Download M6.2.3 - Use variables to write equations using models

6th Grade Math
Essential Skills Study Guide
Here is a great web site: http://www.aaamath.com/index.html
This site has explanations and practice for many skills in this study guide.
M6.1.1 – Compare decimals, fractions and percents; convert fraction to decimals
and percents
Put these in order least to greatest:
4
, 65%, 0.42
5
To convert fractions to decimals, divide the numerator by the denominator.
To convert decimals to percents, multiply by 100 OR move the decimal two places to the
right.
To convert percents to decimals, divide by 100 OR move the decimal two places to the
left.
To convert decimals to fractions, write the number as you would say it with the correct
denominator and simplify.
0.42 =
42
21
=
100
50
4
= 0.80
5
65% = 0.65
In order - 0.42, 65%,
4
5
M6.1.2 – Add, subtract, multiply and divide decimals
To add or subtract decimals, line up the decimals and add or subtract as whole numbers.
To multiply decimals, line up numbers to the right, multiply as whole numbers, count the
decimal places in the factors and put that many decimal places in the product.
To divide decimals, move the decimal in the divisor all the way to the right, move the
decimal in the dividend the same number of places and divide as a whole number. Be
sure your decimal in the quotient is above the new position in the dividend.
M6.1.3 - Convert metrics within the same system
General rule - To convert from larger units (km, kL, kg) to the next smaller unit (m, L, g),
multiply by 1000. To convert from smaller to larger, divide by 1000.
kilometers (km)
kiloliters (kL)
kilograms (kg)
 x 1000 
  1000 
meters (m)
liters (L)
grams (g)
Millimeters to centimeters - Divide by 10
Centimeters to millimeters - Multiply by 10
Centimeters to meters - Divide by 100
Meters to centimeters - multiply by 100
 x 1000  millimeters (mm)
milliliters (mL)
  1000  milligrams (mg)
M6.1.4 - Add, subtract, multiply fractions with unlike denominators
Before you can add or subtract fractions, you must have a common denominator. To find
the least common denominator (LCD) of the two fractions, find the least common
multiple (LCM) of the two denominators by either listing multiples of the denominators
or using prime factorization (see M6.2.1).
Example - On Monday Dylan picked nine-tenths of a pound of strawberries. On Tuesday
he picked one-fifth of a pound of strawberries. What was the total weight of the
strawberries Dylan picked?
Number sentence -
9
1
+
10
5
The LCD would be 10, so you would rewrite the sentence as
9
2
11
1
+
=
or 1 .
10 10 10
10
To multiply fractions, multiply the numerators together, then the nominators together,
then simplify.
2x3=6
2 3 6
Example: x =
5 10 50
5x10=50
=
3
25
Find simplest form by dividing both the
numerator and denominator by the
greatest common factor (GCF)
M6.2.1 - Write the prime factorization of a number using exponents.
Prime factorization is writing a number as the product of its prime factors.
Example: Find the prime factorization of 12.
12
/ \
2 6
/ \
2 3
So, the prime factorization of 12 would be 2x2x3, or 22x3.
M6.2.2 - Write ratios and solve problems using ratios
Ratios tell how one number is related to another number.
A ratio may be written as A:B or A/B or by the phrase "A to B".
A ratio of 1:5 says that the second number is five times as large as the first.
The following steps will allow determination of a number when one number and the ratio
between the numbers is given.
Example: Determine the value of B if A=6 and the ratio of A:B = 2:5



Determine how many times the number A is divisible by the corresponding
portion of the ratio. (6/2=3)
Multiply this number by the portion of the ratio representing B (3*5=15)
Therefore if the ratio of A:B is 2:5 and A=6 then B=15
M6.2.3 - Use variables to write equations using models
An equation is a mathematical statement that has two expressions separated by an equal
sign. The expression on the left side of the equal sign has the same value as the
expression on the right side.
One or both of the expressions may contain variables. Solving an equation means
manipulating the expressions and finding the value of the variables.
An example might be:x = 4+8
to solve this equation we would add 4 and 8 and find that x = 12.
To write an equation from a model:
=x
=1
The equation for this model would be x + 3 = 4.
M6.2.4 - Recognize, continue and write the rule for geometric and number patterns.
How to find a missing number in a sequence



Determine if the order of numbers is ascending (getting larger in value) or
descending (becoming smaller in value).
Find the difference between numbers that are next to each other.
Use the difference between numbers to find the missing number.
Example: Find the missing number: 30, 23, ?, 9
The order of numbers is going down or descending.
The difference between numbers is 30 - 23 = 7
Since the order is descending subtract 7 from 23. The missing number may be 16.
The missing number is 16 since it is 7 more than the last number 9.
M6.2.5 - Measure angles to the nearest degree using a protractor
A protractor is a measuring instrument, just like a ruler. The vertex point is in the lower
middle part of the protractor. The vertex point is placed on the vertex of the angle to
measure it.
A protractor has two scales, each numbered by tens from 0 to 180 degrees.
To measure an angle, place the vertex point on the vertex of the angle. Line up the zero
line with one ray of the angle, read the measurement along the other ray.
Example: Try measuring
this angle with your
protractor.
Vertex
Ray