PRAXIS II Elementary Education 5015  Mathematics Curriculum
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Properties
Rules that apply for addition, subtraction, multiplication, or division of real numbers
 Commutative
 Associative
 Identity
 Inverse
 Distributive

Commutative
You can change the order of the terms or factors.

Associative
You can regroup the terms as you like.
 a + (b + c) = (a + b) + c
 a(bc) = (ab)c

Identity
Finding a number so that when added to a term results in that number; finding a number such that when multiplied by a term results in that number.

Inverse
Finding a number such that when added to the number it results in zero; or when multiplied by the number results in 1.

Distributive
This technique allows us to perate on tems with parentheses without first perfoming operations with the parentheses. This is especially helpful when terms within the parentheses cannot be combined.
a (b + c) = ab + ac

Arithmetic Sequence
a (sub n) = a (sub 1) + (n  1)d
 a (sub 1) is the first term in the sequence
 d = common difference between the terms
 n = the nth term

Net
Twodimensional figure that can be cut out and folded up to make a threedimensional solid


Tetrahedron
4 equilateral triangle net

Octahedron
8 equilateral triangle net

Icosahedron
20 equilateral triangle net

Dodecahedron
12 regular pentagon net

Tessellation
An arrangement of glosed shapes that completely covers the plane without overlapping or leaving gaps; unlike tilings, tessellations do not require the use of regular polygons

Four basic tranformational symmetries that can be used in tessellations
1)
2)
3)
4)
 1) Translation
 2) Rotation
 3) Reflection
 4) Glide Reflection

Sum of the Squares
Sum of the squares of the differences between each item and the mean
(Each number  average)(Same number  average)

Variance
The sum of the squares quanitity divided by the number of items

Standard Deviation
The square root of the variance

Pythagoras Theorem
a2 + b2 = c2

Number of yards in a mile
1,760

One Meter is approximately ______ yards.
One