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Algebraic Expressions

Algebraic Expressions. Important ideas:. An algebraic expression is a mathematical expression that contains a variable. An algebraic expression can be evaluated (solved) by replacing a variable with a number, then following the order of operations (which steps do you do first?)

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Algebraic Expressions

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  1. Algebraic Expressions

  2. Important ideas: • An algebraic expression is a mathematical expression that contains a variable. • An algebraic expression can be evaluated (solved) by replacing a variable with a number, then following the order of operations (which steps do you do first?) • Notice that variables are often written in italics so they are not confused with units of measure.

  3. Let’s talk allowance! • Suppose you get $5 per week. About how much would you get in a year? • $5 x $50 = $250 • Suppose you were offered $100 now, plus $1 a week for the rest of the year. Which would you prefer and why?

  4. Most might prefer $100 now, so they can buy what they want now without having to save up for it. • But… which choice gives you more money in one year? • How do you know?

  5. Read “explore” page 16

  6. If Tehya chooses choice 1, how much money will she be paid? • How do you know?

  7. $1040 • There are 52 weeks in a year. • 52 x 20 = $1040

  8. If Tehya chooses choice 2, how much money will she get paid? • How do you know?

  9. $1024 • There are 52 weeks in a year. • 52 x 12 = $624 • $624 + $400 = $1024

  10. Which method would pay Tehya more money? Explain! • Choice #1 • $1040 is greater than $1024. • Why might Tehya choose the method that pays less?

  11. She might be short of money and need (have an immediate use for) $400 right away. She only loses $16 dollars by taking $400 cash right now.

  12. Choice 1 • How can you calculate the money Tehya has received after 6 week? • After 25 weeks? • Multiply 6 by $20 to get $120 • Multiply 25 by $20 to get $500 • What rule can you write to calculate the money received at any time during the year for choice 1?

  13. Multiply the number of weeks by $20! • $20 xw • “w” is the variable. Remember a variable can be any letter. • $20 xt = $20 xw • From now on I will use * on slides to mean “multiplied by” so we are not getting confused by the “x” meaning “multiplied by”.

  14. 4x * 2 and 4b * 2 are the same. • 4x + 2 and 4b + 2 are the same. • A variable is a symbol that represents a set of numbers. Choice of variable does not affect the expression. • Remember to use the correct order of operations, or you might get a different/incorrect answer.

  15. 3 + 4k • If you use k=2, but do not follow the correct order of operations, the answer you get is 14. • If you use the correct order of operations, the answer you get is 11. • Order of Operations

  16. You have worked with variables before… • For example, in formulas for area and perimeter. • Remember… the constant term of an expression is called constant because the value of that term is not affected by the value of the variable. • Let’s review page 17.

  17. Practice, page 18 • #s 1-10.

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