1. Sixth Grade Math State Test Review
Ms. Mikalauskas - St. Ann School

2. Topic 1: Ratios and Proportional Relationships
Standards: 6.RP.1, 6.RP.2 & 6.RP.3
Ratio Tables
Ratio Relationships between 2 quantities
Equivalent Ratios
Unit Rate, Rate Unit, Rate
Percent of quantity using rate per 100
Ratio reasoning to convert measurement units

3. What is a ratio?
A relationship in which for every x units of one quantity there are y units of another quantity
-Or- How one quantity compares to another quantity
Can be written as
x to y
x:y
Fraction: x/y

4. Ratio Examples
For every 3 girls at the concert there is 1 boy; What is the ratio of girls to boys?
3 to 1; 3:1; 3/1
What is the ratio of boys to girls?
1 to 3; 1:3; 1/3
For every 4 red apples there is 2 green
4 to 2; 4:2; 4/2

5. Ratio Tables Ratio tables can be used to find equivalent ratios.
Red Apples
Green Apples 4 2 8 12 6 16 20 10
Ratio tables can be used to find equivalent ratios.
An equivalent ratio expresses the same relationship to a given ratio.
It can be found by dividing or multiplying both numbers by the same number
x 2
x 2
x 3
x 3
x 4
x 4
x 5
x 5

6. Equivalent Ratio Examples
To make equivalent ratios you can make ratio tables or multiply or divide the given ratio by the same number
Ex: 4:16
Multiply both numbers by 2 (4x2 and 16x2) Equivalent ratio= 8:32
Divide both numbers by 2 (4/2 and 16/2) Equivalent ratio= 2:8

7. Comparing Ratios
You can use ratio tables to compare ratios when one of the corresponding terms are the same
Example: Who uses more sugar in their recipe?
Frank Glen
Flour tbs 2 4 6
Sugar tbs 5 10 15
Flour tbs 3 6 9
Sugar tbs 7 14 21
Frank uses more sugar in his recipe because every time there are 6 tbs of flour he uses 15 tbs of sugar while Glen uses 14tbs.

8. What is a Rate?
A rate is a special type of ratio that compares the quantities with unlike units of measure.
Example: A racecar can travel 10 km in 3 minIf the race car continues to travel at the same rate, how long will it take to travel 25 km.
Solve by making a ratio table until 25 km is reached.
You can also solve like a proportion . What must we multiply 10 by to get 25? Whatever you do to the top you do to the bottom!
10 km km
X = 3 x 3.5 = 7 ½ minutes km
Minutes 5
1 ½ 10 3 15
4 ½ 20 6 25
7 ½
X 2.5
3 mins X 2.5 = x mins

9. Rate Examples: Find the Value of X and missing values
Miles 45 90
Hours 4 x
Miles 45
135
Hours 4 x
Fish 16 48
Bowls 2 x
Pages 9
Minutes 18 1 10 15
Miles 25
125
Gallons 3 5 12
Look for relationships between each quantity. There is always half the amount of pages per minute. How does miles compare to gas?

10. Unit Rates, Rate Units, and RAte
Rate- One quantity per another quantity
$10 for every 4 packs of pepsi
Unit Rate- The value of the ratio
$2.50
Rate Unit- Word form of your two quantities
dollars/packs of Pepsi

11. Rate unit: Miles/Hour

12. Using Unit Rates to make Comparisons
Example: Ethan swam 11 laps in the pool in 8 minutes. Austin swam 7 laps in the pool in 5 minutes. Which boy swam at a faster rate?
You must find out how many laps they can swim with a denominator of 1
7 laps /
5 minutes / 5 =
Austin can swim 1.4 laps in 1 minute.
11 laps /
8 minutes / 8 =
Ethan can swim laps in 1 minute
*we divide by 8 to get a denominator of 1
Austin swims at a faster rate.

13. Unit Prices A unit price is a unit rate that gives the price of 1 item
Example: A mega-lunch special serves 3 tacos for $2.40; a extra-lunch serves 4 tacos for $3.40. Which has a better value?
Divide the dollar amounts by the amount of tacos to get the price for one taco
Mega: $2.40 / 3 = .80 per taco < Better value
Extra: $3.40 / 4 = .85 per taco

14. Constants
If an object is moving at a constant rate of speed for a certain amount of time, it is possible to find how far the object went by multiplying the rate and the time. In mathematical language, we say, 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞 = 𝐫𝐚𝐭𝐞 x 𝐭𝐢𝐦𝐞.
Examples of expression
Distance: Miles, meters, yards, kilometers, feet
Rate: miles per hour, km/minute, feet per second (distance per time)
Time: Hours, seconds, etc.

