _______ What are they?________ 7.- Write: a second-degree polynomial: a fifth-degree polynomial: 8.- Write a third-degree polynomial with a leading coefficient 4 and a constant term – 8

9.- Collect like terms in the polynomial: P(x) = 2 x  x  7 x  6 x  x  5x  2 5

P(x) = How many terms does it have? __________ What is the degree of this polynomial? ________ 10.- What condition is necessary to add or subtract monomials?

11.- If I’m a years old, my mother is three times older than me, my father is two years older than my mother, my brother Mike is five years younger than me, and my sister Alice is twice older than Mike. Write using algebraic language: My age

---------------

Mike’s age ----------

Alice’s age ---------------

My mother’s age -----

My father’s age --------

My age in 7 years ----

Bilingual Program

Unit 5 : EQUATIONS Igualdad

= equality

Identidad

= identity

Ecuación

= equation

Ecuación de primer grado

= a linear equation

Miembro de una ecuación

= equation side

Primer miembro (de una ecuación)

= left-hand side (of an equation)

Segundo miembro

= right-hand side

Incógnita

= unknown

Solución

= solution

Ecuaciones equivalentes

= equivalent equations

Ecuaciones con paréntesis y denominadores

= equations involving brackets and fractions

Quitar denominadores

= cancel fractions

Quitar paréntesis

= multiply out brackets / remove brackets

Ecuación de segundo grado

= a quadratic equation

Unit 6 : SIMULTANEOUS EQUATIONS or SYSTEMS OF EQUATIONS Sistema de dos ecuaciones

= a pair of simultaneous equations

Resolver sistemas de ecuaciones

= solving simultaneous equations

Sustituir en la ecuación

= substitute in equation

Multiplicar los dos miembros de la ecuación por

= multiply both sides of the equation by …

… para que los coeficientes de x sean iguales

= so that the coefficients of x will be the same size

Two equations for which you need a common solution are called simultaneous equations. Simultaneous equations can be solved by the method of substitution or elimination. 

By substitution: you substitute (or replace) one of the unknown with an equivalent expression or value.



By elimination: the original equations are combined to eliminate one of the unknowns making an equation that is easier to solve.

Bilingual Program

SOLVING PROBLEMS WITH THE HELP OF EQUATIONS: 1.- A father divides a quantity of money among his children: to the first, one half, one third to the second and the €180 remaining for the third. What quantity of money has he divided? 2.- What are the measurements of the angles in a triangle if the first is 20º bigger than the second and the third is twice the first? 3.- Jacques is 6 years older than his sister and 12 years ago he was twice hers. How old is everyone? 4.- The difference between the base and the height of a rectangle is 15 cm. If the perimeter of the rectangle is 62 cm, find out the area. 5.- Four segments measure, in total, 78 cm. Knowing that the first is half the second; the third, double than the second; and the fourth, 12 cm bigger than the third, calculate how much every segment measures. 6.- John is 12 years old and his grandmother is 72. How many years have to pass in order to be grandmother’s age four times John’s age? 7.- Mary spent on her first day of travel 1/5 of the money she had; the second day, half remained, and she still had 432 euros left. How much money was there? 8.- The sum of two consecutive numbers that are multiples of 5 is 395. What are the numbers? 9.- A painting company uses 7/8 of a drum of solvent per month. If they then add 190 litres and the drum fills up to 3/5 of its capacity, how many litres fit in the drum? 10.- We want to give out 99 bananas between 3 monkeys in such a way that the first monkey receives 14 bananas more than the second, and the third monkey 16 fewer than the first. How many bananas does each receive? 11.- To unload a boat 4 trucks were used. The first has unloaded 1/6 of the cargo; the second, one quarter; the third, one fifth and the fourth, the third part plus 9 tons. How many tons were carried by the boat? 12.- An athlete trains every day for fifteen minutes more than the previous day. If at the end of the fourth day he has coached nine and a half hours in total, how long did he train on the first day?

