Download must be simplified to and may remain as an

Please keep in mind this is not a complete list of all the concepts
missed by skipping two levels of math. You may want to review the 7th
grade and 8th grade SOLs (links below) for a complete list of all
concepts taught in 7th and 8th grade.
Please feel free to email me with any questions,
[email protected].
As an Algebra student you should know:
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FRACTIONS (SOL: 6.4, 6.6) - how to add, subtract, multiply and
divide fractions and mixed numbers and know how to change an
improper fraction to a mixed number and vice versa
INTEGERS (signed numbers) (SOL: 7.3) – how to add, subtract,
multiply and divide integers.
EQUATIONS (SOL: 7.14, 8.15) – be able to easily solve two-step
equations.
PYTHAGOREAN THEOREM (SOL: 8.10) - apply the theorem to
determine if a triangle is a right triangle, find missing lengths, and
apply to real-life situations (word problems).
ABSOLUTE VALUE – (SOL: 7.1) – identify and calculate absolute
value.
SCATTERPLOTS (SOL: 8.13)– Recognize, read and make
predictions.
TRANSFORMATIONS (SOL: 7.8, 8.8) – be able to identify and
apply the following transformations: translation, reflection,
rotation and dilation.
SURFACE AREA and VOLUME (SOL: 7.5, 8.7) – calculate the
surface area, volume or missing dimension for prisms, cylinders,
cones, and pyramids.
ANGLES (8.6) – describe and identify vertical, supplementary,
complementary, obtuse, acute, right, straight, and reflex angles.
REAL NUMBER SYSTEM (8.2) – know the difference between and
examples of rational and irrational numbers.
Resources:
1) PHSchool movies:
website: phschool.com,
then enter ayp code
Enter ayp Web Code
2) Website: algebralab.org (go to
here
“lessons”)
3) math-play.com. Select “Middle
School Games” on right side. Select 7th grade or 8th grade. Scroll to
down for games.
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FRACTIONS
o NOTES:
 For adding and subtracting fractions, the fractions must
have common denominators. Add/subtract the
numerators, the denominator stays the same.
 Multiplying fractions by multiplying straight across;
numerator times numerator and denominator times
denominator.
 Division, multiply by the reciprocal of the second
fraction.
 Fractions must be “reduced” but may remain in
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3
improper form ( must be simplified to and may
4
2
remain as an improper fraction or changed to a mixed
number)
o Resources:
 PHSchool.com, codes: ayp-0808, ayp-0809, ayp-0810,
ayp-0811, ayp-0812, ayp-0813
INTEGERS
o Notes:
 Add with like signs, add the absolute values and keep
the same sign. EX: -5 + (-3) = -8
 Add with different signs, find the difference of the
absolute values and keep the sign of the number with
the largest absolute value. EX: -8 + 2 = -6 or -3 + 5
=2
 Subtraction – rewrite as adding the opposite (change
subtraction to addition and change the sign of the
second number). Follow the rules for addition. EX: -7 –
2 = -7 + (-2) = -9 or 3 – (-9) = 3 + 9 = 11
Resources:
 PHSchool.com, codes: ayp-0775, ayp-0791, ayp-0792,
ayp-0876
EQUATIONS
o Notes:
 Solve for the variable by “undoing” the equation. First
add/subtract terms to isolate one variable term on one
side of the equal sign and a constant term on the other
side of the equal sign. Multiply both sides by the
reciprocal of the coefficient. (or divide by the
coefficient)
 Check your solution by substituting the value for the
variable in the equation to prove it is equal/balance.
o Resources:
 PHSchool.com, codes: ayp-0064, ayp-0065
PYTHAGOREAN THEOREM
o Notes:
 For right triangles only. a2 + b2 = c2. Used to find the
length of one of the sides of the triangle or to prove a
triangle is a right triangle.
 The legs (a, b) form the right angle; hypotenuse (c) is
the longest side and across from the right angle.
o Resources:
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PHSchool.com, codes: ayp-0888, ayp-0108
ABSOLUTE VALUE
o Notes:
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Algebraic notation: |x| = x.
 Measures the distance from zero. Always a positive
number
 Treat like parenthesis when performing order of
operations
o Resources:
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SCATTERPLOTS
o Notes:
 Graph relates two sets of data on a coordinate plane.
 Relationship may be positive (points trend upward from
left to right), negative (points trend downward from left
to right) or no relationship (seemingly random points)
Line of best fit is a line that best represents the data.
It may or may not go through data points.
Resources:
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TRANSFORMATIONS
o Notes:
 Four types of transformations:
 Translation, move up/down, left/right. Shape
does not change.
 Reflection over x-axis or over y-axis . Shape
“flips” Each point is the same distance from the
x-axis/y-axis. Ordered pair
 Rotation about the origin, shape rotates, size does
not change
1
 Dilation by using a scale factor (such as
or 3)
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Resources:
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PHSchool.com, codes: ayp-0766, ayp-0865, ayp0866, ayp-0894
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SURFACE AREA and VOLUME
o Notes: Calculate surface area and volume from formulas
provided by the Virgina Dept of Education by substituting in
the dimensions known and solve for the unknown dimension
(a length or volume or surface area). Interpret word
problems.
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Resources:
 PHSchool.com, codes: (volume) ayp-0102, ayp-0104,
ayp-0105, ayp-0463, ayp-0856, ayp-0857 (surface
area) ayp-0097, ayp-0098, ayp-0099, ayp-0100
ANGLES
o Notes:
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Acute angle measures between 0 and 90 degrees
 Obtuse angle measures between 90 and 180 degrees
 Reflex angle measures between 180 and 360 degrees
 Right angle measures 90 degrees
 straight angle measures 180 degrees
 Vertical angles are opposite angles formed by
intersecting lines. The measure of vertical angles are
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the same. Intersecting lines forms two pairs of vertical
angles
 Complementary angles are two angles with a sum of 90
degrees
 Supplementary angles are two angles with a sum of
180 degrees
Resources:
 PHSchool.com, codes: ayp-0761, ase-0701,
REAL NUMBER SYSTEM
o Notes:
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All numbers are divided into two groups: Rational
Numbers and Irrational numbers. Rational Numbers
have 3 subsets.
 Natural Numbers – counting numbers. 1.2.3….
 Whole numbers – Natural numbers and zero. 0,1,2…
 Integers – Whole numbers and their opposites. …-3,2,-1,0,1,2,3…
 Rational Numbers – any number that can be written as
a fraction. Any decimal number that repeats or
terminates. ½, 0.86, -98.34, 4.3333…
 Irrational number – a number that does not repeat and
does not terminate. pi, square root of a non-perfect
square.
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Resources:
 PHSchool.com, codes: ayp-0107, are-0806