maths - · pdf file6 i.e.s. fernando iii el santo / proyecto bilingüe a.n.l.: maths...

IES FERNANDO III CENTRO BILINGÜE

MATHS

1º DE E.S.O

I.E.S. FERNANDO III EL SANTO / PROYECTO BILINGÜE A.N.L.: MATHS

4

MATHS UNIT 1: NATURAL NUMBERS

UNIT 1: NATURAL NUMBERS

OUTLINE

ASPECTOS LINGÜÍSTICOS VOCABULARY

VERBO “SER”.

PHONETICS

1 - DECIMAL NUMBER SYSTEM

ACTIVITIES 2 - MULTIPLICATION OF NATURAL NUMBERS.

DEFINITION PROPIERTIES

o ASSOCIATIVE o COMMUTATIVE o DISTRIBUTIVE

3 - DIVISION OF NATURAL NUMBERS 4 - ARITHMETIC EXPRESSION. 5 - SOLVING PROBLEMS. 6 - VOCABULARY

THE IMPORTANCE OF

PHONETICS. THE SOUND / ʃ /

NUMBERS MULTIPLICATION ADDITION SUBTRACTION FACTOR PRODUCT DIVIDEND DIVISOR REMAINDER QUOTIENT BRACKETS TO CHECK

I.E.S. FERNANDO III EL SANTO / PROYECTO BILINGÜE A.N.L.: MATHS 5


1 - DECIMAL NUMBERING SYSTEM The decimal numbering system is a positional system in which each order has a value 10 times greater than its immediate lower.

Thousands of millions

Millions Thousands Ones

Hund

reds

of

thou

sand

s of m

illion

s

Tens

of

thou

sand

s of

milli

ons

Thou

sand

s of m

illion

s

Hund

reds

of m

illion

s

Tens

of m

illion

s

One

milli

on(s

)

Hund

reds

of

thou

sand

s

Tens

of t

hous

ands

One t

hous

and(

s)

hund

reds

tens

ones

X100

,000,0

00,00

0

X10,0

00,00

0,000

X1,00

0,000

,000

X100

,000,0

00

X10,0

00,00

0

X1,00

0,000

X100

,000

X10,0

00

X1,00

0

X100

X10

X1

Activities:

1 - Write the value of 3 in each number. a) 456,321 b) 5,123 c) 913,224 d) 540,032 e) f) g) h) 2 - Write the number 7 in the following positions. The only other number that may be used is 0. a) ones ____________ b) thousands ______________ c) hundreds ___________ d) millions __________ e) ten thousands ___________ f) tens ________________ g) hundreds thousands ___________ h) billions _____________

i) thousands millions ____________ _

3 - Change to the following positions: a) 14 thousands to tens b) 3 millions to one thousands c) 200 tens to one thousands d) 23 thousands to hundreds e) 3 billions to millions



2 - MULTIPLICATION OF NATURALS NUMBERS Definition

Multiplication is a quick way to put equal numbers together. For example: 306·5555555 In multiplication, the numbers that multiply are called factors. The answer is the product. 5 · 6 = 30 Properties of multiplication

o COMMUTATIVE o ASSOCIATIVE o MULTIPLICATIVE o DISTRIBUTIVE

3 - DIVISION OF NATURAL NUMBERS Division is the process of finding how many times one number can fit into another number. For example:

48 6 0 8 Division can be exact or not exact. It is exact if the remainder is 0. It is not exact when the remainder

is greater than 0. To check a division problem, multiply the quotient by the divisor and add the remainder. The sum should be the same as the dividend.

D=d · c + R Where D: Dividend d: divisor c: quotient R: remainder

Activities: 1.- Divide and check (copy the divisions) 2.- Divide and write the name of each term (copy the divisions)

factors product



4 - ARITHMETIC EXPRESSION

In arithmetic expressions with the operations addition, subtraction, multiplications and division, we follow the following order of operations: 1 - Brackets and square brackets

2 - Multiplication and division 3 - Addition and subtraction.

