Welcome to 8th Grade Math! This year I have the pleasure of co-teaching with Mrs. Filip! This will be our second year working together and I know you will all learn and grow in your mathematical endeavors! Take some very important advice:
Keep up with your classwork!
Keep up with your homework!
Ask if you don't understand!
Don't give up!
I offer office hours every morning at 8:15. This is listed in Filip Classroom Stream.
I also have afternoon office hours. These are usually held in Reilly's Language Arts Class.
TEAMWORK!!!
Quarter 4
Wednesday Office Hours during Independent Study 3rd Period 10:14-10:48
*Math This Week!*
Progress Reports!!!
Solid Geometry!
We will be reviewing formulas and calculator use.
This is a one week Unit, Quiz Friday. You will be able to use your formula sheets and a calculator for the Quiz.
rectangular prism = a b c 
irregular prism = b h 
cylinder = b h = pi r 2 h 
pyramid = (1/3) b h 
cone = (1/3) b h = 1/3 pi r 2 h 
Math Project due Monday!!! First big grade of the MP!
Shapes and Angles!
Pythagorean Theorem
a^2 + b^2=c^2
the longest side of a right triangle, opposite the right angle.
Square Root: a number that produces a specified quantity when multiplied by itself. "7 is a square root of 49"
Perfect Square List:
Perfect Square, Factors. 1, 1 * 1; 4, 2 * 2; 9, 3 * 3; 16, 4 * 4; 25, 5 * 5; 36, 6 * 6; 49, 7 * 7; 64, 8 * 8; 81, 9 * 9; 100, 10 * 10;
121, 11 * 11; 144, 12 * 12; 169, 13 * 13; 196, 14 * 14; 225, 15 * 15; 256, 16 * 16
A pair of inverse operations is defined as two operations that will be performed on a number or. variable, that always results in the original number or variable. Another way to think of this is. that the two inverse operations “undo” each other.
SIMILAR TRIANGLES! What are they good for?
We can use Similar Triangles to perform Indirect Measurement.
1. Show the two triangles are similar
2. Set up a proportion that includes the unknown distance.
3. Solve (cross multiply)
Similar Triangles are proportional to each other and have congruent angles. Dilations create similar figures, including triangles.
AA POSTULATE: If two angles in one triangle are congruent (the same) to two angles in another triangle, then the triangles are congruent.
SAS (Side, Angle, Side): If triangles have a congruent angle and corresponding sides including the angle are proportional then the triangles are similar. (you need 2 sides and one angle).
SSS (side, side, side): If the corresponding sides of two triangles are proportional, then triangles are similar.
Triangles, Polygons, and Angle Pairs
You may use your calculator and your notes (or mine, below)
*Remember*
All lines AND Triangles = 180 Degrees!!! If you know two angle measures of a triangle, you can find the measure of the third.
Sum of interior Angles formula: S=(n-2) * 180 (sum = side-2 times 180 degrees)
The Sum of exterior angles always adds to 360 degrees
VOCAB:
Bi-Sector-something that cuts an object into two equal parts. It is applied to angles and line segments. In verb form, we say that it bisects the other object.
Complimentary Angles - angles that add to 90 degrees (form a right angle)
Supplementary angles-angles that add to 180 degrees
Linear Pairs- a pair of adjacent angles formed when two lines intersect.
Adjacent Angles - angles that have a common side and a common vertex (corner point) and don't overlap.
Verticle angles-each of the pairs of opposite angles made by two intersecting lines. They are congruent
Corresponding Angles-When two lines are crossed by another line (called the Transversal), the angles in matching corners are called Corresponding Angles.
Angle Addition Postulate-The postulate states that if we have two adjacent angles, we can add their measures to help us find unknown angles.
Polygon - Closed shaped, multi-sided, with sides, vertices, angles, and 2 dimensional; they are planer shapes all on the same plane.
Triangles - 3 sided; quadrilaterals - 4 sided; pentagon - 5 sided; hexagon - 6 sided; octagon - 8.
Regular Polygons - all sides and angles are the same
Irregular Polygons - not all angles are the same
Concave Polygons - a polygon with one or more interior angles greater than 180°
Convex Polygons - polygons where all angles are less than 180 degrees.
Polygon Rule: number of sides/angles minus 2 multiplied by 180 degrees. n-2*180
example: Triangle has 3 sides so n =3 ... 3-2*180 = 180
Interior Angle Theorem - All interior angles of a triangle are more than 0° but less than 180°. ... The sum of each interior angle and exterior angle is equal to 180° (straight line).
Exterior Angle Theorem - the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
Exterior Polygon Angle Theorem - The sum of exterior angles in a polygon is always equal to 360 degrees.
Alternate Interior angles (parallel lines, transversal) are congruent!
Alternate Exterior angles (parallel lines, transversal) are congruent!
IXLs This Week
W18 (7th Grade Skill); P1, P2, P3
Past IXLs
Q5, 8, O17, P17
O7, 12, 13, 14, 18
Past Learning:
Basics of Transformation
Functions & Relation
A Function is a relationship - but not all relationships are functions!
Tables:
From a table we find the slope by calculating the change this way:
y2-y1
----------
x2-x1
Look for y-intercept where x=0
Graph:
Look at rise over run to find the slope
Y is where the line crosses the y axis
***Proportional Relationships go through points (0,0)***
IXLs this weeK:
O 7, 12, 13, 14, 18
So far we've covered some basic solving for x, squares and square roots, perfect squares, estimating, Exponent rules, graphing points on a grid, slope, forms of slope.
What is required for this class?
Enthusiasm
Dedication
Curiosity
Initiative
Pencil
Scientific calculator