MA.A.1.3.1 Associates Verbal Names With Written Names

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MA.A.1.3.1 Associates Verbal Names With Written
Names
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Negative numbers
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What are negative numbers?

1. All numbers less than or equal to zero
2. All numbers less then negative 1 (i.e., -1).
3. All numbers equal to or less than negative 1
   (i.e., -1).
4. All numbers that students dont want to learn.
5. All numbers less than zero (i.e., 0).

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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
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integers
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What is an integer?

• An integer is a whole number.
• An integer is a negative whole number.
• An integer is a positive whole number, zero,
• or a negative whole number.
• An integer is a number that can be written as
• a ratio of two numbers.

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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.
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coordinate
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Which of the following is a coordinate?

1. 4 and 6
2. (-1.2, -4.5)
3. 23.45
4. c and d

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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.
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inequality
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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 lt
2 or 3x 3 gt 6 - y
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absolute value
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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
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Write the expression for The absolute value of
-1? A.) -1 B.) -1 C.) --1 D.) none of
the above
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Write the expression for The absolute value of
45? A.) 45 B.) -45 C.) -45 D.) --45
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Write the expression for The absolute value of
-32.7? A.) -32.7 B.) -32.7 C.)
--32.7 D.) none of the above
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Write the expression for The absolute value of
-x2? A.) -- x2 B.) - x2 C.) - x2 D.)
x2
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Write the expression for The absolute value of
-(x 3)? A.) -(X 3) B.) -(X 3) C.) X
3 D.) --(X 3)
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Evaluate -1
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Evaluate 45
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Evaluate The absolute value of -32.7?
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Evaluate The absolute value of -x2? A.)
x2 B.) - x2
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Evaluate The absolute value of -(x 3)? A.)
-(x 3) B.) (x 3) C.) -x 3 D.) -x - 3
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bases
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What is a base?
A base is a number that is to be multiplied in an
exponential power expression.
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exponents
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What is an exponent?
An exponent is a number that appears as a
superscript next to 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
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Evaluate
24 ____
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Evaluate
73 ____
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Exponential power
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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.
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Scientific notation
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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 isnt 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

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Write 6,543,210 in scientific notation?

• 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)
• 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.)
• 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.

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Write 43,671 in scientific notation?
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Square root
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What is a square root?
A square root is the number that is multiplied by
itself to get the number that is being
evaluated. For example, v16 4 because 4 4
16
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Evaluate
____
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Perfect square
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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
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Do you know the perfect squares between 1 and
144?
Every student should know the perfect squares up
through 144. They arent that hard. Lets see
if you can name them. 12 _______
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Do you know the perfect squares between 1 and
144?
Good, now lets try 22 _______
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Do you know the perfect squares between 1 and
144?
Next 32 _______
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Do you know the perfect squares between 1 and
144?
Try this one 42 _______
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Do you know the perfect squares between 1 and
144?
How about? 52 _______
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Do you know the perfect squares between 1 and
144?
Keep going . . . 62 _______
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Do you know the perfect squares between 1 and
144?
Youre more than half way! 72 _______
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Do you know the perfect squares between 1 and
144?
This one is easy 82 _______
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Do you know the perfect squares between 1 and
144?
This is the last single digit one 92 _______
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Do you know the perfect squares between 1 and
144?
Everybody knows this one. 102 _______
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Do you know the perfect squares between 1 and
144?
This one is a bit tough for some 112 _______
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Do you know the perfect squares between 1 and
144?
And last but not least 122 _______
Great! Now lets see how knowing this can help
with square roots.
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Radical sign
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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
radical sign for the perfect squares through
144
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Principal square root
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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 v16 4.
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Ratio
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What is a ratio?
A ratio is a mathematical comparison of two
numbers to 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. 45 is a ratio
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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.
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Rewriting a ratio.
Write the answer to the previous problem using
the colon instead of the fractional form for a
ratio.
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Rate
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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 hour feet per
minute kilometers per day dollars per week liters
per second gallons per month ounces 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
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When converting between rate units we use a tool
called Dimensional Analysis.
Dimensional analysis allows us to convert from
one rate unit to another. For example, if we
want to convert the number of inches per day that
a snail moves to compare it to the speed of a man
walking, we would use dimensional analysis to
convert inches per day to miles per hour. Since
certain units can be equated, for instance, 12
inches 1 foot, we can relate them into a rate
unit like this 12 inches 1 foot
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Percent
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What is percent?
A percent is a number representing the ratio
between a quantity and 100. Per cent means
divided by 100 Thus, a numbers percentage is
the relationship between the part associated with
the number versus the 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 .
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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
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• Write 4 / 5 as a percent?
• 80
• 75
• 70
• 60

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Percent proportion
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What is percent proportion?
A percent proportion is a relationship
between two fractions that us often used to solve
percent problems. It looks like this
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Solving percent proportion problems
Using the percent proportion equation
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 60200?100 (The product of the
means the product of the extremes.) 6000
200? ? 6000/200 30
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Part
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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
part60020100 (part)10012000 part 12000
120 100