Bilingual Program

SOLVING PROBLEMS WITH THE HELP OF SYSTEMS OF EQUATIONS: 1) Silvia is 5 years younger than her brother. In 3 years she will be half the age he will be then. How old are they? 2) The base and height of a rectangle are 15cm different. If the perimeter of the rectangle is 62cm, find the area. 3) A mother buys 3 pairs of trousers and 2 T-shirts for 176€. If each pair of trousers costs twice as much as a T-shirt. How much does each garment cost? 4) A kilogram of rice costs 15 cents more than one of sugar. Knowing that 3 kg of rice and 5 kg of sugar cost 9.25 euros, what is the price of 1 kg of each product? 5) At a farm there are pigeons and rabbits. There are a total of 97 heads and 302 feet. How many animals are there in each class? 6) One person bought 22 animals that included all chickens and rabbits. The price of a chicken is 3 euros and a rabbit is 5. How many of each class were bought if in the total paid was 90 euros? 7) In a radio contest, each group of two must answer 10 questions about general culture. Each correct answer earns 5 points and each incorrect answer losses 3 points. If at the end of the contest a group has 18 points, how many answers were answered correctly? 8) Mary has bought 63 packets of biscuits, some of 8 kg and another ones of 11 kg. If the total weight is 576 kg, how many packets are there of every weight? 9) John’s cousin is 12 years younger than John and, in 5 years, twice his age will be the same that John’s plus 4. What is everyone’s age? 10) A pair of shoes and a shirt cost 120 pounds. If the pair of shoes costs twice the shirt, how much does each garment cost? 11) The sum of two numbers is 45 and its difference is 9. What are the numbers? 12) The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children attended? How many adults?

Bilingual Program

SOLVING SYSTEMS OF EQUATIONS: 

Solve the following system using addition.

4x – 3y = 25 –3x + 8y = 10 Hmm... nothing cancels. But I can multiply to create a cancellation. I will multiply the first row by 3 and the second row by 4; then I'll add down and solve.

Solving, I get that y = 5. Neither equation looks particularly better than the other for back-solving, so I'll flip a coin and use the first equation. 4x – 3(5) = 25

4x – 15 = 25 4x = 40 x = 10 Remembering to put the x-coordinate first in the solution, I get: 

(x, y) = (10, 5)

Solve the following system by substitution.

2x – 3y = –2 4x + y = 24 I'll solve the second equation for y:

4x + y = 24 y = –4x + 24 Now I'll plug this in ("substitute it") for "y" in the first equation, and solve for x:

2x – 3(–4x + 24) = –2 2x + 12x – 72 = –2 14x = 70 x = 5 Copyright © 2011 All Rights Reserved Now I can plug this x-value back into either equation, and solve for y. But since I already have an expression for "y =", it will be simplest to just plug into this:

y = –4(5) + 24 = –20 + 24 = 4 Then the solution is (x,

y) = (5, 4).

Bilingual Program

Unit 7: PROPORTIONALITY     

Proportionality Magnitude Ratio1 Proportion 2 Extremes and means



Reading the proportion

       

Cross products Constant of proportionality or proportionality constant Directly proportional3 Inversely proportional4 Double, treble, quadruple Percentage, percentage of % = Percent (Ex: 6 % de … = sixty-five percent of …) How to calculate percents.

a c  b d

“a is to b as c is to d”

Ratio: A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12. 1

We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve. Proportion: A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. 3/4 = 6/8 is an example of a proportion. 2

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number. Example: Solve for n: 1/2 = n/4.Using cross products we see that 2 × n = 1 × 4 =4, so 2 × n = 4. both sides by 2, n = 4 ÷ 2 so that n = 2.

Two quantities are in direct proportion if their ratio stays the same as the quantities increase or decrease.

Two quantities are in inverse proportion when one increases at the same rate as the other decreases.

Dividing

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PROPORTIONALITY

PROBLEMS

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Unit 8: Functions A function is a relationship between two sets that relates each element of the first set with exactly one element of the second. One Important Thing!

"...exactly one..." means that a function is single valued.

This is NOT OK in a function

But this is OK in a function

In a function, we have two variables (one of each set). The variables are typically named x and y: x is the independent variable (the input), and y is the dependent variable (the output) We represent the independent variable in the xaxis (abscissas) and the dependent in the y-axis (ordinate) The pair (x , y) is called an ordered pair. When we represent the ordered pairs on a cartesian coordinate system we get the graph of the function. The point where the two axes intersect is called the origin. It is the point (0 , 0) The values that x may assume are called the domain of the function. The values of y that correspond to the values of x, are called the range.

