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A
ngles
What is it?
Angles have been used in the Circle geometry unit and
(exclusively what we have learned this year) can involve triangles
within circles.
What I learned
The angles of a triangle always add up to 180º, this can be helpful
when you have two given angles of a triangle and missing one
because then you can find the difference, this is the example in
the picture below.
Types of Angles:
Obtuse: An angle greater than 90º but less than 180
Acute: an angle less than 90º
Right: An angle that is 90º
B
edmas
What is it?
Is the system used for solving an algebraic equation. It is required that the equation be
solved by the particular order of Brackets, Exponents, Division, Multiplication,
Addition, and Subtraction
Ex.
(6-4)+4^3-5x6=
2+4^3-5x6=
2+64-5x6=
2+64-30
=38
What I Have Learned
Bedmas was included in many of the units such as polynomials, rationals and
exponents/exponent laws and is sometimes known as order of operations. It is
essential to use when solving algebraic equations. The pictures below show the same
question and 2 different ways one might solve them. The first one shows the correct
work of BEDMAS, where the second one incorrectly does not use it at all.
C
ross multiplication
What is it?
Used in the Similarity unit, cross multiplication is a necessity for
establishing missing side lengths in triangles.
An example of how you would answer a question with cross multiplication
The process involves comparing both shapes and applying ``image over actual``
fractions by matching the two shapes together.
in order to multiply the numerators with the denominators
this creates a "butterfly" looking equation.
What I have Learned
By using cross multiplication you can find the missing side lengths of a triangle by
applying the given measurements to this formula.
D
istributive law
What is it?
Distributive law is used in an equation when the value of the
brackets needs to be combined with the other components of
the expression. The isolated value must be multiplied to the
remaining numbers.
Ex. 3 (6-3)
3×6 - 3×3
18-9
=9
What I Learned
How to answer questions that have an isolated number before an
equation with brackets.
I also learned how to apply distributive law with polynomials.
E
xponent Laws
What are they?
The rules required to answer equations containing exponents.
An exponent has two parts, a base and a power. The base
is the original value and the power is the amount of times you
will be multiplying the base by itself.
What I have Learned
Here are some of the laws that are important to remember.
1) Division Law:
When bases are the same, subtract the exponents
2) Multiplication law
When the bases are the same, add the exponents
3)
If bases are not the same then you must solve exponents and then multiply or divide.
F
ractions with decimals
It is helpful to remember that all fractions can be converted into
a decimal and vise versa. Knowing this can make it easier and
more flexible to order them, add, subtract....
Here is converting rationales to a decimal
Here is converting rationales into fractions
What I learned
In the example it was easier to make fractions into decimals if we
wanted to order them. When we change decimals into fractions,
you have to make them all have a common denominator.
G
reater/ less then
What is it?
Symbols that compare the values of two numbers. This was
demonstrated with rational numbers but can be involved with
any numerical values. ( You can use it to compare any two
numbers or equations.)
Ex.
-1 < 1
Or
-4 > -7
What I learned
This is a similar concept to ordering rationales, except we are
only comparing two numbers instead of numerous ones.
There is a symbol for equivalents too…
H
ypotenuse
What is it?
The hypotenuse is involved with right triangles. As we know, all
triangles consist of three sides. This is what a right triangle
consists of.
2 legs + hypotenuse= triangle
The hypotenuse is located across the right angle. Therefore, only
triangles containing a 90º angle have one. It is the longest side
too.
What I learned
The length of the hypotenuse can be found using the
Pythagorean Theorem (a^2+b^2=c^2) or if the hypotenuse is
given as well as one of the legs, Pythagoras can be used to find
the remaining leg's measurement.
I
mage
What is it?
Used in the scale unit, the image is the result after the
transformation of the "actual" object has been reduced or
enlarged.
(after the scale has been applied)
What I learned
Image over actual is applied when cross multiplying.
J
" ust do it"
What is it?
This means that a question is already in its simplest form, or does
not require further steps before you can solve it.
What I learned
Multiplying fractions is a "just do it" question because unlike
subtraction and addition, it does not need to be put in the lowest
common denominator.
*accidently multiplied the fractions wrong- forgot to flip one into
a reciprocal
li
K
e terms
What is it?
Like terms is another vocabulary word from the polynomials
unit. The first step to solving a polynomial is to sort. This is done
by pairing LIKE terms, or in other words, the same variables with
the same exponents.
What I learned
L
ine of symmetry
What is it?
