Download Integer Review Notes

Summer Packet Problems for Algebra
Integer Review Notes
When adding integers with like signs, add the
numbers and take the common sign.
Ex. 16 + 4 = 20
Subtracting a number is the same as
adding its opposite.
–5 + –7 = –12
Ex. –80 – (–25) = –80 + (+25) = –55
When adding integers with unlike signs,
subtract their absolute values and take
the sign of the integer with the larger
absolute value.
Ex. –16 + 4 = –12
STRATEGY: Use New York Yankees
(Do I change the sign?)
N Y Y
Ex. 7 – 25 = 7 + –25 = –18
–5 + 7 = 2
STRATEGY: Think MONEY $$$$$$
If the signs are the SAME, then the answer is
positive.
Ex. –5 × –7 = 35
5 × 7 = 35
12 ÷ 4 = 3
–12 ÷ –4 = 3
If the signs are DIFFERENT, then the answer
is negative.
Ex.
5 × –7 = –35
–12 ÷ 4 = –3
STRATEGY: good = positive
bad = negative
When good things happen to good people,
that’s a good thing.
10 ÷ 5 = 2
When good things happen to bad people,
that’s a bad thing.
7 × –3 = –21
When bad things happen to good people,
th t’
b d thi
4
5
20
Summer Packet Problems for Algebra
Integers
Integers – integers are used daily in real life. Their uses include thermometers, field position in football,
and money and checking accounts. The following includes examples of each.
Integers are positive and negative whole numbers and zero.
Here is a review of integer rules for you.
To ADD integers with the same sign, add and use the same sign. +2 + +8 = +10, -2 + -8 = -10
To ADD integers with different signs, take the difference of the absolute value of each integer and use
the sign of the largest number. (Note the use of different or difference)
+8 + -2 = +6
To SUBTRACT integers, use “leave, change, change” and you then have an addition problem. Use the
addition rules. +2 - -6 gets changed to +2 + +6 = +8.
To MULTIPLY or DIVIDE integers, use these rules:
•
•
Activity 1
If the signs of both numbers are the same, the product will be POSITIVE +6 ⦁ +2 = +12.
Likewise -6 ⦁ -2 = +12, and
If the signs of both numbers are different, the product will be NEGATIVE -6 ⦁ +2 = -12.
Likewise
= -2
Temperatures and Integers
(No calculators)
1. The temperature in Gaithersburg this morning is 34o F. It will rise 45o today. What will be the high
temperature for today? _____________
2. Last February Anchorage, Alaska started the day with a temperature of 16o F. The temperature dropped
27o that day. What was the final temperature? __________________.
3. The temperatures in Hanover, NH for the week of February 11 were as follows:
-1o , 16o , 21o , -4o , 22o , -2o , and 7o . Find the average temperature for
Hanover, NH for that week.
___________________
4. Ice fishing in Canada is a popular sport. On one day the temperature was -42oF . The next day the
temperature dropped by 17o. What was the temperature the second day? ____________
5. In a very warm climate in South America, the temperature for the day was 93oF . Ms. Juarez heard that it was
9o cooler than the day before. What was the temperature the day before?
_____________
Summer Packet Problems for Algebra
Activity 2
Rational Number Practice
Directions: Evaluate each expression without a calculator.
1.
(-2) + 3
2.
(-14) – ( -7 )
5.
6.
12
7.
8. -9 × -3
9. 6 × -3 × -6
10. -120 ÷ -6
11. (-7) - (-2) - 9
12. ( -41) + ( -9)
13. 6 × -1 × 2
14. (11)(6)
3. (-6) - 24
4.
4 +5
× (-6)
15. (-12.2) + (-6) + 6.75
16.
17. 7 - 2.8
18. 1.7 - (-0.8) + 4.013
19.
20.
-
- (
Summer Packet Problems for Algebra
Activity 3
Summer Packet Problems for Algebra
Number Cubes and Integers Game
Directions: Cut out all three of the number cubes below. Assemble them as individual cubes
by taping them together. Like the one shown in the diagram below. You must use the negative
number cube for the activity on the next page.
-1
-2 -3 -4
-5
-6
8
7
9 10 11
12
Rules for the game are on the next page.
Summer Packet Problems for Algebra
Summer Packet Problems for Algebra
Activity 3 continued
1.
