Mrs. Kolodnicki
Mrs. Camacho
Name:______Date:______
Unit 1: Integers
Vocabulary:Evaluate
Integer
Absolute Value
Additive Inverse / Topics:
Add & Subtract Integers
Multiply & Divide Integers
Compare & Order Integers
Rules & Tricks
For ADDING integers:
SSA-
DSS-
*This can also be helpful for
Multiplying & Dividing
------
For SUBTRACTING integers:
Change to ADDING first by
ADDING THE OPPOSITE / Examples:
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More examples can be found in your Interactive Notebook!
Practice Problems:
On February 28, from 9 a.m. until 2 p.m., the temperature rose fromF to F. What was the total increase in temperature during this time period?
Alyssa has $31 in her wallet. She pays $12 for lunch. Write an addition expression that represents this situation. Then solve.
The temperature drops 2 degrees per hour for 3 hours. Which
expression does not describe the change in temperature?
a.
b.
c.
d.
Which point has a coordinate with the greatest absolute value?
Evaluate the expressions below if a = 4, b = 7 and c = -5
1)b – (-4) 2) c + (-13) 3) 5abc 4)
Unit 2: Fractions & Decimals
Vocabulary:Fraction
Like & Unlike Fractions
Mixed Number
Improper Fraction
Complex Fraction
Decimal / Topics:
Adding & Subtracting Fraction
Multiplying & Dividing Fractions
Converting mixed numbers into improper fractions
All operations (+ - × ÷) with decimals
Rules & Tricks
For Adding or Subtracting fractions:
Create common denominators
(Butterfly method)
“Multiply A-Cross”
“If you try to divide the fish will FLIP!”
------
For adding and subtracting decimals- LINE UP decimal points
For multiplying, count up decimal places for your final answer
For dividing, move your decimal point the same number of places first, then bring it up and divide. / Examples:
=
------
1.25
× 8.6
More examples can be found in your Interactive Notebook!
Practice Problems:
For a party, Amber bought pounds of white grapes. Patrick bought pounds of red grapes. How many more pounds of grapes did Amber buy?Jonathan drove 132 miles in hours. What was his average speed in miles per hour?
A delivery came to Panera bread of
775.50 pounds of dough. Each
sandwich uses 0.25 pounds of dough
to make. How many sandwiches can
be made?
What fraction is between and ?
a. b. c. d.
Unit 3: Rational Numbers
Vocabulary:Rational Number
Terminating Decimal
Repeating Decimal
Bar Notation / Topics:
Changing from fractions, to decimals, to percents
Comparing/Ordering fractions & decimals
All operations with rational numbers
Rules & Tricks
For ADDING rational numbers:
SSA-
DSS-
*This can also be helpful for Multiplying & Dividing
------
Fractions mean Division!!
means 34 / Examples:
Change into a decimal
More examples can be found in your Interactive Notebook!
Practice Problems:
1)) 2) )It takes Allison hour to walk to the library mile away. What is her walking pace?
Mrs. Karacsony finished 75% of her holiday shopping, while Mrs. Kolodnicki
bought 7 out of the 10 gifts she needs and Mrs. Camacho completed of her
shopping. Order the amount of shopping that was completed in order from
least to greatest.
Which of the following rational numbers is
equivalent to a repeating decimal?
a. b. c. d.
Unit 4: Properties & Expressions
Vocabulary:Algebraic Expression
Variable
Constant
Coefficient
Equivalent Expressions
Like Terms
Linear
Commutative Property
Associative Property
Multiplicative/Additive Inverse
Multiplicative/Additive Identity / Topics:
Evaluating expressions using PEMDAS
Translating words to expressions
Combining like terms
Rules & Tricks
Know your key words:
Adding- sum, added to, total
Subtracting- difference, less than, subtracted from
Multiplication-product, times, double, per
Division-quotient, divided by, split, half
Circle or underline key terms to combine them.
Remember your Integer rules (SSA/DSS) / Examples:
Subtract 8 from 5 times a number
Simplify:
More examples can be found in your Interactive Notebook!
Practice Problems:
A rectangle has side lengths and .(a) Write an expression that represents the perimeter of the rectangle.
Express your answer in simplest form.
(b) Factor the expression you found in part (a).
Identify the terms in the expression –5x + 2yz – 8 ______
Identify the coefficients in the expression 8x – y + 6 – 8a ______
Identify the constants in the expression –5 + 9x + 3x2 –53 ______
Simplify:
(12– 4x) – (14 + 8x) –16x + 8x + 9x
To join the gym Amber must pay a $75 enrollment fee and $32 per month. Write an algebraic expression to represent the total cost of m months at the gym, including the enrollment fee.
(9 + 13) + 4 = 9 + (13 + 4) / 1 • 245 = 245
/ a + 0 = a
Unit 5: Factoring
Vocabulary:Distributive Property
Factoring / Topics:
Distributing expressions
Factoring expressions
Finding the GCF of two terms
Rules & Tricks
GCF: Use Prime factorization to break down terms into their prime factors. Then circle common terms.
