Transcript LFP Power Point Notes

INVESTIGATION #1
* Identify Locations (points) on a coordinate grid by using coordinate pairs. (x, y)
For example: (5, 3)
To draw parallel lines use the same slope (rise / run)
To draw perpendicular lines use slopes that are “Opposite Reciprocals”
B
(-1/3) and 3 are
A
Both lines have a slope of ( – 1/3 )
Opposite Reciprocals
Line A has a slope of ( – 1/3 )
Line B has a slope of 3
INVESTIGATION #1 cont.
* Know the defining characteristics of the following geometric shapes...
Quadrilateral:
a four sided shape
Parallelogram:
- the opposite sides are parallel to each other
Rectangle:
- opposite sides are the same length
- the opposite sides are parallel to each other
- all four corners are 90 degree angles
Square:
- all four sides are of equal length
- the opposite sides are parallel to each other
- all four corners are 90 degree angles
Right Triangle:
a triangle with a 90 degree angle
INVESTIGATION #1 cont.
* Know the difference between the following types of measurement…
Length:
the measurement of the distance from one point to another
Perimeter:
the measurement of the distance around a shape
Area:
the measurement of the space inside a shape
(in square units)
INVESTIGATION #2
Length vs. Area
1 unit
2 units
Strategies to find the
area of shapes
1 square unit
(1 unit2 )
4 square units
(4 units2 )
“Divide & Count” - divide into square units and count the number of
squares inside the shape
“Cut & Paste” - Fit partial units together to make complete units
“Area Formulas” - Rectangle: A= L x W
/ Triangle: A = B x H
2
“Surround & Conquer” - Surround the shape with a rectangle.
Subtract the area of the ‘empty space’ from the area of the rectangle.
INVESTIGATION #2 cont.
* You need to be able to draw a square on dot paper
* Be able to explain the relationship between the length (s) of
one side, and the area (A) of the square.
S2 = A
S = √A
32 = 9
3 = √9
* Be able to find the precise length of a tilted line on dot paper without a ruler
Strategy 1 - Create a square so that the line is one side of the
square. Find the area of the square. Take the square root of the
area to get the side length.
Strategy 2 - Create a right triangle so that the line is the
hypotenuse. Solve using the Pythagorean Theorem.
INVESTIGATION #3
Hypotenuse – The longest side of a right triangle. It will
always be opposite of the 90 degree angle.
Hypotenuse
Leg
Leg
c2
Pythagorean Theorem –
a2
+
b2
=
c2
a2
b2
INVESTIGATION #3 cont.
If given two side lengths of a right triangle, you can solve for the
third side by using the Pythagorean Theorem.
Example 1
To solve for the
hypotenuse (c)
c
9
14
a2 + b 2 = c 2
92 + 142 = c2
81 + 196 = c2
277 = c2
c = √277
c ≈ 16.64
Example 2
To solve for a leg
length (a or b)
7
√84
b
a2 + b2 = c 2
72 + b2 = √842
49 + b2 = 84
-49
-49
b2 = 35
b = √35
b ≈ 5.92
INVESTIGATION #3 cont.
Is it a Right Triangle?
If given three side lengths, you can use the
Pythagorean Theorem to check if the triangle is a
right triangle.
Example 1
5, 12, 13
a2 + b2 = c 2
52 + 122 = 132
25 + 144 = 169
169 = 169
Yes, this is a Right Triangle!
Example 2
7, √110, 14
a2 + b2 = c 2
72 + √110 2 = 142
49 + 110 = 196
159 ≠ 196
No, this is a NOT a Right Triangle!
INVESTIGATION #4
SPECIAL TRIANGLES
45 - 45 – 90 (isosceles triangle)
• Legs are the same length
• The hypotenuse is equal to
the leg length times the √2
30 - 60 – 90 (bisected equilateral)
• The short leg is half of the
hypotenuse
• The long leg is equal to the short
leg length times the √3
6√2
6
12
6√3
6
6
Perimeter:
Perimeter:
6 + 6 + 6√2 ≈ 20.49
12 + 6 + 6√3 ≈ 28.39
INVESTIGATION #5
RATIONAL vs. IRRATIONAL NUMBERS
definite length
precise value
Infinite number of decimal places
• Terminating and Repeating decimals are rational
numbers and can be written as a fraction
Repeating Decimal Patterns
1 digit repeat - Denominator is 9
ex.
2/9 = .2222…
8/9 = .8888…
2 digit repeat - Denominator is 99
ex.
61/99 = .616161…
7/99 = .070707…
3 digit repeat - Denominator is 999
ex.
538/999 = .538538…
84/999 = .084084…