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, .
As an Algebra student you should know:
· 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
2) Website: algebralab.org (go to “lessons”)
3) math-play.com. Select “Middle School Games” on right side. Select 7th grade or 8th grade. Scroll to down for games.
· 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 improper form ( 64 must be simplified to 32 and may 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
o 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:
§ PHSchool.com, codes: ayp-0888, ayp-0108
· ABSOLUTE VALUE
o Notes:
§ Algebraic notation: |x| = x.
§ Measures the distance from zero. Always a positive number
§ Treat like parenthesis when performing order of operations
o Resources:
·
· 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.
o Resources:
· 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
§ Dilation by using a scale factor (such as 12 or 3)
o Resources:
§ PHSchool.com, codes: ayp-0766, ayp-0865, ayp-0866, ayp-0894
§
· 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.
o 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:
§ 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 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
o Resources:
§ PHSchool.com, codes: ayp-0761, ase-0701,
·
· REAL NUMBER SYSTEM
o Notes:
§ 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.
§
o Resources:
§ PHSchool.com, codes: ayp-0107, are-0806