Bilingual Program

Increasing Functions

Decreasing Functions

Constant Functions

A function is increasing if the y-

A function is decreasing if the y-

The graph of a Constant

value increases as the x-value

value decreases as the x-value

Function is a horizontal

increases.

line:

A function whose graph is a straight line is called a linear function: Its formula (or algebraic expression) is:

The slope m tells us if the function is increasing,

f(x) = mx + b m is the slope or gradient

decreasing or constant:

m<0

decreasing

m=0

constant

m>0

increasing

Other useful words in this unit are: 

Tabla de valores

= table of values



Representación de una función = representation of a function



Punto de corte con el eje x

= x-intercept



Punto de corte con el eje y

= y-intercept



Máximo

= maximum point



Mínimo

= minimum point

Bilingual Program

UNIT 9 – STATISTICS

BASIC CONCEPTS AND DEFINITIONS:     

population5 sample6 experimental unit or sampling unit7 size8 mid-interval value9

Different types of data:  Qualitative data: It is described using words.  Quantitative data: It consists of numbers.  Discrete data: It can only take particular values.  Continuous data: It can take any value.  

collecting data - Recopilar datos handling data - Recuento/manejo de datos

   

absolute frequency relative frequency absolute cumulative frequency relative cumulative frequency



GRAPHS o o o o



 abscissas axis  ordinate axis bar chart frequency polygon histogram pie chart

CENTRALIZATION MEASURES o sample mean or average10 o mode 11 o median

A population is any entire collection of people, animals, plants or things from which we may collect data. It is the entire group we are interested in, which we wish to describe or draw conclusions about. 6

A sample is a group of units selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions about the larger group. 7

A unit is a person, animal, plant or thing which is actually studied by a researcher; the basic objects upon which the study or experiment is carried out. 8

Number of elements/items of the population/sample.

The mid-interval value is the value halfway along the interval. The mean is the sum of the values divided by the number of values. 11 The mode is the value that occurs most often. 10

Bilingual Program

Unit 10: 2-D SHAPES

Polígono Figura plana Cuadrilátero Área Polígono regular Radio Diagonal Apotema Triángulo Triángulo equilátero Triángulo isósceles Triángulo escaleno Triángulo rectángulo Triángulo acutángulo Triángulo obtusángulo Ángulo recto Ángulo agudo Ángulo obtuso Ángulos complementarios Ángulos suplementarios Linea recta Semirrecta Segmento Rectas paralelas Rectas perpendiculares Circunferencia Diámetro Cuerda Arco Centro (de la circunf.) Círculo Semicírculo Figuras circulares Sector circular Corona circular

= polygon = 2-D shape = quadrilateral = area = regular polygon = radius = diagonal = apothem = triangle = equilateral triangle = isosceles triangle = scalene triangle = right-angled triangle = acute triangle = obtuse triangle = right angle = acute angle = obtuse angle = complementary angles: their measures add up to 90 degrees = supplementary angles: their measures add up to 180 degrees = straight line = ray = segment = parallel lines = perpendicular lines = circumference = diameter = chord = arc = central point = circle = semicircle = circular shapes = circular sector = circular crown

Paralelogramo Trapecio Trapezoide

= parallelogram = trapecium (UK) --- trapezoid (US) = --- trapecium (US)

Bilingual Program

Rectángulo Cuadrado Rombo

= rectangle

Romboide Pentágono Hexágono

= rhomboid

Heptágono Octógono Eneágono Decágono

= heptagon

Fórmula Base Altura de un triángulo Perímetro

= formula

Diagonal mayor Diagonal menor Base mayor

= major diagonal

Base menor Lado Vértice Eje

= shorter base

Punto medio Longitud Longitud del lado Cateto Hipotenusa

= middle point

Teorema de Pitágoras

= Pythagorean Theorem: The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

= square = rhombus = pentagon = hexagon = octagon = nonagon = decagon = base = height/altitude of a triangle = perimeter = minor diagonal = bigger base = side = corner or vertex (pl. vertices) = axis = length = side-length = cathetus (pl. catheti) = hypotenuse

Bilingual Program

UNIT 11 - 3-D SHAPES Cuerpo

= 3-D shape

Poliedro

= polyhedron ( pl. polyhedra)

