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Journal Writing Warm Up

Journal Writing Warm Up. Bell Quiz 2-1b. Name four different ways you would organize the people in this class into groups. Explain your reasoning. Interpreting expressions Part 2. Speaking the language of math. Words to know. Algebraic Expression - Variable – Coefficient –

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Journal Writing Warm Up

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  1. Journal Writing Warm Up Bell Quiz 2-1b • Name four different ways you would organize the people in this class into groups. • Explain your reasoning.

  2. Interpreting expressionsPart 2 Speaking the language of math

  3. Words to know • Algebraic Expression - • Variable – • Coefficient – • Terms – • Like Terms – • Factors – • Formula -

  4. Variables • A variable is a symbol, usually an English letter, written to replace an unknown or changing quantity. • What variables would be choices for the following situations: • a. the number of cars on a road • b. time in minutes of a ball bounce • c. distance from an object

  5. Remember: when you replace a value with a variable you need to tell the reader what the variable means. c = number of cars on the road t = time in minutes d = distance from object Whenever you replace a value with a variable, you should define the variable in a word sentence so your reader understands what you mean. BEST PRACTICES TIP

  6. Algebraic Expressions • An algebraic expression is a mathematical phrase combining numbers and/or variables using mathematical operations. An equation is two equal expressions. • The parts of expressions and equations are called terms. • The terms that are only numbers are called constants, because they are always the same. They don’t vary. • The number that the variable is multiplied by is called the coefficient. Constants Coefficient

  7. Terms that are multiplied together are called factors. factors Using the distributive property, the product becomes: Why can’t you subtract the 12 from the 4x?

  8. Remember in 4x – 12, the variable x has a value but we don’t know what it is. Because of the order of operations, Until we know what multiplication to do, we cannot subtract. • 4x-12 when x = 3 • 4(3) -12 • 12-12 • 0 • 4x – 12 when x = 7 • 4(7) – 12 • 28 – 12 • 16 That makes sense! We still have to use the order of operations, even if a value is unknown.

  9. Understanding groupings • Some expressions have more than one operation or have groupings. It is important to understand the language for these as well. • Try These: The sum of eight and the product of 12 and x Four times the quotient of a number and nine Two times the difference of the number of cookies and six The sum of x and ten multiplied by the difference of x and four The product of four twos increased by eleven.

  10. Simplifying Algebraic Expressions • Because a variable represents a changing or unknown value, • the answer to any operation performed on a variable • is also going to be changing or unknown • so we can’t find a single term answer, we can only simplify. • = • We don’t know x so we can’t find 4 times x, • but we can multiply the constant by four to get -12. Hey, isn’t that the distributive property?

  11. Formulas A formula is an algebraic expression or equation which defines the relationship between varying parts in a situation. Like recipes in cooking, formulas help us put ingredients together to get the final result.

  12. Using some common formulas To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. If the dimensions of the pasture are 300 feet by 225 feet, how much fencing should the ranch hand purchase to enclose the pasture? Quick Quiz: What is the distance around a rectangle called? How do you find it? What variables would you use?

  13. Solution: Begin by drawing a diagram of the pasture and labeling what you know. To find the amount of fencing needed, you must add all the sides together; By substituting the dimensions of the pasture for the variables, the expression becomes Now we must evaluate by adding the values together. The ranch hand must purchase 1,050 feet of fencing. P = L + L+ W + W P = 300 + 300 + 225 + 225

  14. What do the variables in these formulas mean? Arect = lwAsqr = s2 Psqr= 4s Atri = (1/2)bh Acir = ∏r2 Ccir = ∏d Vcube = s3 SAcube= 6s2

  15. Patterns and Expressions In mathematics, we look for patterns in the numbers that we see. Expressions and equations can be written to describe a pattern. • Consider a theme park charging admission • of $28 per person. • A formula or rule can be written to describe • the relationship between the amount of • money taken at the ticket booth and the • number of people entering the park.

  16. In words, the relationship can be stated as • “The money taken in dollars is twenty-eight times • the number of people who enter the park.” Rewriting the English phrase into a mathematical phrase, it becomes D = 28(p) Hey, we just wrote our own formula!

  17. HOME WORK Interpreting Expressions worksheet

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