Patterns, Functions, & Algebra – Patterns (Notes)
Name Date
I can … / Essential Question:Key Concepts / Notes
Sequence
- Definition
- Definition
- Example
- Definition
- Example
- The owner of a sporting goods store is following a pattern to arrange baseballs into 7 rows for a wall display. The table to the right shows the number of baseballs in the first four rows of this pattern.
- A grocery store has a triangular pyramid of soup cans on display. Steven counts the number of cans in each of the top five layers. Each successive layer continues following the same pattern.
- The table to the right contains the results of a biology experiment.
Section #2 – Patterns/Sequences with Rows
- The first four rows of a number array are shown to the right.
- The first five rows of a number array are shown to the right.
Section #3 – Extended Response Questions
- Nancy decided to breed gerbils to sell to a pet store. She started with 2 gerbils and determined that they should quadruple in number every 4 months. Nancy sold all of the gerbils at the end of 1 year.
- A pattern of shaded and un-shaded squares is shown to the right.
b)Find the number of shaded squares in the 50th figure. Show your work or explain your answer.
- Maria is making a quilt. She has a large piece of fabric that is 0.02 millimeters thick. The fabric is cut in half, and one piece is placed on top of the other to make a pile. The pile is cut half, and then one half is placed on top of the other to make a higher pile.
Summary, Reflection, & Analysis
Patterns, Functions, & Algebra – Patterns (Exercise)
Name Date
- In the sequence …, 1, 4, 16, 64, … , determine what the pattern is and then find the next 3 terms.
- In the sequence …, 4, - 1, - 6, - 11, … , determine what the pattern is and then find the next 3 terms.
- Suppose the pattern of dots continues infinitely with more dots being added at each step. Determine a formula for the number of dots for the “n”th step. How many dots will be in step 14?
- A large corporation uses a telephone chain to notify employees of company closings due to bad weather. The plant manager calls 5 people in the first round of the telephone chain. Each of those people calls 5 other people in the second round of the telephone chain. If the pattern continues, how many employees are called in the 4th round of the telephone chain?
- The depth of a lake is measured at the same location and on the same day every year for a number of years. The table below shows the measurements.
If the pattern continues, what will be the depth
of the lake in 2003?
- Last spring, the employees of an Akron tire company contributed to a local charity. The graphic represents the total dollar contributions as of several dates in April.
Determine on what date the charity could have expected
to reach its goal of $1,000 if the pattern of donations remains
about the same. Provide an explanation as to how you arrived
at that answer.
- The first five rows of a number array are shown below.
What is the sum of the numbers in row 9?
- Mr. Abraham was given a special offer by the bank. They told him that if he opened a savings account and put $1 on it, they would promise that it would triple at the end of every year. Assuming this pattern continues, how many years will it take Mr. Abraham to turn his $1 into $50,000?