Decimals for whole numbers
Ex: What is decimal for “two million, two”?
Decimals for numbers between whole numbers
Ex: Which is larger 3.1 or 3.12?
Estimating by rounding up or rounding down
Ex: Round 4.356 up and down to tenths spot.
Answer: Up it is 4.4 Down it is 4.3
Estimating by rounding to the nearest
Ex: Round 4.356 to the nearest tenth.
Decimals for simple fractions
Know decimals for fractions that have a denominator of 2, 3, 4, 5, 10, 20, and 50.
Ex: What is decimal for 11/20?
Decimals for mixed numbers
Ex: What is the decimal for 3 1/4 ?
Ex: Where is -3.25 is located on the number line below?
Ex: What is larger -3.4 or -3.6?
Ex: Simplify 12/40?
Answer: Divide both numerator and denominator by 4 and get 3/10.
Multiplying by 10, 100, ...
Ex: 45.6 x 100 =
Answer: 4560 since decimal moves two times to the right.
Ex: Calculate 34
Answer: 34 = 3 · 3 · 3 · 3 = 81
Scientific notation for large numbers
Ex: What is 45,000 in scientific notation?
Answer: 4. 5 x 104
Multiplying by 1/10, 1/100, ...
Ex: What is 64.5 x 1/100
Answer: .645 since the decimal point moves twice to the left.
Percent of a quantity
Ex: What is 15% of 200?
From decimals to fractions and percents
Ex: What is the fraction and decimal for 12%?
Answer: Decimal is .12 and fraction is 12/100 = 3/25.
Ex: If 450 students took the test how many made a B?
Answer: 81 ( .18 x 450)
More powers of Ten
Ex: 56.47 x 104 =
Scientific notation for small numbers
Ex: What is .0045 written in scientific notation?
Answer: 4.5 x 10-3
Ex: Know how to use a ruler to measure in inches and centimeters.
Converting lengths AND Weight and Capacity in the customary system of measurement
Ex: Know the conversions given below:
1 mile = 5280 feet
1 inch = 2.54 cm
1 km ».62 miles
1 meter »39.37 inches
1 pound = 16 ounces
1 kilogram » 2.2 pounds
The Metric system of measurement
Ex: 4km = meters
Answer: 4000 (remember your chart: km hm dkm m dm cm mm)
Ex: Use your protractor to measure the given angle.
Answer: ÐABC is 45 degrees.
Kinds of Angles
Ex: What is an obtuse angle?
Answer: An angle that is between 90 and 180 degrees.
Ex: What is the area of a rectangle with sides of 9 cm and 5 cm?
Answer: 45 cm2
Ex: What is the volume of a cube that is 3 cm on each side?
Order of operations
Ex: 5 + 3 · 22 - (4 + 1)
Describing Patterns with variables
Ex: From the three given instances what is the general pattern?
4 x 1 = 4
5 x 1 = 5
8 x 1 = 8
Answer: a · 1 = a
Translating words to Algebraic expressions
Ex: Translate the expression “ the sum of a number and two divided by the product of the number and three”
Evaluating Algebraic Expressions
Ex: Evaluate 5n2 when n = 2
Answer: 20 since in 5 · 22 you do powers first
Parentheses or Brackets
Ex: Evaluate (3 + 2) (20 – (3 + 10)
Answer: 35 since you do inner most parentheses first
Ex: If I buy n tickets and y are sold what is my probability of winning?
Ex: Graph -2< n £4 on a number line
Zero and Opposites
Ex: -(-(-3)) =
Rules for adding positive and negative numbers
Ex: -5 + 3 =
Ex: How many degrees does the minute hand of a clock move in 1 minutes?
Answer: 6 degrees since 360/60 is 6.
Adding positive and negative fractions
Ex: 2/5 + 1/3 =
Answer: 11/15 (Remember to get a common denominator when adding)
Ex: If events A and B are mutually exclusive and P(A) = 30% and P(B) = 40%, what is
P(A or B)?
Commutative and Associative properties
Ex: Which is commutative and which is associative of the following:
4 + 3 = 3+ 4 (1+ 2) + 3 = 1 + (2 + 3)
Answer: Commutative Associative
Ex: What is the name of the polygon that has 8 sides?
Ex: If points A, B, C, and D are points in a straight line, what is AB if
AD = 10 cm
BC = 5 cm
CD = 2 cm
Answer: 3 cm
Two models for subtraction
Ex: If points A, B, C, and D are points in a straight line, AD – CD =
The slide model for subtraction
Ex: -6 -3 =
Solving a - x = b
Ex: 8 – n = 10
Counting and probability with overlap
Ex: Draw a Venn diagram that shows that 20 people play soccer, 10 play tennis, and 4 do both.
Angles and parallel lines
Ex: Know how to find the missing angles given any picture. Key words to know are parallel, perpendicular, ray, line, line segment, etc.
Ex: All angles in a quadrilateral add up to how many degrees?
Answer: 360 degrees
The triangle-sum property
Ex: All angles in a triangle add up to how many degrees?
Answer: 180 degrees
Ex: In which quadrant are the x and y values all negative?
Answer: Third (-,-)
Ex: Make a t-chart of three possible solutions to y = 2x + 1 and then graph it.
Ex: What happens to the graph of a figure when -3 is added to the x-coordiante and 2 is added to the y-coordiante?
Answer: The figure moves to the left 3 units and up 2 units.
Ex: If A’ is the reflection of A and the distance from A to the reflection line is 4 cm, AA’ =
Answer: 8 cm
Ex: The letter A has what type of line of symmetry?
Area model for multiplication
Ex: What is the area of a right triangle that has a base of 5 cm and a height of 8 cm?
Answer: 20 cm2
Volumes of rectangular solids
Ex: What is the volume of a cube that is 5 cm on each side?
Answer: 125 cm3
Multiplication of fractions
Ex: 6/7 x 7/9 =
Ex: What is the probability that it will rain three days in a row if the probability for rain every day this week is 70%? Assume that each day is independent from the day before.
Answer: 34.3% (.7 · .7 · .7)
Multiplication with negative numbers and zero
Ex: -5 · -2 · -1 =
Size changes - Expansions
Ex: What happens to the sides of ΔA’B’C’ if ΔABC is multiplied by 3?
Answer: The sides get three times longer.
Size changes - Contractions
Ex: What happens to the sides of ΔA’B’C’ if ΔABC is multiplied by ½ ?
Answer: The sides contract to ½ the original size.
Picturing Multiplication with negative numbers
Ex: What happens to ΔA’B’C’ if ΔABC is multiplied by -3?
Answer: The sides get three times longer and the figure rotates 180 degrees.