18 + 12x
18 =
12x=
Factoring is the OPPOSITE of distributing!
5 (x+ 2) = / Examples:
Factor or Distribute:
More examples can be found in your Interactive Notebook!
Practice Problems:
Find the GCF of each pair18, 66 / What is the GCF of and ?
a. 9
b.
c.
d.
Simplify the following expression: 4a + 6b – 5a + 3b
- 8ab
- –a + 9b
- 9a + 9b
- 10a – 2b
Patrick got $50 for his birthday and plans to earn $x each week for the next 5 weeks. Write an expression to represent his total amount of money at the end of the 5 weeks. Factor your expression.
Use the Distributive Property to
(–8x– 3)6 = ______/ Rewrite each expression
3(12 – 4x) = ______
Which expression is equivalent to
a.
b.
c.
d. / Factor
Unit 6: Equations
Vocabulary:Equation
Solution / Topics:
Solving 1 and 2 step equations
Translating words into equations.
Solve equations with rational numbers.
Rules & Tricks
LOOK and see what operations are happening first, then do the OPPOSITE!
5 + y = 7
4x = 24
Instead of PEMDAS, use SADMEP to work backwards to solve for your variable.
Do adding or subtracting first
Then multiplying and dividing! / Examples:
Solve:
What is the solution to the equation ?
a.
b.
c.
d.
More examples can be found in your Interactive Notebook!
Practice Problems:
Solve for x:Vinny wants to join a new gym. There is an initiation fee of $29.99 and each month of membership costs $14.50. If Vinny pays $160.49, write and solve an equation to determine how long his membership will last.
Five more than twice a number is equal to 19. What is the number?
Solve:
- x = –15
- x = –8
- x = –19
- x = –9
What is the equation for the following set of data:
a.
b.
c.
d.
Unit 7: Inequalities
Vocabulary:Inequality / Topics:
Solving 1 and 2 step inequalities
Translating words into inequalities.
Solve inequalities with rational numbers.
Rules & Tricks
LOOK and see what operations are happening first, then do the OPPOSITE!
When dividing or multiplying by a negative number, the inequality flips!
Ex: / Examples:
The basketball team needs to score at least 82 points this season to set a new school record. They have already scored 37 points. Write an inequality to represent this situation, solve the inequality, and then graph the solution on the number line.
More examples can be found in your Interactive Notebook!
Practice Problems:
Solve for x: 6(x – 4) < 24Which inequality is shown on the number line below?
Graph the solution set of the inequality ?
What is the solution of 4x + 7 < 35?
a. x < 28
b. x24
c. x < 42
d. x < 7
Unit 8: Ratios
Vocabulary:Ratio
Rate
Proportion
Constant of Proportionality
Unit Rate
Direct Variation / Topics:
Recognizing a proportional relationship on a graph, in a table, and with an equation.
Setting up and solving a proportion
Finding unit rate with rational numbers and integers.
Rules & Tricks
Proportions:
Graphs: Straight line, starting at the origin
Tables: Divide y by x to see if all of the constants are equal.
x / y
2 / 3
8 / 12
Equations: y = kx, where k is the constant of proportionality. / Examples:
Olivia read 22 pages during a 30-minute study hall. At this rate, how many pages would she read in 45 minutes?
Josh can jog miles in hours. Find his speed in miles per hour.
More examples can be found in your Interactive Notebook!
Practice Problems:
A map has a scale of 1.5 inches : 250 miles. If the distance from NewYork City to Los Angeles is 16.5 inches on the map, what is the actual
distance between the cities?
What is the unit price if 8 cans of corn cost $10.80?
Which table shows a proportional relationship?
What is the constant of proportionality?
Unit 9: Percents
Vocabulary:Percent
Tax
Discount
Interest / Topics:
Finding a percent of a number
Calculating tax, discount, total bill
Calculating interest, and final balance in a bank account
Make predictions based on percents given.
Rules & Tricks
Percent Proportions:
_____ = ______
Another way…
I bought a $25 sweater, but it was on sale for 15% off. What is the new price? / Examples:
A trampoline costs $220 and the sales tax is 6.25%. What is the total cost of the trampoline?
What is the sales price of a $128 bicycle with a discount of 60%?
More examples can be found in your Interactive Notebook!
Practice Problems:
Based on these data, predict how many outof 1,800 students would choose sandwiches.
A video game that normally sells for $80 is on sale for $68.
What is the percent of discount for the sale price?
Pat bought 5 CD’s at $12 each. He had a coupon for 10% off. The sales tax was 8%. Find the total cost of the 5 CD’s after the discount and sales tax are applied.
Jonathan invests $389 into a savings account that earns interest 3.4% simple interest. He plans on leaving the money in the account for 8 years. What will the final balance of the savings account be after 8 years?
Unit 10: Probability
Vocabulary:Probability
Experimental Probability
Theoretical Probability
Sample Space
Counting Principal
Permutation / Topics:
Finding probability of one event and multiple events simultaneously.
