VocabularyDay 1 CIM MA.A.1.3.1 Associates Verbal Names With Written Names

VocabularyVocabulary Day 1 CIMDay 1 CIM

MA.A.1.3.1 Associates Verbal Names With Written Names


Negative numbers


What are negative numbers?

a. All numbers less than or equal to zero

b. All numbers less then negative 1 (i.e., -1).

c. All numbers equal to or less than negative 1 (i.e., -1).

d. All numbers that students don’t want to learn.

e. All numbers less than zero (i.e., 0).


What are negative numbers?

Negative numbers are numbers that are less than zero.

Examples: -3

-0.472

-1/2

-984.32794078

-46 3/8

-83


integers


What is an integer?

a. An integer is a whole number.

b. An integer is a negative whole number.

c. An integer is a positive whole number, zero, or a negative whole number.

d. An integer is a number that can be written as a ratio of two numbers.


What is an integer?

An integer is a whole number that can be written as a positive whole number, zero, or a negative whole number.

The numbers . . . , -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . consisting of the negative whole numbers, zero, and the positive whole numbers are called integers. -3 and 31 are both examples of integers. They contain no decimals or fractional components.


coordinate


Which of the following is a coordinate?

a. 4 and 6

b. (-1.2, -4.5)

c. 23.45

d. c and d


What is a coordinate?

A coordinate is a pair of values that represent a point on a coordinate plane, also known as an ordered pair, (x,y).

The coordinate plane is also known as the Cartesian Coordinate System. It is made up of a horizontal and a vertical number line that intersect at right angles, called the x-axis and y-axis respectively.


inequality


What is an inequality?

An inequality is a math statement or expression formed by placing a less than or greater than sign between two expressions.

For example, 1 < 2 or 3x + 3 > 6 - y


absolute value


What is absolute value?

Absolute value is the distance of a number from zero on the number line. It is written as |n|, where n is a real number.

For example, |-4| = 4 or |x| = x and |-x| = x


Write the expression for:

The absolute value of -1?

A.) -|1|

B.) |-1|

C.) -|-1|

D.) none of the above



The absolute value of 45?

A.) |45|

B.) -|45|

C.) |-45|

D.) -|-45|



The absolute value of -32.7?

A.) -|32.7|

B.) |-32.7|

C.) -|-32.7|

D.) none of the above



The absolute value of -x2?

A.) -|- x2|

B.) -| x2|

C.) |- x2|

D.) | x2|



The absolute value of -(x + 3)?

A.) |-(X + 3)|

B.) -|(X + 3)|

C.) |X + 3|

D.) -|-(X + 3)|


Evaluate:

|-1| =


Evaluate:

|45| =


Evaluate:

The absolute value of -32.7?


Evaluate:

The absolute value of -x2?

A.) x2

B.) - x2


Evaluate:

The absolute value of -(x + 3)?

A.) -(x + 3)

B.) (x + 3)

C.) -x + 3

D.) -x - 3


bases


What is a base?

A base is a number that is to be multiplied in an exponential power expression.


exponents


What is an exponent?

An exponent is a number that appears as a superscript nextto a number called a base. It tells you how many times the base needs to be multiplied.

The entire number is called a power or exponential power.

For example, 24 = 2 · 2 · 2 · 2 = 16; 4 is the exponent

a8 = a · a · a · a · a · a · a · a; 8 is the exponent


Evaluate:

24 = ____


Evaluate:

73 = ____


Exponential power


What is an exponential power?

An exponential power is a term that includes a base and an exponent. It is the number that is to be multiplied times itself the total number of times expressed by the exponent. It is many times called just a power.

2763

92

3x

12(ac)


Scientific notation


What is scientific notation?

Scientific notation is a way of writing very big or very small numbers so they are easier to manipulate arithmetically.

When you first see a number written in scientific notation, it might look hard to read. But it really isn’t once you understand why it is written like it is and practice writing numbers that way.

Scientific notation involves two parts:

• The base number • The power of ten



Write 6,543,210 in scientific notation?

1. Move the decimal point from the right of the zero (6543210.) to the right of the left-most digit, between the 6 and 5 (6.543210)

2. Count the number of place values the decimal has been moved to the left. (In this case, it has moved to the left six places.)

3. This number is now the exponent that will be used as the power of 10, so it is written as 106.

The answer then becomes 6.543210 x 106.

Drop any insignificant zeros on the end of the decimal.


