A whole number is divisible by another number if the remainder is 0 when the first is divided by the second. A whole number is even if it is divisible by 2. A whole number is odd if it is not divisible by 2.
Rule
Examples
A whole number is divisible by: - 2 if the one s digit is divisible by 2.
2, 4, 6, 8, 10, 12,…
- 3 if the sum of the digits is divisible by 3.
3, 6, 9, 12, 15, 18, 21, 24, …
- 4 if the last two digits are divisible by 4.
4, 8, 12, …, 104, 108, 112, …
- 5 if the ones digit is 0 or 5.
5, 10, 15, 20, 25, 30, 35, …
- 6 if the number is divisible by both 2 and 3.
6, 12, 18, 24, 30, 36,…
- 9 if the sum of the digits is divisible by 9.
9, 18, 27, 36, 45, …
- 10 if the ones digit is 0.
10, 20, 30, 40, 50, …
Directions: Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd. 1. 80
2. 93
3. 324
4. 81
5. 23,512
6. 48
7. 45
8. 3,579
9. 7,000
10. 24,690
A sequence is a list of numbers in a specific order that follows a pattern or rule. Example: 41, 37, 33, 29,… The pattern is subtract by 4, the next two numbers are 25 and 21. Directions: Describe each pattern, then find the next two numbers in the sequence. 1. 72, 77, 82, 87, … 2. 3, 6, 12, 24,… 3. 32, 29, 26, 23,… 4. 1, ½, ¼, 1/8, …
addition:
subtraction: multiplication: division:
altogether total number sum in all perimeter combined how many spend/spent joined increase
left difference remained how much more how many more...than how much change less change "er" words decrease
twice product each area times per every
Rounding: about estimate
separate half equal number divided something into groups quotient share something equally per - in question a piece - in question
Fraction to Decimal conversion Fractions
Decimals
½
.50
1/
3
.33
2/
3
.66
¼
.25
¾
.75
1/
5
.20
2/
5
.40
3/
5
.60
4/
5
.80
1/
8
.125
3/
8
.375
5/
8
.625
1/
10
.10
3/
10
7/
10
9/
10
An angle is a figure formed by two rays with the same endpoint (vertex). An acute angle is any angle that measures less than 90°.
An obtuse angle is an angle measuring between 90°and 180°. Examples of obtuse angles.
Examples of acute angles. 135°
88°
33°
18°
7°
2. 60 °
3. 30°
4. 45 °
110°
Directions: Create the following obtuse angles using a protractor.
Directions: Use a protractor to create the following acute angles. 1. 10°
174°
1. 120°
2. 150 °
3. 135°
4. 175 °
Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees.
Two angles are called supplementary angles if the sum of their degree measurements equals 180°(a straight angle).
.30
Directions: Find the complementary angle of each of the following angles.
Directions: Find the supplementary angle of each of the following angles.
.70
1. 20°
1. 57 °
2. 35 °
2. 150 °
3. 83 °
3. 45 °
4. 64 °
4. 63 °
5. 45 °
5. 172 °
6. 16 °
6. 90 °
.90
139°
41°
Note that these two angles can be "pasted" together to form a straight line!
41°
139°
The measures of central tendency are the numerical values used to describe the overall clustering of data in a set, or the overall “average” of a set of data. Mean is the arithmetic average of a set of numbers. Mode is the score or data point found most often in a set of numbers. Median is the middle point of a set of rank-ordered numbers where half of the numbers are above the median and half are below it. The range is calculated as the difference between the highest and lowest values in a set of numbers. An outlier is a value that is much higher or much lower than the other values in a set of data. range = 509 – 5 = 504 Data set: 5, 36, 36, 97, 120, 247, 509
Mode occurs most often
Median
Mean (average)
the middle value
5 + 36 + 36 + 97 + 120 + 247 + 509 = 1050 1050 ÷ 7 = 150
Directions: Circle the outliers in each set of data. Complete the table below.
Data
Mean
Mean (not including outlier)
6, 8, 5, 7, 6, 4, 27 19, 2, 4, 2, 7, 8 1, 13, 1, 4, 6 3, 16, 2, 2, 0, 1, 4
Median
Median (not including outlier)
Mode
Range
Range (not including outlier)
1 yard = 3 feet
Distance
1 yard = 36 inches 1 foot = 12 inches
Inches – Feet – Yards – Miles
Capacity (The amount of space that can fill a container. Capacity usually refers to fluid measures.)
Ounces – Cups – Pints – Quarts – Gallons
Weight
Ex. 24 feet = _8_ yards ( 24 ÷ 3 = 8 ) 2 yards = _72__ inches ( 2 x 36 = 72 )
Directions: Convert the following measurements to the appropriate units. 1. 12 feet = ____ yards
Ounces – Pounds – Tons Multiply when converting to a smaller unit. Divide when converting to a larger unit.
2. 48 inches = _____ yards 3. 24 inches = ____ feet 4. 9 feet = _____ yards
(Note: A fluid ounce is different from the ounce that measures weight.)
5. 3 yards = ____ inches 6. 7 yards = ____ feet
1 gallon = 4 quarts
1 gallon = 8 pints
1 gallon = 16 cups
1 quart = 2 pints
1 quart = 4 cups
1 pint = 2 cups
1 cup = 8 ounces
1 pint = 16 ounces
Silver dollar 1 oz
Box of sugar
1 pound (lb) = 16 ounces (oz) 2000 pounds (lbs) = 1 ton (T)
Ex. 2 gallon = _32_ cups ( 2 x 16 = 32 ) 12 pints = _6_ quarts (12 ÷ 2 = 6 )
1 lb
Pick-up truck: 1 T
Ex. 2 tons = _32_ pounds ( 2 x 1000 = ) 32 ounces = _2_ pounds (32 ÷ 16 = 2 )
Directions: Convert the following measurements to the appropriate units.
Directions: Convert the following measurements to the appropriate units.
1. 22 cups = ____ pints
1. 3 lbs = ____ oz
2. 3 gallons = ___ pints
2. 3 T = ___ lbs
3. 36 quarts = ___ gallons
3. 64 oz = ___ lbs
4. 8 cups = ___ quarts
4. 8 oz = ___ lbs
5. 5 pints = ___ ounces
5. 5000 lbs = ___ T
6. 48 ounces = ___ quarts
6. 4 lbs = ___ oz
The greatest common factor is the greatest number that is a factor of two or more numbers.
Least common multiple is the smallest quantity that is divisible by two or more given quantities without a remainder.
Ex.: GCF (8,28)= 4
Ex. LCM(5, 7) = 35
8: (1,2,4,8)
5: 5, 10, 15, 20, 25, 30, 35, …
28: (1,2,4,7,14,28)
7: 7, 14, 21, 28, 35, 42, 49,…
Directions: Determine the GCF of the following groups of numbers. 1. GCF(14, 40) 2. GCF(15, 45)
Directions: Determine the LCM of the following groups of numbers. 1. LCM(3, 8) 2. LCM(12, 15)
3. GCF(21, 9)
3. LCM(7, 5)
4. GCF(12, 52)
4. LCM(6, 18)
5. GCF(18, 30)
5. LCM(16, 48)
6. GCF(25, 60)
6. LCM(4, 9)
A prime number is a natural number that has exactly two distinct factors: 1 and itself.
Prime factorization is the breaking down of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer.
Ex.: 2, 3, 5, 7, 11, 13, 17, 19
Ex.: 24
A composite number is a positive integer which has more than two factors.
2 × 12 2×3×4
Ex.: 4, 6, 8, 9, 10, 12, 14, 15
2 × 3 × 2 × 2 = 23 × 3
Directions: Determine if the numbers below are prime or composite.
Directions: Create a prime factorization tree for the given numbers below.
1. 31
2. 61
3. 51
4. 73
5. 63
6. 53
1. 34
2. 98
3. 57
4. 54
5. 45
6. 56
Scatter plot is a graph of data points, usually from an experiment, that is used to observe the relationship between two variables. If a line is drawn from left to right between the points it will indicate if the scatter plot has a positive correlation (positive slope), negative correlation (negative slope), or no correlation (points all over the board).
The slope of a line can be determined by its visual appearance. Directions: Draw each of the lines below and label them by slope and description. Line a is has a positive slope. It is increasing from left to right. Line b has a negative slope. It is decreasing from left to right. Line c has a zero slope. It is a horizontal line. Line d has an undefined slope. It is a vertical line.
Directions: Label each of the scatter plots below as having a positive correlation, negative correlation, or no correlation.
1.
2.
Surface area of a geometric solid is the sum of the areas of the faces and/or any curved surfaces of the figure that create the geometric solid. 3. 4.
6. 5.
Directions: Draw each of the cubes below shading and labeling the corresponding sides.