Predict based on probability
Draw sample space or tree diagram representing a situation.
Determining independent and dependent events.
Rules & Tricks
Independent Events:
Dependent Events:
/ Examples:
Draw a tree diagram for all the possibilities of spinning one spinner then the other.
P(even number, blue): ______
A bag contains 3 red and 4 blue marbles. What is the probability of drawing 2 red marbles in a row without replacement?
More examples can be found in your Interactive Notebook!
Practice Problems:
What is the probability of tossing tails on a nickel and tossing an even numberon a number cube with faces numbered 1 through 6?If the probability that it will rain on Thursday is ,what is the probability that it will not rain on Thursday?
What is the experimental probability of summer being someone’sfavorite season? Express as a fraction in simplest form.
For a class project, Alyssa counted the people that entered a hardware store near
her school. On the first day, 8 out of 12 people were men.
a) What is the experimental probability that a person entering the hardware
store will be a man?
b) If 315 people enter the hardware store, how many people
should Pamela expect to be men?
A deli has five types of meat, two types of cheese, and three types of bread. How many different sandwiches, consisting of one type of meat, one type of cheese, and one type of bread, does the deli serve?
Unit 11: Statistics
Vocabulary:Mean, Median, Mode, Range
Interquartile Range
Mean Absolute Deviation
Biased/Unbiased / Topics:
Evaluating data based on bias
Calculating mean, median, mode and range, IQR, and MAD.
Explaining when to use different measures of center (mean, median, mode)
Constructing a box and whisker plot.
Comparing 2 sets of data.
Rules & Tricks
Mean Absolute Deviation!
Step 1: Take the mean
Step 2: Subtract each number from the mean. (all answers need to be positive)
Step 3: Take the mean of those answers / Examples:
The number of hours five boys spent at baseball practice are 3, 6, 3, 7, and 3.
- Calculate the mean. ______
- Calculate the mean absolute deviation. ______
More examples can be found in your Interactive Notebook!
Practice Problems:
Which of the following represents two dependent events?a. drawing a card from a deck, not replacing it, and drawing another card
b. rolling a number cube and flipping a coin
c. drawing a card from a deck, replacing it, and drawing another card
d. rolling two numbers cubes
Booker has a bag of marbles. There are 10 blue marbles, 6 yellow marbles,
and 4 red marbles. Booker reaches into the bag without looking and picks
a marble. What is the probability he picks a red marble?
a. b. c. d.
The table shows the maintenance costs for Dylan’s car over the past 5 years.
Which measure of central tendency would most accurately
display the annual cost of maintaining Dylan’s car during
this five year period?
a. Mean
b. Mode
c. Median
d. Range
Allison asked 25 seventh grade students what their favorite band was.
Would this be a valid representation of the school’s entire student population?
a. Yes, because she allowed the students to choose any band.
b. No, because she surveyed students and not teachers.
c. No, because she only surveyed 25 students in the seventh grade. She would need to survey more students, and students from other grades.
d. Yes, she surveyed seventh grade students and they are a valid representation of
other grades.
Unit 12: Geometry
Vocabulary:Scale Factor
Area
Perimeter
Surface Area
Volume / Topics:
Using a scale to determine a new size.
Calculating area, perimeter, surface area and volume of typical figures and irregular figures.
Rules & Tricks
Don’t forget to use your formulas!!
Real Life examples:
Perimeter:
Area:
Volume:
Surface Area: / Examples:
Calculate the area and perimeter of the parallelogram. The figures are not drawn to scale.
Area:
Perimeter:
More examples can be found in your Interactive Notebook!
Practice Problems:
Alyssa made a model of the solar system. In the model, a circle with a diameter of 6 centimeters represents the orbit of Neptune. What is the circumference of the circle to the nearest hundredth?If the area of a circle is expressed as 64 ft2, what is the radius?
How many blocks were needed to make
the rectangular prism below?
Olivia would like to wrap a gift box for her mother. The box is a
rectangular prism with edges measuring 16 inches, 8 inches, and 4 inches.
What is the surface area of the gift box?
Unit 13: Geometry II
Vocabulary:Complementary
Supplementary
Vertical Angles
Compound Area
Shaded Area / Topics:
Identifying and solving for complementary, supplementary and vertical angles.
Calculating compound and shaded areas.
Constructing triangles from given descriptions.
Rules & Tricks
Area of Compound Figure
Find the areas and
______them!
Area of Shaded Area
Find the areas and
______them! / Examples:
Line A intersects Line B. If and ,
find:
a. the value of x ______
b. The measure of angle 1______
c. The measure of angle 2______
More examples can be found in your Interactive Notebook!
Practice Problems:
Find the area of the figure below.Two complementary angles are in the ratio .
What is the measure of the smaller angle?
Which two angle measures are complementary?
a.
b.
c.
d.
In the figure shown, line x is parallel to line y.
What type of angles are <1 and <3?
Calculate the area of the shaded region.