Write 43,671 in scientific notation?


Square root


What is a square root?

A square root is the number that is multiplied by itself toget the number that is being evaluated.

For example, √16 = 4 because 4 · 4 = 16


Evaluate:

= ____


Perfect square


What is a perfect square?

A perfect square is a number that is the square of an integer.

For example, 16 is a perfect square because 4 · 4 = 16


Do you know the perfect squares between 1 and 144?

Every student should know the perfect squaresup through 144. They aren’t that hard.

Let’s see if you can name them.

12 = _______



Good, now let’s try:

22 = _______



Next:

32 = _______



Try this one:

42 = _______



How about?

52 = _______



Keep going . . .

62 = _______



You’re more than half way!

72 = _______



This one is easy:

82 = _______



This is the last single digit one:

92 = _______



Everybody knows this one.

102 = _______



This one is a bit tough for some:

112 = _______



And last but not least:

122 = _______

Great! Now let’s see how knowing this can help with square roots.


Radical sign


What is a radical sign?

A radical sign is the sign used to identify the Operation of taking the square root of a number.

Here are the square roots shown with the radicalsign for the perfect squares through 144:

144 = 12

121 = 11

100 = 10

81 = 9

64 = 8

49 = 7

36 = 6

25 = 5

16 = 4

9 = 3

4 = 2

1 = 1


Principal square root


What is a principal square root?

A principal square root is the positive value of a square root of a number.

For example, the principal √16 = 4.


Ratio


What is a ratio?

A ratio is a mathematical comparison of two numbersto each other that have the same dimensional units (so units are not required).

The two numbers can be separated by either a colon (:)or placed on both sides of a fraction line.

e.g. 4:5 is a ratio; 3 is also a ratio of 3 to 8.

8


Calculate a ratio.

A math class has a total of 23 students. 10 are boys.Write the ratio of boys to girls in this class as a fraction?

[Note: Since we are comparing students to students,there is no need to include dimensions.]


Rewriting a ratio.

Write the answer to the previous problem using the coloninstead of the fractional form for a ratio.


Rate


What is a rate?

A rate is a measurement that compares two scalar dimensions, normally, but not always, between quantity and time, to each other. It is a ratio that says how long it takes to do something, or how two dimensions relate to each other in the physical world. It compares two different kinds of units, or two different things measured in different portions of the same units.

Examples of rate units are:

miles per hourfeet per minutekilometers per daydollars per weekliters per secondgallons per monthounces per pound (notice different portions of the same units here)

Rates are usually in dimensions of length (distance) in the numerator and time in the denominator, but not always


When converting between rate units we use a tool called“Dimensional Analysis.”

Dimensional analysis allows us to convert from onerate unit to another.

For example, if we want to convert the number of inchesper day that a snail moves to compare it to the speed of aman walking, we would use dimensional analysis to convertinches per day to miles per hour. Since certain units can beequated, for instance, 12 inches = 1 foot, we can relatethem into a rate unit like this:

12 inches 1 foot


Percent


What is percent?

A percent is a number representing theratio between a quantity and 100.

“Per cent” means “divided by 100”

Thus, a number’s percentage is the relationshipbetween the part associated with the number versusthe whole quantity, represented by 100.

It is equivalent to a fraction with 100 in the denominator.

It is written as a number followed by the symbol “%.”


Write 21 / 70 as a percent?

21 / 70 is the same as 21 divided by 70.

21 / 70 = .3 = 3/10 (10/10) = 30 / 100 = 30%


Write 4 / 5 as a percent?

a. 80%

b. 75%

c. 70%

d. 60%


Percent proportion


What is percent proportion?

A percent proportion is a relationship betweentwo fractions that us often used to solve percentproblems. It looks like this:

part ?

whole 100


Solving percent proportion problems:

Using the “percent proportion” equation:

part ?

whole 100

The fraction of part-to-whole is expressed in this equation:

What percent of 200 is 60?

60 is the part; 200 is the whole.

So the equation becomes:

Solving: 60:200=?:100 (The product of the means = the product of the extremes.)

6000 = 200?; ? = 6000/200 = 30


Part


What is a part?

A part is a piece of the whole in a math problem.

For example, What is 20% of 600?

“What” represents the part, 600 is the whole.

So the percent proportion problem is:

part:600=20:100

(part)100=12000

part = 12000 = 120 100

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VocabularyDay 1 CIM MA.A.1.3.1 Associates Verbal Names With Written Names