For example: Solve this operation: 3 + 2 · (8 - 4) = 3 + 2 · 4 = 3 + 8 = 11

5 - SOLVING PROBLEMS 1 - Two buses on the same road carry 75 people. In one bus there are 15 more people than in the other bus. How many people are in each bus? a) 50 and 25 people b) 40 and 55 people c) 45 and 30 people d) 55 and 45 people 2 - Three brothers gather their cards. Miguel has 15 cards. Antonio has 3 less than Miguel. Javier has 4 more than Miguel. How many cards do the three brothers have all together? 3 - A school is planning a dental check-up for all the students. In total, there are 650 students in ESO, 224 in Bachillerato, and 341 in Módulos. If they want to finish the check-ups in 5 days, how many students will have to go each day? 4 - The 72 boys and girls at a camp split up into teams of 6 people to play a game. Each team needs 9 red flags to play. How many flags are needed in total for the game? 5 - At a bakery, they have 40 dozen eggs to make 50 cakes. The extra eggs are used for cookies. Each cake uses 6 eggs. Every dozen cookies uses 4 eggs. How many cookies can they make? 6 - Marta bought 120 shirts for 7€ each. She sells them for 12€. She is left with 25 shirts, so she sells them on sale for 10€. What is the total profit Marta earns from all of the shirts? 7 - A salesperson buys a pack of 12 handkerchiefs for 36€, and sells them for 10€ a pair. How many handkerchiefs must he sell to earn 300€ in profit? 8 - Marisa wants to buy a 20kg sack of fruit. However, she doesn't have enough money. Instead, she buys 15 kg and saves 10€. How much did she pay for the 15 kg? (Those problems are from text book “1º Secundaria, Serie Trama, ed. Oxford” )



6 – VOCABULARY

Vocabulary Pronunciation Translation

Addition sust. [ə'dɪʃən] Adición; suma Bakery n. /'beikəri/ Panadería Brackets nombre /'brækət / Corchete Camp n. /kæmp/ Campamento Decimal sustantivo. /'desəməl / Decimal Dividend sust. /'divədend / Dividendo Division sust. / dɪ'vɪʒən/ División Divisor sust. / dɪ'vaisər/ Divisor Dozen sust. /'dʌzn̩/ Docena Factor sust. /'fæktər / Factor Handkercheives n. /'hæŋkərtʃi:vz/ Pañuelos Hundreds /'hʌndrəds/ Cientos Millions /'mɪljəns/ Millones Multiplication sust. /'mʌltəplə'keɪʃən / Multiplicación Number sust. /'nʌmbər / Número Ones /wʌns/ Unidades Pair sust. /per / Par Product sust. /'prɑ:dəkt / Producto Profit n. ['prɒfɪt] Ganancias Quotient sust. /'kwəʊʃənt/ Cociente Remainder sust. /rɪ'meɪndər/ Resto Sale sust. /seɪl/ Rebajas Subtraction sust. /səb'trækʃən/ Sustracción; resto System sust. /'sɪstəm/ Sistema Team n. /ti:m/ Equipo Tens /tens/ Decenas Thousands /'θaʊzn̩ds/ Miles To Add verbo. /æd/ Sumar To Check v. /tʃek/ Comprobar To Divide v. /di'vaɪd / Dividir To Multiply v. /'mʌltəplaɪ / Multiplicar To Split Up v. /splɪt/ /ʌp/ Dividirse To Solve v. /sɑ:lv / Resolver; Solucionar To Subtract v. /səb'trækt/ Restar



ANEXO

NUMBERS 1. one – uno 2. two – dos 3. three – tres 4. four – cuatro 5. five – cinco 6. six – seis 7. seven – siete 8. eight – ocho 9. nine – nueve 10. ten – diez 11. eleven – once 12. twelve – doce

13. thirteen – trece 14. fourteen – catorce 15. fifteen – quince 16. sixteen – dieciséis 17. seventeen – diecisiete 18. eighteen – dieciocho 19. nineteen – diecinueve

20. twenty – veinte 30. thirty – treinta 40. forty – cuarenta 50. fifty – cincuenta 60. sixty – sesenta 70. seventy – setenta 80. eighty – ochenta 90. ninety – noventa

21. twenty one – veintiuno 34. thirty four – treinta y cuatro 48. forty eight – cuarenta y ocho 53. fifty three – cincuenta y tres 67. sixty seven – sesenta siete 79. seventy nine – setenta y nueve 82. eighty two – ochenta y dos 95. ninety five – noventa y cinco

