Unit 3 Variables, Formulas, and Graphs

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# Unit 3 Variables, Formulas, and Graphs - PowerPoint PPT Presentation

Unit 3 Variables, Formulas, and Graphs. Read through the following slides. Take your time, review them as necessary, take notes if you need to. Complete all of the tasks assigned within the slides. General Pattern :. General patterns are essentially formulas or rules .

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### Unit 3Variables, Formulas, and Graphs

Take your time, review them as necessary, take notes if you need to.

Complete all of the tasks assigned within the slides.

General Pattern:
• General patterns are essentially formulas or rules.
• They can be expresses using just words
• “To find 10% of a number, multiply the number by 0.1 (or 1/10).
• They can be expressed as a number sentence that contains a variable (a letter or symbol that represents a possible numeric value).
• 10% of n = 0.1 * n
• These are all examples of general patterns:

P+P=2*P C/1=C a*(b+c) = (a*b) + (a*c)

Special Case
• A special case is a number sentence WITHOUT any variables.
• 10% of 40 = 0.1 * 40
• These are all examples of special cases:

4+4=2*410/1=103*(6+5) = (3*6) + (3*5)

How do I remember the difference?
• General Pattern = Rule = Formula = missing information (variables)
• Special Case = Specific = It will contain specific numbers, no variables.
• Try this….which is the general pattern? Which is the special case? (write your answer in your Math Notebook or on a piece of paper – have it with you on Monday)

15 + (-15) = 0 B + (-B) = 0

How do I convert a general pattern into a special case?

General Pattern  Special Case

• All of the given numbers and function symbols remain the same.
• Replace the variable with a number. If the same variable is repeated (there are two “B”s), then you MUST use the same number for all of the “B”s. If the variables are different, “A” and “B” then you should use a different number for each different variable.
• Examples:
• GP  B+B= 2 * B
• SC  4+4= 2 * 4

-GP a+b+6 = 6+b+a

-SC 2+9+6 = 6+9+2

How do I know if I used the correct value?
• If you follow the pattern (or rule) of the general pattern, your special case will ALWAYS be true…
• R * 1 = R We know that any number times one will equal itself… you can replace R with any number and it will remain true…
• 5 * 1 = % 0.5*1 = 0.5 -62 * 1 = -62
• It works even with patterns that do not fit “rules we know.”
• (R+T) + (5-T) = R+5 (R+T) + (5-T) = R+5
• (3+2) + (5-2) = 3+5 (1+2) + (5-2) = 1+5
• 5+3=8 3 + 3 = 6
• 8=8 6=6
How do I convert a special case into a general pattern?

Special Case  General Pattern

• Identify all of the numbers and function symbols that remain the same throughout all of the examples. These will remain the same in your general pattern.
• Identify any numbers that change in each example. Replace these with variables in your general pattern.

Example:

• Special Cases: 10÷ 10= 1

5÷ 5= 1

4.6÷ 4.6= 1

• -General Pattern: D ÷ D= 1
NOW YOU TRY IT:

Complete Math Journal Page 84 #s 1-4 AND 86 #s 2, 4 and 6.