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Evaluating Expressions 1 What do you use when substituting a value? 1 What does evaluate mean? 1 1 What does substitute mean? What is a variable? 1 1 Give some examples of variables. What is a constant? 1 What is a coefficient? 1 1 When substituting -3 for x into x², how would we write it? Where does the exponent go? What is a term? 1 What separates one term from another? 1 In the expression 6 x 2 2 x 3 y 4 what are the constants and the coefficients? Describe the difference between an expression and an equation. What is the proper way to write an x times 3? 2 2 2 2 2 2 3 Parentheses Ex: 2x+4 when x = 3 Calc: 2(3)+4 Plug in number and find numerical answer (solve) Plug in something A letter or symbol that represents a number (emphasize this!!!) Various answers x, y, r, , <3 …. A constant is a number by itself with no variable. The value of this term never changes, ie: remains CONSTANT (the SAME) A coefficient is a number in front of a variable. The coefficient is being multiplied with the variable With parentheses. The exponent goes outside (-3)2 A number or variable or a coefficient with a variable. Terms do NOT have + or + or - Ex: 3x – 4 +7yz has 3 terms. (draw lines where you see the – and + Constant: -4 (NOT 4!!!!) Coefficients: -6, -2 and 3 (NOT 6 and 2!!!) An equation has an equal sign and an expression does not. 3x: the number (coefficient) goes in the front. If they just say “number” ask: What is this number called when it is in front of a variable? Coefficient Four. How many terms does the expression 6 x 2 2 x 3 y 4 have? How can we determine the number of terms? Separate the terms with the + and – signs. What is the difference between a constant A constant term does not have a variable. The and a coefficient? value of this term never changes. A coefficient has a variable next to it. The value of this term can change. 2x: if x = 3 then the value is 6, if x = 10, the value is 20. If the variable is alone (ex: x), does it have a YES. There is always a coefficient of invisible coefficient? (If yes, what is it?) 1. If there was not any x’s (zero) then why would we write it? For ex x+ 3x = 4x b/c 1x+3x: 1+3=4. if there were only 3, why would we even write the “x” term? Give an example of an Algebraic Expression Algebraic : various answers; must have and a numerical expression. Be able to variables (no equal sign) explain the difference. Numerical: various answers; cannot have variables (no equal sign) Algebraic expressions have variables, numbers and operation symbols. Numerical expressions only have numbers and operation symbols. 3 3 Lead in: What is different about algebra vs “old/8th grade” math? So what do we think ALGEBRAIC expressions have different than numerical expressions? What is an example of something you would have done in 8th grade? (or earlier) What does this have? Now if we want to make it ALGEBRAIC, what would we change? How would you read/say 3( x 2) ? What is the proper way to write the sum of a number and a variable term? (ex. 4 increased by 2x) Algebra has variables Variables A numerical expression: 3+4 Numbers and symbol (plus sign) Put in variables: 3x+4x “Three times the QUANTITY x minus 2” 2x+4. The variable term should go FIRST. Explain that it is not wrong to write 4+2x, but it is “improper,” Just like it is not “wrong if we write “juan”(its still the same name) but it is “improper.” Also 2x+4 is how students will see it on tests so they need to get used to the “proper” way of writing algebra.