Name:
Date:
Period:
Geometry and Measurements
Pythagorean Theorem/ Midpoint-Distance Formulas/
Rates and Measurements
Lesson: A-12/ A-9 / 2-7/5-5/4-6/11-1
Mini Packet
Tennessee State Standard
Common Core State Standards
F-LE-2 Construct linear and exponential functions,
including arithmetic and geometric sequences,
given a graph, a description of a relationship, or
two inputoutput pairs (include reading these from a
table).
SPI 3102.4.3 Solve problems involving the distance
between points or midpoint of a segment.
FIF-3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a
subset of the integers. For example, the Fibonacci
sequence is defined recursively by f(0) = f(1) = 1,
f(n+1) = f(n) + f(n1) for n ≠ 1.
SPI 3102.4.4 Convert rates and measurements.
SPI 3102.1.1 Interpret patterns found in sequences,
tables, and other forms of quantitative information
using variables or function notation.
SPI 3102.4.2 Solve contextual problems using the
Pythagorean Theorem.
Name:
Date:
Lessons Covered: A-12
Pythagorean Theorem
Period:
Additional Topic
Objective: TSW use the
Pythagorean theorem to find an
unknown side in a right triangle.
Pythagorean Theorem
Formula:
Diagram:
Find c (Hypotenuse)
Examples:
Find a or b (legs
Examples:
What do I do?
What do I do?
John leaves school to go home. He walks 6 blocks North and then 8 blocks east. How far is John from the
school?
Name:
A-12
Date:
Pythagorean Theorem
Period:
Additional Topics
Part A
a = 9 b = 40 c=
a = 10 b = 24 c=
a = 8 b = c=17
The sail of a sailboat is in the
shape of a right triangle. The
hypotenuse is 24 feet long and
the leg along the boat measures
15 ft. What is the height of the
sail to the nearest foot?
a = b = 8 c=10
Tanner and Steven are walking to
Dunkin’ Donuts from their house.
They start out by walking 9
blocks east and 12 blocks south.
What is the distance from their
house to Dunkin’ Donuts?
A 13 feet ladder is placed 5 feet
away from a wall. The distance
from the ground straight up to the
top of the wall is 13 feet Will the
ladder the top of the wall?
Name:
Date:
Period:
Part B
a =13 b = c=20
The slide at the playground has
a height of 6 feet. The base of
the slide measured on the
ground is 8 feet. What is the
length of the sliding board?
The pool table at the Shanks
household has a rectangular
playing surface that is 88 inches
long and 44 inches wide? A
person makes a shot from one
corner of the table to the
opposite corner. What is the
length of the shot?
a =6 b = c=18
a =22 b = 31 c=
a = b = 15 c=19
A baseball “diamond” is actually
a square with sides of 90 feet. If
a runner tries to steal second base,
how far must the catcher, at home
plate, throw to get the runner
“out”? Given this information,
explain why runners more often
try to steal second base than third.
Name:
Lessons Covered: 5-5
Objective: TSW apply the formula for
midpoint and use the distance formula
to find the distance between two points.
Finding the coordinates of a
Midpoint.
Find the coordinates of the
midpoint of CD with endpoints
C(-2,-1) and D(4,2).
Date:
Period:
5-5
The Midpoint and Distance
Formulas
Finding the coordinates of
an endpoint.
M is the midpoint of AB. A has
coordinates (2,2) and M has
coordinates (4,-3). Find the
coordinate of B.
Find the distance between
the two points.
Find the distance from point
A(-2,3) to B(2,-2) .
Name:
Date:
Period:
Part A
Find the coordinates of the midpoint of each segment.
AB with endpoints A(5, 4 ) and
B(9, 8)
JK with endpoints J 2,  1
and K 8, 6 
RS with endpoints R 3, 2 
and S 1,  6 
Find the coordinate of the endpoint of each segment.
M is the midpoint of AB. A(-2,9)
and M( 2,5). Find the coordinate
of B.
T is the midpoint of SY. Y (7,-3)
and T (4,4). Find the coordinate
of S.
N is the midpoint of PQ. P (-5,-6)
1 3
and N (− , ). Find the
2 4
coordinate of q.
Use the Distance Formula to find the distance, to the nearest tenth, between each pair of points.
W(1, 14) and Y(5, 6)
M 3, 5  and B 4,  2 
G 4,  9  and H 0, 8 
Name:
Date:
Period:
Part A
Find the coordinates of the midpoint of each segment.
1. AB with endpoints A(2, 1) and B(8, 3)
2. CD with endpoints C(0, 5) and D(6, 1)
3. EF with endpoints E 3,4  and F(9, 4)
4. M is the midpoint of AB . A has coordinates (3, 6), and M has coordinates (7, 4).
Find the coordinates of B.
5. M is the midpoint of DE . D has coordinates (9, 2), and M has coordinates (5, 2).
Find the coordinates of E.
Use the Distance Formula to find the distance, to the nearest tenth, between each pair of points.
6.A(1, 1) and B(4, 5)
7.C(4, 1) and D(8, 3)
8. E( 2 , 5) and F(3, 9)
Name:
Date:
Lessons Covered 4-6/11-1
Objective: TSW recognize
sequences and find a given term of
a sequence
Skills Covered: Identify arithmetic
and geometric sequences; find a
given term of a sequence
Vocabulary
Sequence: ___________________________________________________
Term: ___________________________________________
a1: _________________a2: ___________________
a3: _________________an: ___________________ where n= ___________________
Period:
Functions
Name:
Lessons Covered 4-6/11-1
Objective: TSW recognize
sequences and find a given term of
a sequence
Part A
1. Is the sequence
9, 13, 17, 21, … arithmetic? If so,
find the common difference and
the next 3 terms.
Date:
Skills Covered: Identify arithmetic
and geometric sequences; find a
given term of a sequence
Period:
Functions
2. Is the sequence
10, 8, 5, 1, … arithmetic? If so,
find the common difference and
the next 3 terms.
3. Find the 16th term of the
arithmetic sequence:
4, 8, 12, 16, …
4. Find the 25th term of the
arithmetic sequence with
a1 = -5 and d = -2.
5. Find the 15th term of the
arithmetic sequence:
1 3 5 7
, , , ,…
4 4 4 4
6. A bag of cat food weighs 18
pounds at the beginning of day
1. Each day, the cats are fed 0.5
pounds of food. How much does
the bag of cat food weigh at the
beginning of day 30?
7. Find the next 3 terms of the
geometric sequence:
1
1
−9,3, −1, 3, −9, …
8. What is the 9th term of the
sequence?
2, -6, 18, -54, ….
9. List the first 4 terms of the
sequence given by
𝑎𝑛 = 3(2)𝑛−1 . Is the sequence
arithmetic, geometric, or
neither? Explain.
Name:
Lessons Covered 4-6/11-1
Objective: TSW recognize
sequences and find a given term of
a sequence
Date:
Period:
Skills Covered: Identify arithmetic
and geometric sequences; find a
given term of a sequence
Functions
Part B
1. List the first 4 terms of the
sequence given by:
𝑎𝑛 = −2(4)𝑛−1 . Is the
sequence arithmetic or
geometric? Explain.
2. List the first 4 terms of the
sequence given by:
𝑎𝑛 = 5𝑛 + 1. Is the sequence
arithmetic or geometric?
Explain.
3. Find the 11th term of the
sequence:
3, 6, 12, 24, ….
4. Find the 15th term of the
geometric sequence with
a1 = -5 and r = -2.
5. Find the 15th term of the
sequence:
2.5, 8.5, 14.5, 20.5, …
6. Write a formula to the nth
term of the sequence:
-22, -31, -40, -49, …
7. The first row of a concert
hall has 6 seats. Each row
afterwards has 3 more seats
than the one before it. How
many seats are in the 15th row?
Write a rule for the sequence.
8. Billy earns money by mowing lawns each summer. He offers
2 payment plans. Plan 1 is to pay $150 for the entire summer.
Plan 2 is to pay $1 the first week, $2 the second week, $4 the
third week, $8 the fourth week, and so on. If you were one of
Billy’s customers, which plan would you choose if the summer
is 10 weeks long? Explain your choice.
Name:
Date:
Lessons Covered: 2-7 & A-9
Objective: TSW convert rates
and measurements within
systems and between systems.
Period:
Additional Topics
Converting Rates and
Measurements
RAIL ROAD TRACKS
Start with
numerator of
what you
want to find
This track will
be a
conversion
fact
This track has
the same
units as the
previous
bottom
This track will
be a
conversion
fact
This track has
the same
units as the
previous
bottom
This track will
be a
conversion
fact
Multiply
straight
across
Only thing
left is units
that you
want
Divide the top
by bottom to
achieve final
answer
Units that are
the same
should be
eliminated
Repeat as
many tracks
as necessary
End with
denominator
of what you
want to find
When dealing with square or cubic units (sqft/sqyds/ cm2) you must square or
cube the conversion facts.
Convert: 3 quarts to ounces
Convert: 10 sq.yds. to sq.cm.
Conversions
1 hour = 3600 seconds
1 meter = 3.28 feet
1 kg = 2.2 lbs
1 m/s = 2.2 miles/hour
1 mile = 5280 feet
1 km = 0.62 miles
1 lb = 0.45 kg
1 foot = 12 inches
1 yard = 3 feet
1 light second = 300,000,000 meters
1 quart = 0.946 liters
1 inch = 2.54 cm = 25.4 mm
Name:
Date:
Part A
Directions: Convert each set of units.
1. 100 yards to feet.
2. 20 hours to minutes.
3. 3 weeks to hours.
4. 150 seconds to minutes.
5. 2 miles to yards.
6. 1 year to minutes.
7. 60 miles
feet
sec
hr to
8. 7 gallons/hour to liters/second
Period:
Name:
Date:
Part B
9. 565,900 seconds into days
10. 17 years into minutes
11. 43 miles into feet
12. 165 pounds into kilograms
13. 22,647 inches into miles
14. 186,282 meters/ second into miles/ second
15. 27 miles/gallon into kilometers/ liter
16. 10 square feet to square meters
17. 2 square yards to square inches
Period: