Current Vocabulary List By Chapter in Houghton Mifflin Math Book--some words have further explanations on the page, so watch for links and scroll down. You are expected to know these! Without learning these you will have a weak linK!!
Mean Median Mode Range
These all have to do with data. Mean, median, mode, have to do with the central tendency....think of the average or middle of a group of numbers.Mean is an average found by adding up the numbers in a collection of data. Then dividing by how many you added. Example:
1+2 +3 +4 +5 = 15
Then divide 15 by 5 as in 15/5 and the
answer is three.
Median is the exact middle of a number after they are put in order. For instance in the group; 22 33 44 55 57 68 70 74. The middle is between 55 and 57. Logically you know that would be 56, but if you didn't know you could add 55 and 57 = 102. Then divide it in half and you would get 56.
Mode is the number that occurs the most in a collection of data. Example
23 44 56 34 23 34 23 The mode would be 23 because it occurred the most. Sometimes there is no mode. Sometimes there are more than one.
Range is the difference between the highest number and the lowest. Picture the mountain range with the high peaks and the low valleys.
Remember H - L In the group above, the highest was 56, the lowest was 23 so the difference would be 33.
Sports statisticians and broadcasters use so many mathematical calculations based upon ratios that are turned into decimals or percents.
Consider the baseball player that comes up to bat. Let's say it is the beginning of the season, the first game,he is one for three. He has had one hit out of three at
bats. The ratio is 1/3 . Divide three into 1.00 and the result (quotient) is .333. Remember the denominator is the divisor that goes into the numerator. The answer to a division problem is a quotient.
Diameter of a circle.
Notice that a diameter goes all the way from one end to the other and through the center. while a radius goes from the
edge of a circle to the center. Both are used in finding either the circumference (the distance around the circle) or area (the total inside in sq. units)
CIRCUMFERENCE = pi x d (PI IS 3.14 AND D IS DIAMETER)
Area of a circle is = pi x r x r (3.14 times radius squared)
15 5 2
3 1 10
Factors of 15 both Factors of 20
This is a picture of a Venn diagram showing how factors of
15 and 20 share the factors of 5 and 1.
Venn Diagram--named after the great mathematician John Venn . He loved logic and probability.
Factors are numbers that when multiplied together give you another number. Numbers made up of only one and itself are considered prime. Numbers made of of more than that are called composite. A man named Erastosthenes came up with a sieve to sort these way back there in Ancient Greece. (He also discovered the circumference of the earth.) You can find this Sieve in your math book p 105.
4 x 5
2 x 2 x 5 = 20 Do you see a 4, a 10 and the 20 all in this line?
This is a factor tree showing first a composite number of 20
Then two factors
of 4x5 then the
prime factors which end the tree.
Notice how you could make 2 x 10 from the prime factors which also equals 20!
Factor Trees help find the greatest common factor of two numbers.
4 x 4
2 x 2 x 2 x 2 = Two to the fourth
If you look at the bottom of this tree you can see that compared to the factor tree of 20, they both share a 2 x 2 which makes four. So the greatest common factor of 16 and 20 is four!
So if you wanted to simplify 16/20 you would factor out a four (divide it out ) and you would get 4/5.
Now that we have a fraction of 4/5 we can easily change that to a decimal, then a percent.
Divide 5 ) 4.00
Can you see that the quotient would be .80 ?
Multiply .80 X 100 to change it to a percent
That is equal to 80%
Or there is another way to do that by changing that fraction!
Start again with 4 x 2 8
5 x 2 10
Notice how 4/5 changed to eight tenths. Could you easily write the decimal of 8/10 as .8 ?
Once you have .8 , times it by 100 and you get 80%
Think of other denominators that easily change to
a 10 100 or 1000 .
Let's make a table of that!
Denominator x by = denominator
2 2 x 5 = 10
4 x 25 = 100
5 x 2 = 10
20 x 5 = 100
So if you had a fraction like 3/4 you would multiply
both the numerator and the denominator by 25 to get 75/100 = .75 and that x 100 = 75%
How is that for cool!
To balance and equation, there is one very important rule:
Whatever you do to one side of the equation, you must also do to the other side.
It is important to keep it in balance.
Let us start with a simple equation of x + 3 = 14
Get the x alone by getting rid of the +3
Use the opposite operation of -3 - 3 -3
X = 11
Subtract three from both sides of the = sign
Then check the equation. If X = 11 as we said, then it must be true that 11 + 3 = 14
Yes, it is.
Now try 12 + x = 22
Solve by doing the opposite
operation -12 -12
x = 10
Check: 12 + 10 = 22 Yes, it does
So if adding and subtracting are opposite operations. What would the opposite of divide be.......
A look at positive and negative integers on a number line.
One way to do work on integers is to make use of a number line
To add positive go to the right....
-4 + 2 = -2
Place a mark on -4 move to the right 2 and you are on -2. To add a negative go left.
3 + -6 = -3
To subtract integers remember this rule. Subtracting an integer is the same as adding its opposite.
So -100- -75= -25
In multiplying integers remember the product of two integers with different signs is always negative.
-7 x +3 = -21
The product of integers with same signs is always positive.
If one is zero, the product is 0.
In dividing integers remember the quotient of two integers with the same sign is always positive +45/+9= +5 and
-72 /-8 = + 9
The quotient of two integers with different signs is always negative.
36 /-9 = -4
. . . . . . . . . . . . . .
Chapter 1: base of a power, exponent, power of 10, period, equivalent, standard form, word form, short word form, expanded form, decimals, digit, rounding numbers,sum, difference, product, quotient, divisor, metric measurement
Chapter 2:mean, median, mode, range, frequency table, histogram, data set, measures of central tendency cluster, gap , outlier, stm and leaf plot, box and whisker plot, quartile, extreme, bar graph, double bar graph, double line graph, pictograph,
Chapter 3:composite number, factor, improper fraction,multiple, ratio, decimal, percent, fraction, numerator, dividend, denominator, divisor, prime factorization, greatest common factor, greatest common divisor, least common multiple, equivalent fractions, simplest form, common denominator, least common denominator,repeating decimal, terminating decimal, rules of divisibility,venn diagramfactor tree, greatest common factor,