Transcript In Word Problems Back of WS #2 – Problem #8

th
8
Grade Math
1st Period
Nov. 5, 2012
You have 7 min.
to complete your Do Now! Quiz
•
•
•
•
You MUST show your work
You may use a calculator
You may use your notes
You may NOT talk
HW Review on 11-7 PowerPoint
Warm-Up
At Emmit’s Evergreen
Farm, the taller trees are
braced by wires. A wire
extends from 2 feet below
the top of a tree to a stake
in the ground. What is the
tallest tree that can be
braced with a 25-foot wire
staked 15 feet from the
base of the tree?
Warm-Up: Answer
At Emmit’s Evergreen
Farm, the taller trees are
braced by wires. A wire
extends from 2 feet below
the top of a tree to a stake
in the ground. What is the
tallest tree that can be
braced with a 25-foot wire
staked 15 feet from the
base of the tree?
18
ft
Using The Pythagorean Theorem
In Word Problems
Back of WS #2 – Problem #8:
What is the length of the diagonal of a 10 cm by
15 cm rectangle?
Draw a picture:
Using the Pythagorean Theorem
Looking for length of
the hypotenuse
a2 + b2 = c2
102 + 152 = x2
100 + 225 = x2
325 = x2
325 = 𝑥 2
18.028 ≈ 𝑥
The diagonal of a 10
cm by 15 cm rectangle
is approx. 18.028 cm.
Using The Pythagorean Theorem
In Word Problems
Back of WS #2 – Problem #9:
The diagonal of a rectangle is 25 in. The width is
15 in. What is the length?
Draw a picture:
Using the Pythagorean Theorem
Looking for length of
a leg
a2 + b2 = c2
x2 + 152 = 252
x2 + 225 = 625
-225 -225
x2 = 400
𝑥 2 = 400
x = 20
The length of the
rectangle is 20 in.
You Try!
Back of WS #2 – Problems #10-15
• For Problem #15, fill in the following picture:
HW
• Back of WS #2 – Problems #10-15
• Front of WS #2 – Problems #1-7 (if you haven’t
completed it already)
• Tomorrow’s Do Now! Quiz will have:
– Four Pythagorean Theorem word problems
th
8
Grade Math
2nd Period Only
Nov. 5, 2012
You have 7 min.
to complete your Do Now! Quiz
•
•
•
•
You MUST show your work
You may use a calculator
You may use your notes
You may NOT talk
HW Review on 11-7 PowerPoint
No Warm-Up
Using The Pythagorean Theorem
In Word Problems
Back of WS #2 – Problem #8:
What is the length of the diagonal of a 10 cm by
15 cm rectangle?
Draw a picture:
Using the Pythagorean Theorem
Looking for length of
the hypotenuse
a2 + b2 = c2
102 + 152 = x2
100 + 225 = x2
325 = x2
325 = 𝑥 2
18.028 ≈ 𝑥
The diagonal of a 10
cm by 15 cm rectangle
is approx. 18.028 cm.
Using The Pythagorean Theorem
In Word Problems
Back of WS #2 – Problem #9:
The diagonal of a rectangle is 25 in. The width is
15 in. What is the length?
Draw a picture:
Using the Pythagorean Theorem
Looking for length of
a leg
a2 + b2 = c2
x2 + 152 = 252
x2 + 225 = 625
-225 -225
x2 = 400
𝑥 2 = 400
x = 20
The length of the
rectangle is 20 in.
You Try!
Back of WS #2 – Problems #10-15
• For Problem #15, fill in the following picture:
Remediation: Using Square Roots &
Cube Roots to Solve Equations
Solve 𝑥 2 = 64.
• Option 1: Think, “What squared gives me 64?”
– Remember: Squaring is multiplying something by
itself 2 times. For example, 52 = 5 ∙ 5.
• Option 2: Think, “x is being squared; how do I
undo squaring?”
• Either way, the answer is 8 = 64.
Remediation: Using Square Roots &
Cube Roots to Solve Equations
Solve 𝑥 2 = 35.
• Option 1: Think, “What squared gives me 35?”
– However, you can’t square a whole number or a
fraction to give you 35.
– Use Option 2 instead.
• Option 2: Think, “x is being squared; how do I
undo squaring?”
• The answer is 35.
FYI
Unless the problems says otherwise:
• You may leave irrational answers as square
roots in traditional Pythagorean Theorem
problems (not word problems).
• You should give numerical approximations of
irrational answers in Pythagorean Theorem
word problems; round to the number of
decimal places specified in the directions.
Remediation: Using Square Roots &
Cube Roots to Solve Equations
Solve 𝑥 3 = 64.
• Option 1: Think, “What cubed gives me 64?”
– Remember: Cubing is multiplying something by
itself 3 times. For example, 53 = 5 ∙ 5 ∙ 5.
• Option 2: Think, “x is being cubed; how do I
undo cubing?”
• Either way, the answer is 4 =
3
64.
Remediation: Using Square Roots &
Cube Roots to Solve Equations
Solve 𝑥 3 = 20.
• Option 1: Think, “What cubed gives me 20?”
– However, you can’t cube a whole number or a
fraction to give you 20.
– Use Option 2 instead.
• Option 2: Think, “x is being cubed; how do I
undo cubing?”
3
• The answer is 20.
HW
• Back of WS #2 – Problems #10-15
• Front of WS #2 – Problems #1-7 (if you haven’t
completed it already)
• Tomorrow’s Do Now! Quiz will have:
– Two equations you need to solve by square
rooting or cube rooting
– Two Pythagorean Theorem word problems
th
8
Grade Math
4th Period
Nov. 5, 2012
You have 7 min.
to complete your Do Now! Quiz
•
•
•
•
You MUST show your work
You may use a calculator
You may use your notes
You may NOT talk
HW Review on 11-7 PowerPoint
Warm-Up
At Emmit’s Evergreen
Farm, the taller trees are
braced by wires. A wire
extends from 2 feet below
the top of a tree to a stake
in the ground. What is the
tallest tree that can be
braced with a 25-foot wire
staked 15 feet from the
base of the tree?
Warm-Up: Answer
At Emmit’s Evergreen
Farm, the taller trees are
braced by wires. A wire
extends from 2 feet below
the top of a tree to a stake
in the ground. What is the
tallest tree that can be
braced with a 25-foot wire
staked 15 feet from the
base of the tree?
18
ft
Using The Pythagorean Theorem
In Word Problems
Back of WS #2 – Problem #8:
What is the length of the diagonal of a 10 cm by
15 cm rectangle?
Draw a picture:
Using the Pythagorean Theorem
Looking for length of
the hypotenuse
a2 + b2 = c2
102 + 152 = x2
100 + 225 = x2
325 = x2
325 = 𝑥 2
18.028 ≈ 𝑥
The diagonal of a 10
cm by 15 cm rectangle
is approx. 18.028 cm.
Using The Pythagorean Theorem
In Word Problems
Back of WS #2 – Problem #9:
The diagonal of a rectangle is 25 in. The width is
15 in. What is the length?
Draw a picture:
Using the Pythagorean Theorem
Looking for length of
a leg
a2 + b2 = c2
x2 + 152 = 252
x2 + 225 = 625
-225 -225
x2 = 400
𝑥 2 = 400
x = 20
The length of the
rectangle is 20 in.
You Try!
Back of WS #2 – Problems #10-15
• For Problem #15, fill in the following picture:
HW
• Back of WS #2 – Problems #10-15
• Front of WS #2 – Problems #1-7 (if you haven’t
completed it already)
• Tomorrow’s Do Now! Quiz will have:
– Four Pythagorean Theorem word problems
Common Core Math I
5th Period
Nov. 5, 2012
HW Review:
How to Estimate a Line of Best Fit
• Sketch a straight line that
runs as close to as many
data points as possible.
• Estimate the coordinates of
two points on your line, and
use them to write your line’s
rule (y = mx + b form).
– (0, 0) and (6, 2)
– 𝑚=
∆𝑦
2−0
=
∆𝑥
6−0
1
𝑥+b
3
– 𝑦=
– (0, 0)  b = 0
1
3
– 𝑦= 𝑥
2
6
= =
1
3
HW Review: Practice
• Sketch a straight line that
runs as close to as many data
points as possible.
• Estimate the coordinates of
two points on your line, and
use them to write your line’s
rule (y = mx + b form).
– (0, 50) and (800, 150)
– 𝑚=
∆𝑦
150−50
=
∆𝑥
800−0
1
𝑥+b
8
– 𝑦=
– (0, 50)  b = 50
1
8
– 𝑦 = 𝑥 + 50
=
100
800
=
1
8
No Warm-Up
Notes: Using Linear Models to Predict
Given that your best fit
1
line is 𝑦 = 𝑥:
3
• What shadow location
would you predict
when the flag height is
12 feet? 25 feet?
– Graphical answers (see
right)
– Algebraic answers: 𝑦 =
1
12 = 4
3
1
25
1
𝑦 = 25 =
=8
3
3
3
Notes: Using Linear Models to Predict
Given that your best fit line is
1
𝑦 = 𝑥:
3
• What flag height would
locate the flag shadow 6.5
feet from the base of the
pole? 10 feet from the base
of the pole?
– Graphical answers (see
right)
– Algebraic answers: 6.5 =
1
𝑥
3 6.5 =
3 1
3( 𝑥)
19.5 = x
3
1
3
10 = 𝑥
1
3 10 = 3( 𝑥)
3
30 = x
Practice:
Using Linear Models to Predict
Given that your best fit
1
line is 𝑦 = 𝑥 + 50:
8
• Predict the flight
time for westbound
flights 1200 miles in
distance.
• Predict the distance
for westbound
flights with 12 hours
of flight time.
Practice:
Using Linear Models to Predict
Given that your best fit line is
1
𝑦 = 𝑥 + 50:
8
• Use your rule to predict
the flight time for
westbound flights 1200
miles in distance.
– 𝑦=
200
1
8
1200 + 50 =
• Use your rule to predict
the distance for
westbound flights with
12 hours of flight time.
– 720 =
5360
1
𝑥
8
+ 50  x =
CW/HW
• CW: "CW/HW: Using Linear Models to
Predict"