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Vocabulary
True or False? Explain your Reasoning
Error Analysis
Add/Subtract
Multiply/Divide
100
...-3, -2, -1, 0, 1, 2, 3... we call these numbers what?
Integers
100
True or False (explain your reasoning): The sum of two negative integers is always positive.
False. When adding two negative integers, the sum will always be negative. For example, -2+(-3) results in two negative(-) counters and three negative(-) counters; there is nothing to cancel out.
100
Describe and Correct the Error: -2(-7) = -14
The product should be positive. 14.
100
Explain how you can tell if a sum is positive, negative or zero without even adding. Explain your answer. A: -8 + 20 B: -30 + 30 C: -10 + (-18)
A: The answer will be positive because 20 has a greater absolute value than -8 (it is further away from 0). 20 is positive therefore our answer is positive. B: The answer will be 0 because the integers are opposites/additive inverses. C: The answer will be negative because both integers are negative.
100
Evaluate the expression -(5^2)
-25
200
Adding -4 to its _____________ will result in a sum of 0.
additive inverse/opposite
200
True or False (explain your reasoning): The product of three positive integers is positive.
True. The product of the first two positive integers is positive. The product of the result and the third positive integer is positive.
200
Describe and Correct the Error: (-63)/(-9) = -7
The quotient should be positive. 7.
200
Write two integers with different signs that have a sum of -25. Explain how you solved.
Sample Answer: -26+1 = -25. Starting at -26 on the number line, adding 1 means moving to the right one step which results in an answer of -25.
200
(-3)^2
(-3)*(-3) = 9
300
What are the names of the two models we use to model our integer addition problems?
Number line model and counter/chip model
300
True or False (explain your reasoning): An integer and its absolute value are always opposites.
False. A positive integer and its absolute value are equal not opposites.
300
Describe and Correct the Error: 0/(-5) = -5
The quotient should be 0. 0/(-5) = 0.
300
The floor of the shallow end of a swimming pool is at -3 feet. The floor of the deep end is 9 feet deeper. Which expression can be used to find the depth of the deep end? Why? -3 + 9 OR -3-9 OR 9-3
-3-9. The deep end is 9 feet deeper than the shallow end which is -3 feet. -3-9 = -3+(-9) = -12. The deep end is -12 feet.
300
12(-1)(2)
-24
400
What is the definition of absolute value?
It is the distance of a number from 0 on the number line. It is always positive.
400
True or False (explain your reasoning): The product of three negative integers is positive.
False. The product of the first two negatives is positive. The product of the positive result and the third negative integer is negative.
400
Describe and Correct the Error: -5+-10 = 15
The answer should be negative
400
Evaluate the expression when a= -2, b= -8, c= 5 4-a-c Explain how you solved
4-(-2)-5 = 1
400
A football jersey is marked down $10 each week for 3 weeks. Find the total change in price of the football jersey.
-10(3) = -30. The price decreased $30.
500
Why is absolute value important when we are adding integers with different signs?
It is important because we keep the sign of the addend that has the greater absolute value. The absolute value tells us which addend is furthest away from 0 and that is the sign we should keep.
500
True or False (explain your reasoning): When adding 10+(-12) your answer is positive because the addend (10) is the bigger number and you keep the sign of the bigger number.
False. Your answer is negative; you keep the sign of the addend that has the larger absolute value. -12 has a larger absolute value than 10.
500
Describe and Correct the Error: -7-(-12) = -19
The opposite of -12 should be added. -7-(-12) = -7+(12) = 5.
500
Write two different pairs of negative integers, (x) and (y), that make the statement (x)-(y) = -1 true
Sample answer: (x)= -2 (y)= -1 and (x)= -3 (y)= -2
500
Evaluate the expression when x= 10, y= -2, z= -5 -x^2 + 6z/y
65