Math 8 Tips and Vocabulary Mr. Dodds September 12, 2013
Positive groups of positive numbers are positive
Negative group of negative numbers are positive
Positive groups of negative numbers are negative
Negative groups of positive numbers are negative
Integer = a positive or negative non-fraction number
e.g. …-3, -2, -1, 0, +1, +2 +3
Sum
= the answer from adding two numbers
e.g. the sum of 2 + 3 is 5
Product = the answer from multiplying two numbers
e.g. the product of 2 x 3 is 6
Quotient= the answer from dividing two numbers
e.g. the quotient of 6 ÷ 3 is 2
(+3) x (-5) is the same as (+3)(-5)
(the product is -15)
(-4) x (-6) is the same as (-4)(-6)
(the product is +24)
(-15) ÷ (+3) is the same as (-15)
(+3)
(the quotient is -5)
(+24) ÷ (-6) is the same as (+24)
(-6)
(the quotient is -4)
(-15) ÷ (+3) = (-5)
Expression
Answer (called the sum, product, or quotient
depending on +, x or ÷)
Equation
Multiplying and dividing are related
(-12) ÷ (+4) = (-3)
(-3) x (+4) = (-12)
(-12) ÷ (-6) = (+2)
(+2) x (-6) = (-12)
Number Line Models
Start at zero. Multiplication:
(+3) x (-2)
Number of Size of
step
steps
For a negative number of steps, face the negative end of
the number line before walking.
For negative step sizes, walk backwards.
(+4) x (+2) = Face forwards, walk forwards 4 steps of positive 2
(+3) x (-2) = Face forwards, walk backwards 3 steps of negative 2
(-2) x (-5) = Face backwards, walk backwards 2 steps of negative 5
Use whatever method works best for your own understanding.
If models help, use them. If models confuse you, don’t use them!
Showing your work in math
What is your thought process that led you to your answer? Use:
Numbers
Operations (+, -, x, ÷)
Describing words (calculate, area, reduce, length, etc.)
You must show your work to receive full marks – only writing down the
answer does not show that you understand the material. Examples:
Solve: 42 x 5
Answer A)
Answer B)
✔
Answer C) ✔
1
210
42
x 5
1 210
42 x 5 = (40 x 5) + (2 x 5)
42 x 5 = 200 + 10 = 210
Solve: 50 + (3 x 4) ÷ (6/3)2
Answer A)
Answer B) ✔
53
Brackets:
50 + 12 ÷ (2)2
Exponents:
50 + 12 ÷ 4
Multiply/Divide:
50 + 3
Add/Subtract:
53