Rational vs Irrational Numbers
Right Triangles
Squares and Square Roots
Finding Area
Double Jeopardy: Real World Applications
100
What is a rational vs irrational number?
Rational number: any real number that can be expressed as a fraction
Irrational number: any real number that CAN NOT be expressed as a fraction
100
What degree makes a right triangle.
Draw what it looks like and label the following sides of the triangle: leg (x2) and hypotenuse.
A right triangle has a 90 degree angle. 
100
Explain what squaring a number means.
Multiplying a number (the base) by itself twice.
100
What is the area of a square (formula a = ?)
a = s2
100
A soccer field is a rectangle 100 meters wide and 130 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance? Round your answer to the tenths place. (You can use a calculator)
hint: draw picture
a2+b2 = c2
1002 +1302 = c2
10,000 + 16,900 = c2
26,900 = c2
√26900 = √c2
√26900 = c
164 = c
That distance is 164 meters.
200
Are the following characteristics of an irrational or rational number: non-repeating decimals or non-terminating decimals
irrational number
therefore... rational numbers are repeating decimals or terminating decimals !!
200
What is the Pythagorean Theorem?
Explain what all variables represent in the equation.
a2 + b2 = c2
the square of the hypotenuse side is equal to the squares of the legs (other two sides of the triangle) added to together.
200
Explain what a square root means.
You can use √x to explain.
Find what number you can multiply by itself to get x.
200
What is the area of a triangle (formula a= ?)
a = 1/2bh
200
What is the length of the diagonal of a 7 cm by 6 cm rectangle? Round to the tenths place (no calculators)
a2+b2 = c2
72+62 = c2
49 + 36 = c2
85 = c2
√85 = √c2
√85 = c
85 is closer to 81 with a difference of 4, so about 9.2.
√81= 9
√100 = 10
so...
9.2 = c
The length of the diagonal is 9.2 cm.
300
Is √36 a rational or irrational number?
rational number - all perfect squares are whole numbers, all whole numbers are rational numbers and can be represented as a fraction over 1
300
Solve for the hypotenuse of the right triangle.
Hypotenuse DF = 13
300
What is the square root of √32. Round to the nearest tenths place.
5.7
32 is closer to 36 with a difference of 4, so about 5.7.
√25 = 5
√36 = 6
300
Find the area of a square with side lengths of 9 cm.
a = 81 cm2
300
A 35-foot ladder is leaning against the side of a wall. The base of the ladder is 21 feet from the base of the wall. How far above the ground is the point where the ladder touches the wall.
Hint: start by drawing a picture and finding the right triangle.
a2+b2 = c2
212 + b2 = 352
441 + b2 = 1225
b2 = 1225 - 441
b2 = 784
√b2 = √784
b = 28
The ladder touches the wall 28 feet above the ground.
400
Is 𝜋 (pi) a rational or irrational number?
irrational number - it is a non-terminating decimal and can not be expressed as a fraction
400
Solve for the leg of the right triangle.
leg t = 5
400
(√25)2 = ?
25
400
Find the area of a triangle with a base of 6 cm and a height of 10cm.
a = 30 cm2
400
Claire wants to hang a banner from the second-story window in her house. She needs to find a ladder that, when rested against the outside wall of her house, will be long enough to reach the second-story window. If the window is 16 feet above the ground and Claire places the foot of the ladder 12 feet from the wall, how long will the ladder need to be? (You can use a calculator.)
hint: draw a picture and find the right triangle
a2+b2 = c2
122 +162 = c2
144 + 256 = c2
400 = c2
√400 = √c2
20 = c
The ladder will need to be 20 feet long.
500
List two types of numbers that are rational numbers?
any two of these:
1. Natural numbers
2. Whole numbers
3. Integers
4. Decimals that are repeating or terminating ex: 3.33333 and 0.75)
All of these types of numbers can be expressed as a fraction or ratio and therefore are rational numbers.
500
Solve for the hypotenuse of the right triangle. Round your answer to the nearest tenths place (no calculators)
x = 9.2 m
500
Write out the first 12 perfect squares. (no calculators)
ex:
12 = 1 √1 = 1
22 = 4 √4 = 2
continue ...
12 = 1 √1 = 1
22 = 4 √4 = 2
32 = 9 √9 = 3
42 = 16 √16 = 4
52 = 25 √25 = 5
62 = 36 √36 = 6
72 = 49 √49 = 7
82 = 64 √64 = 8
92 = 81 √81 = 9
102 = 100 √100 = 10
112 = 121 √121 = 11
122 = 144 √144 = 12
500
Find the area of the blue square
82 square units
500
A baseball diamond is a square that is 90 feet on each side. What is the distance a catcher has to throw the ball from home to second base? (You can use a calculator.)
a2+b2 = c2
902 +902 = c2
8100 + 8100 = c2
16,200 = c2
√16,200 = √c2
127.3 = c
The distance from home to second base is 127.3 ft.