15. Example
I drove my car on cruise control at 65 miles per hour for 3 hours without stopping. How far did I go?
STEP 1: WRITE YOUR FORMULA!
Distance= rate x time
STEP 2: PLUG IN WHAT YOU KNOW
Distance = 65 x 3
STEP 3: SOLVE
Distance = 195 miles

16. Converting Units
Conversion factor- rate that compares equivalent measures
Dimensional analysis- convert measures by measurement units when you multiply by a conversion factor
Example: how many inches is a 4.5ft sidewalk?
4.5 ft x 12in.
1 1ft = 54 inches
Example: There is 15 gallons of water on a camping trip. How many quarts of water are there? (4qt= 1 gal)
15 gal x 4 qt.
1 1 gal = 60 quarts

17. Common Conversions
There will be a reference sheet with some of these conversions for you. However, it does not hurt to be familiar with them.

19. HOW TO CONVERT
When converting draw an arrow from what you have to what you are going to.
The amount of columns you count is the amount of times you move your decimal.
Example: meters converted into:
Centimeters (2 columns to the right of meters) - move decimal twice to the right = cm
Kilometers (3 columns to the left of meters) - move decimal three times to the left = km
Example 2: 48 centigrams
Kilograms (5 columns to the left of centi) - move decimal 5 times to the left =
Milligrams (1 column to the right of centi) - move decimal once to the right = 480 mg

20. Topic 2: Percentages
A rate in which the first term is compared to 100. The percent is the number of hundredths that represents the part of the whole

21. Example
STEP 1: WRITE YOUR FORMULA!
STEP 2: Plug in what you know
Part 80%
64, %
STEP 3: Cross-Multiply and Solve
100 x = 80 x 64,000
100 x = 5,120,000
X = 51,200 = =

22. Writing Percents, decimals, and Fractions

23. Changing a Fraction To a Decimal

24. Changing a Percent to a Decimal

25. Changing a Percent to a Fraction

26. Change a Fraction into a Percent

27. Topic 3: Fractions Adding Subtracting Multiply Dividing
Standards: 6.NS.1
Adding
Subtracting
Multiply
Dividing
Equivalent Fractions
Simplifying
GCF & LCM (6.NS.2, 6.NS.3, & 6.NS.4)

28. Least Common Multiple
Least common multiples are used to find the Least common denominator in order to solve fraction addition and subtraction problems

29. Greatest Common FActor
GCF is used when simplifying fractions

30. Adding and Subtracting Fractions
Least Common Multiple: 3 5
4 | 6|
STEP 1: Find the LCD
STEP 2: Stack Fractions and convert to LCD
STEP 3: Add or subtract numerators ONLY
STEP 4: Denominator stays the same
STEP 5: Reduce Fraction + 4 6 1 1 4
x 3 12 3 9 + 6
x 3 12 10
Greatest Common Factor: 12
10 |
12 |
10 / 2 5
12 / 2 = 6

31. Multiplying Fractions
STEP 1: Put any whole numbers over 1
STEP 2: Multiply the numerators
STEP 3: Multiply the denominators
STEP 4: Simplify using the GCF

32. Mixed Numbers -> Improper Fractions

33. Improper Fractions -> Mixed Numbers

34. Multiplying Mixed Numbers
STEP 1: Change Mixed numbers into improper fractions
STEP 2: Multiply numerators and denominators
STEP 3: Change improper fraction to mixed number
STEP 4: Simplify

35. Dividing Fractions STEP 1: Keep the first
STEP 2: Change division to multiplication
STEP 3: Flip the second fraction
STEP 4: Multiply
STEP 5: Simplify

36. Dividing Fractions with Whole Numbers

37. Topic 4: Decimals Adding and subtracting Multiplying Dividing
Standards: Computing multi-digit numbers 6.NS.2, 6.NS.3, & 6.NS.4
Adding and subtracting
Multiplying
Dividing

38. Adding and Subtracting Decimals

39. Multiplying Decimals

40. Dividing Decimals

41. Topic 5: Integers Rational Numbers Positive and Negative Numbers
Standards: 6.NS.5, 6.NS.6, 6.NS.7 & 6.NS.8
Rational Numbers
Positive and Negative Numbers
Number Lines
Order
Absolute Value

42. Rational Numbers and their opposites
Given a nonzero number, 𝑎, on a number line, the opposite of 𝑎, labeled −𝑎, is the number such that 0 is in between and the distance between 0 and 𝑎 is equal to the distance between 0 and −𝑎
The opposite of 0 is 0

43. Positive and Negative Number Examples
Gain
Added
Above sea level
Deposit (Money ^)
Temperature
Negative
Loss
Debt
Below sea level
Withdrew (Money v)
Temperature

44. Number Lines
Not all number lines increase or decrease by intervals of one
Follow these steps to correctly label number lines:

45. Integer order
Listing numbers in least to greatest or greatest to least can be found by using a number line.
Order from least to greatest: A, E, D, B, C
Order from greatest to least: C, B, D, E, A

46. Absolute Value Always positive Explains a numbers distance from zero
Written as |x|

47. Comparing Absolute Value
Change to value first
|7| = |-7|
7 = 7
|-6| > |-4|
6 > 4
|-3| > |0|
3 > 0
-|-2| < |2|
-2 < 2
|1| < -|-5|
1 < -5

48. Topic 6: Graphing on the Coordinate Plane
Quadrants
X and y Axis
Plotting
Locating

50. Axis
The x-axis goes left to right across the coordinate plane (horizontal)
The y-axis goes up and down the coordinate plane (vertical)
Coordinates are always plotted (x,y) (*alphabetical)
Start at origin - move along x and then move along y

51. Example

52. Topic 7: Order of Operations
LEFT TO RIGHT
Used when solving multi-step problems
LEFT TO RIGHT
LEFT TO RIGHT

53. Topic 8: Properties Associative Property. 5 + (2 + 4) = (5 + 2) + 4.
Distributive Property. 6(3 + 5) = (6 x 3) + (6 x 5)
Multiplicative Identity Property. 34 x 1 = 34.
Additive Identity Property = 95.
Commutative Property =
Zero Property of Multiplication. 19 x 0 = 0.

54. Associative Property Addition:
Parenthesis can move without affecting the outcome of your problem
Multiplication:
Parenthesis can move without affecting the outcome of your problem

55. Distributive Property

56. Commutative Property
The order may change when only one operation is present and the outcome will not change.

57. Topic 9: Exponents Additional Rules: 4 = 4
Anything to the power of zero = 1
Anything to the power of 1 is itself
4 = 4 1

58. Topic 9: Word Problems Choosing Operations Step-by-Step
Write out your answer with appropriate units
Underline the question your are solving for
SHOW ALL WORK!

59. Topic 10: Algebraic Expressions
Standards: 6.EE.1-6.EE.9
Writing expressions
Using substitutions to solve for unknown variables
Combining like terms
Evaluating Expressions

60. Definitions Term- separated by addition or subtraction
Coefficient- Number before a variable
Variable- Any unknown number represented by a letter
Constant- A number that is not affected by a variable

62. Writing Algebraic Expressions
Use math key words to determine the correct operation
Use the variable given in the problem
Write as an algebraic expression
Example: Miss M. has 5 less pencils (p) than Mrs. Brass. Write an expression to show how many pencils Ms. M has.
p-5

63. More Examples

64. Using Substitution

65. What is a “Like Term”?

66. Combining Like Terms

67. Combining Like Terms - Example:

68. Combining Like Terms - Example:

69. Topic 11: Geometry
Shapes
Perimeter
Area
Volume

70. Perimeter of Shapes
The length of it’s outside

71. Area of A Rectangle

72. Area of Parallelograms

73. Rhombus

75. Finding area on a coordinate plane
In order to find the area of an object on a coordinate plane- a base of the object must line up with the grid lines.
If it does not, follow these steps:
Connect points to form a rectangle around the object.
Find area of the shapes that were formed and subtract
Giant rectangle Area
Add areas of blue, green, and orange triangles
Subtract to get area of the inside object

77. Topic 12: Statistic Variability and Distributions
Standards: 6.SP.1, 6.SP.2,6.SP.3, 6.RP.4 & 6.RP.5
When given a list of numbers you can find the following:
Mean (Average)
Median (Middle)
Mode (Most common)
Range (Greatest – Least)
Distributions

82. Box Plots
A box plot is a graph that is used to summarize a data distribution
A box plot is a graph made using the following five numbers: the smallest value in the data set, the lower quartile, the median, the upper quartile, and the largest value in the data set.
To make a box plot:
Find the median of all of the data.
Find Quartile 1: the median of the bottom half of the data
Find Quartile 3: the median of the top half of the data
Draw a number line, and then draw a box that goes from Q1 to Q3.
Draw a vertical line in the box at the value of the median.
Draw a line segment connecting the minimum value to the box and a line segment that connects the maximum value to the box.

83. Example: “Box and Whiskers”
The mean daily temperatures in degrees Fahrenheit for the month of February for a certain city are as follows: 𝟒, 𝟏𝟏, 𝟏𝟒, 𝟏𝟓, 𝟏𝟕, 𝟐𝟎, 𝟑𝟎, 𝟐𝟑, 𝟐𝟎, 𝟑𝟓, 𝟑𝟓, 𝟑𝟏, 𝟑𝟒, 𝟐𝟑, 𝟏𝟓, 𝟏𝟗, 𝟑𝟗, 𝟐𝟐, 𝟏𝟓, 𝟏𝟓, 𝟏𝟗, 𝟑𝟗, 𝟐𝟐, 𝟐𝟑, 𝟐𝟗, 𝟐𝟔, 𝟐𝟗, 𝟐𝟗
STEP 1: Find median by putting number in order: 4, 11, 14, 15, 15, 15, 15, 17, 19, 19, 20, 20, 22, 22, 23, 23, 23, 26, 29, 29, 29, 30, 31, 34, 35, 35, 39, 39 = 22.5
STEP 2: Find median for bottom half (Q1) 4, 11, 14, 15, 15, 15, 15, 17, 19, 19, 20, 20, = 16
STEP 3: Find median for bottom half (Q3) 23, 23, 23, 26, 29, 29, 29, 30, 31, 34, 35, 35, 39, 39= 29.5
STEP 4: Lowest and highest : 4 and 39
Median
Q3 Median
Q1 Median
Highest #
Lowest #