Line of symmetry or reflection symmetry is an image that when
folded, is identical on both sides, like a mirror. There can be
numerous lines of symmetry that can divide the shape/image.
Here are some examples:
What I learned?
Letters, flags and numbers all have lines of symmetry. The lines
can be called vertical, horziontal or oblique.
The letter O is an example of all three.
M
onomials
What is it?
Monomials are an algebraic expression with one term.
What I learned?
The degree of a monomial is the only exponent. Monomials
always consist of a constant and a variable.
The picture shows the different parts of a polynomial with a
monomial example.
N
umber lines
What is it?
A visual representation of how and where numbers are ordered.
It can be used for integers, rationales etc.
What I learned
Here is an example of ordering rational numbers on a number
line
Both number lines have positive and negative spectrums.
O
rdering rationales
What is it?
Ordering fractions, decimals or percents from ascending or
descending value.
What I learned
When ordering rationales it is easiest to make them all in the
same form. ( fractions, decimals, or percents)
In this example I convert all the numbers into a decimal format to
make it easier to organize.
Here is the same question, but instead of making them in to
decimals, I change them to fractions
P
ythagorean theorem
What is it?
Is a formula used to find the missing side length of a right triangle.
The formula is A^2 +B^2= C^2
A and B are the legs of the triangle, the one creating the right angle. C is
the hypotenuse, the line across the right angle.
Depending on the question, it may be necessary to find A, B or C.
It is important to make sure your answer is squared.
What I learned
To establish if the given meaurements indicates a right triangle you have to
see if the statement is true.
In this case, we know that the triangle has an obtuse angle because 484 is
greater than 250.
Q
uadrant
What is it?
A quadrant is what a graph is divided in to. Quad means four, so
that means the coordinates graph has four sections
What I learned?
As you can tell from the image above, quadrants 3 and 2 have
negative coordinates and the 4 and 1 have positive. By using
quadrants it is easier to describe the position of the plotted
coordinates and the area that they are in.
R
adius (or radii)
What is it?
Used in our circle geometry unit, a radius is the line connected to
the center point as well as the circumference of the circle.
Twice the radius equals the diameter.
When a tangent line is attached to the radius it produces a right
angle.
What I learned
The radius can be involved in finding the area of a cylinders and
circles. For example
S
cale diagrams/factors
What is it?
A scale factor is the reduction or enlargement of an "actual".
A scale diagram is the visual of the scale.
What I have learned
Scale factors can be represented by fractions, ratios or percents.
Any scale greater than 100% is an enlargement and any less is a
reduction.
Scale factors can be used on maps, blueprints, etc.
T
rinomials
What is it?
Trinomials are polynomials with three terms
This means that there are three different variables. The constants
can be different values.
Here is shown how to simplify a trinomial.
What I have Learned
A term is a piece of a polynomial
There can be monomial, ( a polynomial with one term), or a
binomial (one with two).
U
nlike terms
What is it?
Unlike terms were involved in our polynomials unit.
Because the variables and exponents in this equation aren't the
same, they are all unlike terms and therefore they cannot be
simplified any further.
What I learned
The coefficients can be different, but the variables and the
degree of their variables have to be the same in order to "sort"
any more.
In other words, it has to be like terms to simplify the equation.
V
ariables
What is it?
Variables are represented by a letter symboling an unknown
value.
Variables are used in our linear and polynomials units.
What I learned
Variables may be attached with exponents or constants, but can
be isolated too.
W
hole Numbers
What is it?
A number that is 1, 2, 3, 4..... Basically the opposite of rational
numbers.
What I learned
Integers are different then a whole number. They are similar
except they include negative numbers. A negative number is not
classified as a whole number.
X
- axis
What is it?
The X axis is the horizontal line on a coordinate graph.
What I learned
When plotting coordinates, the first number is placed along the X
axis, this is exampled in the graph above.
Ex. (-5, 7) the -5 would be placed on the horizontal line
Y
- axis
What is it?
The vertical line on a coordinates graph. It intersects the X-axis
What I learned
The second number when written in coordinates is placed based
on the y axis.
Above, I showed how to plot on coordinate grid
Normally, the X axis is the dependent variable, and the y is the
independent.
Z
ero pairs
What is it?
Zero pairs are the cancellation of numbers that when the value is
applied it equals zero
In the picture, you can see that what happens to one side, has to
happen to the other, making a zero pair on one and a different
value to the other.
What I learned
By using zero pairs it simplifies the expression by eliminating
terms.