Arista

= edge

Arista básica

= basic edge

Cara

= face

Tetraedro

= tetrahedron

Cubo o hexaedro

= cube or hexahedron

Octaedro

= octahedron

Dodecaedro

= dodecahedron

Icosaedro

= icosahedron

Prisma

= prism

Prisma triangular

= triangular prism

Prisma cuadrangular

= square prism

Prisma pentagonal

= pentagonal prism

Prisma hexagonal

= hexagonal prism

Ortoedro

= orthohedron

Pirámide

= pyramid

Cilindro

= cylinder

Cono

= cone

Esfera

= sphere

Área lateral

= lateral area/ side area

Área de la base

= base area / area of the base

Metro cuadrado

= square metre

Metro cúbico

= cubic metre

Bilingual Program

DECIMAL METRIC SYSTEM

LENGTH

CAPACITY

MASS

Unit

Abbrev iation

Number of Meters

Unit

Abbre viation

Number of Liters

Unit

Abbrev iation

Number of Grams

kilometer

1,000

kiloliter

1,000

metric ton

1,000,000

hectometer

100

kilogram

1,000

dekameter

dam

dal

hectogram

100

meter

dag

decimeter

0.1

0.10

gram

centimeter

0.01

decigram

0.10

millimeter

0.001

centigram

0.01

0.001

hectolit er dekalite r liter decilite r centilite r millilite r

dekagram

Milligram

AREA

VOLUME

Unit

Abbreviation

Number of Square Meters

Unit

Abbreviation

Number of Cubic Meters

square kilometer

km2

1,000,000

cubic meter

cubic decimeter

dm3

0.001

cubic centimeter

cm3 also cc

0.000001

square meter

square centimeter

cm2

0.0001

10,000

100

hectare are

Bilingual Program

Name:

Mark:

Think and answer if the following sentences are true (T) or false (F) The more questions you guess, the more sweets you get. 1.- Seventeen is a prime number. 2.- The highest common factor of five and nine is one. 3.- Three cubed plus one is equal to five multiplied by two. 4.- Thirteen is a compound number. 5.- Three thousand four hundred and seventy-six is divisible by eleven. 6.- The square root of thirty-six is positive and negative six. 7.- The lowest common multiple of three and nine is twenty-seven. 8.- The square root of ninety-one is nine and the rest is ten. 9.- Four times five is twenty-five. 10.- The absolute value of five is negative five. 11.- The opposite of the absolute value of â&#x20AC;&#x201C; 4 is + 4. 12.- We can write all the multiples of 2. 13.- If the area of a square is 81 m2, its side is 9 m. 14.- One to the power of six is six. 15.- Five squared is the same as five times five. 16.- If I take four parts of a cake divided into six parts, I take the same amount of cake that if I take two of three. 17.- Seven tenths is bigger than seven over fifteen. 18.- Two fifths of 20 is 50.

Bilingual Program

Think carefully, do all the operations you need and answer to the following questions: The more questions you guess, the more sweets you get. 1. Some months have 31 days. How many days are there in a year counting the months of 31 days? 2. One kg of cucumbers costs £ 1.20. How much do 2 kg of tomatoes cost? 3. Can a man marry his widow’s sister? 4. Who is my grandmother’s daughter? 5. Today is 12th February. I have an appointment with the dentist in 30 days. What day do I have the appointment? 6. Divide

by ½ and add

. What’s the result?

b) 7

7. If there are 3 apples and you take 2 of them, how many apples do you have?

a) 1

b) 3

c) 2

8. How many minutes are there in three hours and a quarter minus a quarter to two hours? a) 75

b) 90

c) 100

9. A doctor gives you 3 pills and you have to take one every half an hour. How much time do you have pills for? a) Half an hour

b) An hour

c) An hour and a half

10. Can a person who lives in Adra be buried in Granada? a) Yes

b) No

c) If he gets a licence, yes

11. A farmer has 17 sheep. All of them except 9 die. How many sheep remain alive? a) 8

b) 9

c) 17

12. How many animals of each sex did Moses take on his ark in the Great Flood? a) 0

b) 1

c) 2

13. How many animals eat with their tail? a) none

b) all of them

c) only one

14. My name is Charles. I have 3 brothers and 2 sisters. How many sisters does my sister Mary have? a) 2

b) 5

c) 1

15. You’re in a race and you pass the second position. In what position are you? a) 1st

b) 2nd

c) 3rd

16. While going to the water source, a zebra meets 6 giraffes. Each giraffe is transporting 3 monkeys on its back and each monkey has 2 birds on its right shoulder. How many animals are going to the water source? a) 1

b) 37

c) 61

17. Yesterday it was my mother’s birthday. She‘s years old. My sister is one year younger than me. If we add my age and my sister’s age we get my mother’s age. How old am I?

Bilingual Program

MATHS SCHOOL DAY

In 2000, the Spanish Federation of Societies of Mathematics Teachers (FESPM) decided to propose the day 12th May as the Maths School Day. Since then, in schools we celebrate activities related to Maths to commemorate it. The aim is to share this day with all the education community and society in general.

Why on May 12th? This date was chosen because it was the day when Pedro Puig Adam was born. He was a Spanish mathematician, internationally well known in the field of mathematics education.

Pedro Puig Adam (Barcelona, May 12th 1900 - Madrid, January 12th 1960) Spanish mathematician. He published about thirty educational works, trying to contribute to the renovation of the teaching of the mathematics in Spain. He was in contact with majority of the groups in Europe with advanced ideas about teaching maths in the fifties. His work has been more recognized abroad than in his own country.