EXAMPLES

times equals

minus equals

divided by equals

plus equals

I.E.S. FERNANDO III EL SANTO / PROYECTO BILINGÜE A.N.L.: MATH 10

MATHS UNIT 2: POWERS

UNIT 2: POWERS

OUTLINE

ASPECTOS LINGÜÍSTICOS VOCABULARY

EL VERBO”SER” EL VERBO “HABER”

PHONETICS

1 – POWERS

SQUARING CUBING RAISING TO A HIGHER POWER

2 – OPERATING WITH POWERS. MULTIPLYING DIVIDING THE POWER OF A POWER POWERS WITH AN INDEX 0 OR 1

3 – SCIENTIFIC NOTATION (VERY BIG NUMBERS) 4 - ACTIVITIES. 5 - VOCABULARY

THE SOUND :/ h / /ə / /eə/

POWER SQUARE CUBE RULE ITSELF HIGH INDEX TO THE POWER

OF. . . TO RAISE



1 – POWERS

The small “n” is a power or an exponent. It tells us how many times we must multiply the factor “a” by itself.

Squaring a number: means “3 squared” or “the second power of three” and

Cubing a number: means “4 cubed” or “the third power of four” and

Raising to higher powers: means “2 to the power of 4” or “the fourth power of two” or “two to the fourth power” and

means “3 to the power of 8” or “the eighth power of three” or “3 to the eighth power” and

2 – OPERATING WITH POWERS We can operate with powers, but only for powers of the same factor. There are three rules to

remember.

A.- MULTIPLYING When multiplying powers with the same factor that multiply by itself, add the powers.

B.- DIVIDING

When dividing powers with the same factor that multiply by itself, subtract the powers.

C.- THE POWER OF A POWER

When we have the power of a power of a number, we must multiply the powers

D.- POWER WITH AN INDEX 0 OR 1

Anything to a power of 0 is equal to 1.

Anything to a power of 1 is equal to itself.



3 – SCIENTIFIC NOTATION. (VERY BIG NUMBERS)

When writing very big numbers it is useful to use a power of ten. This form also known as Standard Index Form or Standard Form or Scientific Notation. It’s always written as

Where

: is always between 1 and 10 : tell us how many places to move the decimal point.

For example:

4 - ACTIVITIES

1. Write the names of the following powers: a.

b.

c.

d.

e.

f.

2. Multiply the following powers and write their names

a.

b.

c.

d.

3. Divide the following powers and write their names:

a.

b.

c.

d.

e.

4. Solve the following expressions and write their names:

a.

b.

c.

d.

e.

f.

g. =

h.



5 – VOCABULARY English Pronunciation Spanish Always adverbio /'ɔ:lweɪz/ Siempre Dividing /də'vaɪdɪŋ / Dividiendo Exponent sust. /ɪk'spəʊnənt/ Exponente Expressions nombre /ɪk'spreʃənz/ Expresiones Factor sust. /'fæktər / Divisor Following adjectivo /'fɑ:ləʊɪŋ / Siguiente Form n. /fɔ:rm /| Forma Higher adjectivo /'haɪər / Superior How many. . . ? /haʊ/ /'meni/ Cuántos. . . ? Index number sust. /'ɪndeks/ /'nʌmbər / Itself pronombre /ɪt'self/ Si Mismo Multiplying /'mʌltəplaɪɪŋ / Multiplicando Power sust. /'paʊər / Potencia Rules nombre /ru:lz/ Reglas Small "n" sust. /smɔ:l/ "n" minúscula To Cube verbo. /kju:b/ Cubo To Operate v. /'ɑ:pəreɪt / Operar To Raise v. /reɪz/ Elevar To Square v. /skwer / Cuadrado To the power of . . . Elevado a . . . Useful adjectivo /'ju:sfəl/ Útil Written as. . . Escrito como. . . Write v. /raɪt/ Escribe



ANEXO

EXAMPLES:

ORDINAL NUMBERS

1st first

2nd second

3rd third

4th fourth

5th fifth

6th sixth

7th seventh

8th eighth

9th ninth

10th tenth

maths - · pdf file6 i.e.s. fernando iii el santo / proyecto bilingüe a.n.l.: maths...

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