2.
3.
4.
5.
Rules for the Equation Game
Cut all nets out and tape together into number cubes.
Pick two number cubes. One should be the negative number cube.
Roll both cubes and write the two numbers down.
The first number, positive or negative, goes into the first equation or inequality
blank. The second number goes into the second blank in the equation or inequality.
Solve the equation or inequality you have made. It may help to put the equations on
a separate sheet of paper
Example: On the first die, I roll a -6. On the second die I roll a 4. I fill in the equation
to look like this:
-6 x + 3 = 4 I then solve the equation, showing steps
-3
-3 (Answers may be left as fractions)
--------------------Remember that if you multiply
-6 x
= 1
or divide by a negative number
-6
-6
in the final step of an
inequality, change the direction
x = -1
of the inequality symbol.
6
1. ____y - 9 = _____
2. _____x + 2 = ______
3. ______y + 12 = ________
4. ____x - 10 = _____
5. _____r - 4 < _____
6 .________x - -2 > _________
7.____x + - 3 = _____
8. _____r + 8 > _____
9. ______s + -4 ≤ ________
10.____x - - 16 = _____
11. ____r + 18 = _____ 12. _____q - 8 = ________
13. ____y - 9 ≥ ____
14. ____s - -10 = _____
15. r + 8 = _________
?
Summer Packet Problems for Algebra
Activity 4
Real World Math – Unexpected Events – Applying Math Concepts
to Everyday Life.
Checking accounts are an important part of life. You use a checkbook to keep
track of the money you have as you pay out money and receive money.
Below you will find a check register. Each transaction will be a Debit (-) or a
Credit(+). After each transaction, you will compute the new balance.
Transactions are on the next page. The first few are done for you.
Check Register
Transaction
Payment or Debit (-)
Deposit or Credit(+)
- 70 00
1. Replace window
+30
2. Sell CDs
00
3. Trip to vet
4.
5.
6.
7.
8.
9.
10.
11.
12.
Final Balance
x
x
x
x
Balance
100
00
30
00
60
00
Activity 4 continued
Summer Packet Problems for Algebra
1. You are playing baseball and break a neighbor’s window. Pay your
neighbor $70 to replace the window.
2. You earn $30 selling some old CDs.
3. Your cat is sick and you take it to the vet. It costs you $45.
4. You win the school raffle and get $50.
5. You buy your brother a birthday present and spend $25.
6. A magazine pays you $15 for a poem you wrote.
7. You return a book to the Media Center and pay a fine of $35 for
overdue books.
8. You break your leg playing soccer. You rent crutches for $100.
9. You have to stop at the store and buy $60 worth of dog food.
10.You and your brother go to the movies. You pay for both of you for $25.
11. You are caught walking your dog without a leash. The fine is $75.
12. You get $60 for being a winner in the school fundraiser.
Activity 5
Solve the Mystery of Who Stole the Banana Today.
A person wearing a red hat, yellow shirt, and blue pants stole the banana. Who was it?
Use organizer below to help solve the mystery. Write yes in a box under the clothing next to a person’s
name if it is true. Write no in the box if it is not true.
Red Hat
Yellow Shirt
Blue Pants
Bonnie
Connie
Donny
Ronny
1. Bonnie and Connie wore red baseball caps today. Ronnie did not wear a hat. Donny was
wearing a red cap.
2. Bonnie wore a white shirt to work today. Connie, Donny, and Ronny all wore yellow
“Banana Land” shirts.
3. Connie wore a black skirt today. Bonnie and Donny wore blue jeans. Ronny wore white
shorts
Activity 6
Summer Packet Problems for Algebra
Final Product
Create a math game!
Here’s your opportunity to show your creativity.
Create a math game that uses equations
You must have the following in your game:
•
•
•
•
•
•
•
Name of your game.
Objective of the game.
Directions on how to play your game.
Rules of the game.
At least 20 math equations and inequalities.
¾ of the math problems need to have negative numbers.
An accurate answer key to your problems.
Rubric:
Name of the Game
Objective of the Game
Directions/Rules of the Game
At least 20 math problems
(equations)
¾ of the problems have negatives
Accurate answer key
TOTAL:
Points Possible
1
1
2
4
2
2
12
Points Earned