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: