PATTERNS ALL AROUND US – Integrated Math 1.5
Find arithmetic and geometric sequences in the world around you, be it in
nature, the media, etc. You will need to find 3 examples of geometric
sequences and 3 examples of arithmetic sequences. You need to represent
them visually, algebraically (explicit and recursive relationship in function
notation) and numerically. You will need to interpret the first common ratio
and first common difference in the context of the problem and demonstrate
how the formulas generate the sequence.
Requirements for the Project:
o An image/video that describes the sequences
o An explicit AND recursive relationship in function notation
o A table for the sequences
o A graph for the sequences using www.desmos.com
o An explanation of the first common ratio and first common difference and
demonstrate how the formulas generate the sequence.
Due date requirements:
 You must carry and have this project instruction page with you at all times.
Tentative schedule
Monday
Tue
December 1
Wednesday
2
Pick 3 real life arithmetic
and geometric sequence.
A total of 6 sequences.
9
Create presentation
using google drive.
Share with Mr. Wu
Thurs
3
Create table and write the
6 recursive and explicit
arithmetic and geometric
equations for your
examples.
10
Create presentation using
google drive. Share with
Mr. Wu
Friday
4
Create table and write
the 6 recursive and
explicit arithmetic and
geometric equations for
your examples.
11
Create presentation
using google drive. Share
with Mr. Wu
7
Write 6
explanations
for your
arithmetic and
geometric
sequences.
8
Write 6
explanations
for your
arithmetic and
geometric
sequences.
Christian.wu@bayfront
charter.com
Christian.wu@bayfrontch
arter.com
Christian.wu@bayfrontc
harter.com
Graph all 6
sequences.
14
Practice
Presentation
Graph all 6
sequences.
15
16
17
18
Grading Rubric: (20% of grade)
Postings of Pattern All Around Us
5-4
Deadline
Met all deadlines: Check in dates AND due
date. Class time was used wisely. Much
time and effort went into the planning and
design. It is clear the student worked at
home as well as at school.
Pages
Images: All images/videos are related to
the topic and make it easier to
understand.
Explanation: Explanation is detailed and
clear. Correct terminology and notation are
always used, making it easy to
understand what was done. Explanation
shows complete understanding of the
mathematical concepts used to solve the
problem(s).
Accuracy: 90-100% of the functions are
without mathematical errors
Graph: All units are described (in a key or
with labels) and are appropriately sized
for the data set. Graph fits the data well
and makes it easy to interpret. Title is
creative and clearly relates to the problem
being graphed (includes dependent and
independent variable). It is printed at the
top of the graph. The X axis has a clear, neat
label that describes the units used for the
independent variable (e.g, days, months,
participants’ names). The Y axis has a clear,
neat label that describes the units and the
dependent variable (e.g, % of dogfood
eaten; degree of satisfaction).
3-2
Missed one, two, or three deadlines.
Class time was used wisely. Student
could have put in more time and
effort at home.
Images: All images/video relate to the
topic.
Explanation: Explanation is a little
difficult to understand, but
includes critical components.
Correct terminology and notation are
used, but it is sometimes not easy
to understand what was done.
Explanation shows some
understanding of the mathematical
concepts needed to solve the
problem(s).
Accuracy: Most of the functions (75 –
89%) are without mathematical
errors.
Graph: All units are described (in a
key or with labels) but are not
appropriately sized for the data
set. Graph distorts the data
somewhat and interpretation of the
data is somewhat difficult. A title is
present at the top of the graph. The X
axis and Y axis has a label.
Table: Data in the table is accurate
and easy to read.
Table: Data in the table is well organized,
accurate, and easy to read.
Presentation – (5% of grade)
10-8
Presentation
□ You were present on the day
of the presentation.
□ Shows a full understanding
of the topic.
□ Stands up straight, looks
relaxed and confident.
Establishes eye contact with
everyone in the room during
the presentation.
□ Facial expressions and body
language generate a strong
interest and enthusiasm
about the topic in others.
□ Listens intently. Does not
make distracting noises or
movements.
7- 3
□ You were present on the day of the
presentation.
□ Shows a good understanding of
parts of the topic.
□ Sometimes stands up straight and
establishes eye contact.
□ Facial expressions and body
language are used to try to generate
enthusiasm, but seem somewhat
faked.
□ Sometimes does not appear to be
listening but is not distracting.
Name: _____________________________________________________ Per: _____
1-0
Missed all deadlines: Check in
AND due date. Class time was
not always used wisely, but
student did do some additional
work at home.
Images: Images/video do not
relate to the topic.
Explanation: Explanation is
difficult to understand and is
missing several components
OR was not included. There is
little use, or a lot of
inappropriate use, of
terminology and notation.
Explanation shows very
limited understanding of the
underlying concepts needed to
solve the problem(s) OR is not
written.
Accuracy: Some/None of the
functions (0-75%) are without
mathematical errors.
Graph: Units are neither
described NOR
appropriately sized for the
data set. Graph seriously
distorts the data making
interpretation almost
impossible. A title is not
present. The X axis and Y axis
is not labeled.
Table: Data in the table is not
accurate and/or cannot be
read.
2-0
□ You were present/not present
on the day of the presentation.
□ Does not seem to understand
the topic very well.
□ Slouches and/or does not look
at people during the
presentation.
□ Very little use of facial
expressions or body language.
Did not generate much interest
in topic being presented.
□ Sometimes does not appear to
be listening and has distracting
noises or movements.
Patterns All Around Us Project
This organizer is to help you with collecting data for your project. Since this worksheet is to be completed in a span
of two weeks, it is important to be organized with the information that you find. The letters are in order for a
specific reason. Your first assignment is to complete all the sections with the letter A. Your second assignment is to
complete all the sections with the letter B, then the third, C, the fourth, D.
Write down 3 examples of arithmetic sequence in real life. Specify the common difference. Write the recursive and
explicit formula.
EXAMPLE
A) Arithmetic sequence in real life:
A) Common difference:
B) Explicit formula:
C) Recursive formula:
E) Explanation on how you got your explicit
and recursive formula:
A) Arithmetic sequence in real life:
A) Common difference:
B) Explicit formula:
C) Recursive formula:
E) Explanation on how you got your explicit
and recursive formula:
A) Arithmetic sequence in real life:
A) Common difference:
B) Explicit formula:
C) Recursive formula:
E) Explanation on how you got your explicit
and recursive formula:
Write down 3 examples of geometric sequence in real life. Specify the common ratio. Write the recursive and
explicit formula.
EXAMPLE
A) Geometric sequence in real life:
A) Common difference:
B) Explicit formula:
C) Recursive formula:
E) Explanation on how you got your explicit
and recursive formula:
A) Geometric sequence in real life:
A) Common difference:
B) Explicit formula:
C) Recursive formula:
E) Explanation on how you got your explicit
and recursive formula:
A) Geometric sequence in real life:
A) Common difference:
B) Explicit formula:
C) Recursive formula:
E) Explanation on how you got your explicit
and recursive formula: