JOCELYN G. TAMARES Teacher I

Lets EXPLORE!!!!

ACTIVITY 1. TRANSLATING TO SYMBOLSLook at the words below. Think of ways to represent them into symbols that convey the same meaning. Draw your symbols on the box.

LOVE HAPPINESS SPEED DANGER DIRECTION

ACTIVITY 2. SIGNS.......

1. What does each sign represent? 2. How do these signs help in avoiding accidents?

ACTIVITY 3.Winona was 24 when her son Anton was born.

1. Fill in the table below. Antons age 1 4 7 12 18 25 Calculation 1+24 ____ ____ ____ ____ ____ Winonas Age 25 ____ ____ ____ ____ ____ 2. Explain in words how to find Winonas age if you know Antons age. 3. Write a mathematical sentence for Winonas age. 4. If you let the variable a stands for Antons age in years, write an expression for Winonas age in terms of a.

ALGEBRA What is algebra?

Is defined as a branch of mathematics which symbols, usually letters of the alphabet, are used to represent unknown numbers and in doing so generalize the facts in arithmetic.

1. NUMERALS 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 2. SYMBOLS OR SIGNS A . SYMBOLS OF RELATIONSHIP = equals, is equal to, is > is greater than, is more than < is less than is not equal to is greater than or equal to is less than or equal to

B. OPERATIONAL SYMBOLSENGLISH WORDS

ALGEBRAIC TRANSLATION

+

Added to, the sum of, increase by, plus, total of, more than Minus, decreased by, subtracted to, subtracted from, reduced by, diminished by, less than, less, remainder of , difference of, take away Times, multiplied by, the product of, of Quotient of, divided by, ratio of, over The square of x, x squared, the second power of x, x to the second power Square root of

, ( ), ,[ ],

x2

C. SYMBOLS OF GROUPING Parenthesis ( ) Brackets [ ] Braces { } Bar

3. LETTERS OR VARIABLES TO REPRESENT UNKNOWN NUMBERS , x ,y, z ,a, b, ,

is a single or a combination of mathematical operations, symbols, variables and constants which represent a number Examples:

7 y 3y 2 y

4

3

2a b c 2n 13

3

2

is any symbol for anumber which may consist of a single number with or without operation symbols, or of two or more numbers with operation and grouping symbols. Examples:

2a b c

3

2

28 100 z 10 (1x2) (6 z 3) 345

CONSTANT

is a fixed quantity or one that does not change its value in relation to variables is a value or quantity which never change regardless of the condition of the problem. is a symbol (blank, box, letter) which may take one or more than one values from a given set of allowable values called replacement set or domain. is a value or quantity which changes depending upon the condition of the problem

VARIABLE

10a + b 10 a and b 3x 5 3 and 5 x P = 4s 4 P and s

constant variables constants - variable constant - variables

TERM

is a part of an algebraic expression separated by plus or minus sign is a constant which determines the number of times a variable is to be multiplied is the numerical factor in a term Are the variables, the letter coefficients or the unknown quantities

NUMERICAL COEFFICIENT

LITERAL COEFFICIENT

BASE

Is the repeated factor in a product

EXPONENT

Is a number written at the upper right hand of a symbol to indicate the number of times that symbol is used as a factor.

EXAMPLES:

3x

2

3 is the numerical coefficient x is the base 2 is the exponent x2 is the literal coefficient

This means (3)(x)(x)

5 2y a

3

5 and 2 are the numerical coefficient y is the base 3 is the exponent

a and y3 are the literal coefficient

This means (5)(a) + (2)(y)(y)(y)

TYPES OF ALGEBRAIC EXPRESSION ACCORDING TO THE NUMBER OF TERMS

MONOMIAL Is an algebraic expression consisting of one term. 30x; - 10xyz; 2(x+y) BINOMIAL Is an algebraic expression consisting of two terms 30x 10xyz; - 12n+83ab2c TRINOMIAL Is an algebraic expression consisting of three terms 30x 10xyz +4xy; 12n3 + 4mn - 15 POLYNOMIAL/MULTINOMIAL Is an algebraic expression consisting of two or more terms 5y3 -2y2 +y -5; 3m5n3 -3abc +4p2q 8y +6

FIRM - UP

ACTIVITY 1. GUESSING GAMEGive the possible value/s of the variables in each of the following conditions. 1. 0 a is the sum of two opposite integers 2. 1 x is the lowest prime number 3. 24 Y is the multiple of 4, 8, and 24 4. 1, M is the greatest common factor of 120, 2,3,4 15 and 60 ,5,6, N is a whole number and is less than 10 7,8,9 5. 15

1. 2. 3. 4.

5.

6. p is the sum of the first 2 consecutive odd 6. numbers 7. 7. d is an integer between 5 and -5 8. b is an odd number between 1 and 10 8. 9. k is a counting number between 0 and 9 10. z is a multiple of 12 greater than 20 but less 9. than 50 10. 11. 11. x is the product of 8 and +8 12. y is the whole number between -1 and 1 12. 13. c is the number of square roots of the perfect 13. square between 10 and 30 14. 14. x is the number of the absolute values of 5 15. and + 5 15. n is an even number less than 10.

6 -4,-3,-2,1, 0, 1, 2, 3, 4 3,5,7,9 1,..8 24,36,48 -64 0 4 5 0,2,4,6,8

ACTIVITY 2.x + 2y = 10 9 + 3 = 6x2 105 - 12 + 13 y < 15 12 3 + 6 3x + 18 23 +5 = 15 2 2m + 3n NUMERICAL EXPRESSIONS 105 - 12 + 12 3 + 6 _______ 13 ________ 23_______ 2 +5 = 15 ( 5 4) 5 ________ ________ 40 15 3 -2+6 _______ ________

WHERE DO I BELONG?

6y 4x 5 ( 5 4) 5 A = bh 40 15 3 -2+6 5x xy (4 +10) 3(2)(a) ALGEBRAIC EXPRESSIONS x + 2y = 10 9 + 3 = 6x2 _______ ________ y < 15 3x + 18 _______ ________ (4 +10) 3(2)(a) 2m + 3n 6y _______ ________ 4x 5 A 5xbh = xy _______ ________

DEEPEN

ACTIVITY 1Determine the constant and variables, literal coefficient, and numerical coefficientEXPRESSIONS CONSTANTS VARIABLES LITERAL COEFFICIENT NUMERICAL COEFFICIENT

1. - 5x 2. 4/5k2 3. 5p3 + 1 4. -5( x 2y) 5. 4x2 + 3y 6. 2x + 10 7. 7y + 3x z 8. 14 + p -5 9. P =2( l +w ) 10. 3x2 + 1

ACTIVITY 2.Write the following expressions using exponents, whenever appropriate.

1. 4yy 2. zzz 3. - 7mmm 4 . 2xyy 5. dddddd 6. 14pppq 7. (3n)(3n)

8. - 6 bbbcc 9. 14 + 5tttmmm 10. 2xxx nnn 11. (2a+c)(2a+c)(2a+c) 12. 21aaaabc fff 13. yyz aa +def

14. ssss mm 15. a + cdd b(bd) bb 16. (b c )(b c) 17. 3mmd + 2mn + pppq 18. 2(a + 3)(a + 3)(a + 3) (a + b)(a + b) 19. ab + bc + cd 20. 3(x + 1)(x + 1)(x + 1)(x + 1) (7 x )( 7 x )( 7 x )

ACTIVITY 3.What do the following expressions mean?7 a

o o o o o

1. 2. x3y4 3. 7a2b 2x 3 4. 4 5. ( 7m) 2

______ o ______ o ______ o ______ o ______ o

6. ______ 4+ 3 ______ 7.12x 8. (gt)4 ______ 4+ b ______ 9. 5a 10.4x3+y4______

2b 3 11a

TRANSFER

ACTIVITY 1. WHATasAM I? Classify each expression monomial, binomial, ortrinomial.

1. 4xy 2. 2x + 1 3. 3x + 2y 4. 2a + 3b + c 5. 9xy2

6. 14x3y3z4 7. x2 + 3x + 7 8. 17xy3 + x2y2 2x3y 9. 25a5 10. 11(x2 + y2) 11. 10x2 + 15x + 19 12. 18x3 + 4 13. 63g 14. 3ae 15. -16x2 - 9x - 20

ACTIVITY 2.Simplifying Numerical Expressions1 5 8 9 2 6 10 11 3 4 7

12

13 16 18 17

14

15

19

Across:

1.) 4.) 6.)

4 3 ?5 3 A 22 2 2 2

3

33 2

10

2

5

2

?7 16 7 A? 2 3 A ?8 5 A 8.) 10.) 3 2 2 3 4 1012.) 5 5 4 3 1 14.) 2 6 13 3 6 11 11 9 6 16.) 16 100 32 42 5 1 18.) 2 7 y 3 3 3 3 19.) 3 3 3 2

6 7

1

2

2 5

2

3 3

Down:

2. 1218 4 26 39 12 3 3. 3 2 y 2 3 4. 6 5 5. 7. 9. 11.2

2 3 1 2 3 4 12 2 2 3 2

?

2

3 5 6

A?

2

7 3 3

A

1 2

? 3 2

2

52 42 2

A

2 5 2 3 11

32

2 44

12. 13.

3 10 1 4

2

7 y 2 20 96 34 143 14. 215. 17.

9

2

13

4

2

2