Lesson: Arithmetic and geometric patterns

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Lesson Objective

I can recognize the difference between arithmetic and geometric patterns, and create a rule about the sequences

Lesson Plan


6.PRA.8 - Recognize when information given in a table, graph, or formula suggests a proportional or linear relationship.

6.PRA.9 - Produce and interpret graphs that represent the relationship between two variables (x and y) in everyday situations


Essential Question

SWBAT recognize the difference between arithmetic and geometric patterns, and create a rule about the sequences with 80% accuracy.

Explain how patterns suggest a relationship. What kind of relationships do they suggest? Justify.


Lesson Agenda

Agenda Item/ Time (Board Configuration)

 5 E’s

Learning Activities



Teacher will do…

Students will do …

10 minutes

Daily Math Review (Warm-Up/ Do Now)

Please fill in the missing item on each line     


  1. 1  3  5  7 _______ 11


  1. 7 ______ 21   28   35   42


  1. 1  2  3  5  8 _______


Silently complete Do Now

5 minutes

Mental Math

Verbally give students the Mental Math Problem

Respond verbally with an answer

5 minutes



Begin a monologue on patterns.  Patterns such as 3, 6, 9, 12- are familiar to us since they are among the patterns you first learn as young students


As you advance, you will experience number patterns again through the huge concepts of functions in math


Today we will explore arithmetic and geometric patterns


Engage in the conversation and give examples of simple patterns





10 minutes



Explore (Conceptual Development)

Provide 8 examples of sequences

Complete the 8 sequence problems given to them



10 minutes



(Guided Practice)

Explain the difference between a arithmetic pattern and geometric patterns.  Arithmetic means we are either adding or subtracting in each sequence, and geometric means we are either multiplying or dividing in the pattern

Actively listening and taking notes


25 minutes



Extend/ Elaborate


Set up 6 work stations for students to circulate through


Divide the students into groups of 5

Rotate through work stations to observe patterns in different situations


They are to determine the following: 

  1. Is the pattern arithmetic and geometric?
  2. What is the pattern specifically doing?
  3. What will the next two numbers in the sequence be?


10 minutes




(Assessment/ Closure)

Give the students the following Exit Slip:

  1. What will be the 7th number in this sequence?

1, 3, 9, 27, 8

2.  The rule for a pattern is “multiply a number by 2, then add 1.”  If the first number in the sequence is 0, what are the next five numbers in the sequence?

3.  What rule determines the next number in this sequence?

2, 6, 18, 54, 162

Write an algebraic expression to describe the rule.


Discuss their results from their findings and summarize it to turn in


MCAS Finish Line (6th grade) Pg. 122- Patterns


Arithmetic and geometric patterns


Lower Level Learners:  Find the next three terms in each sequence and give the rule.

2, 5, 8, 11

1, 10, 100

10, 9, 8, 7

Lesson Resources

6 PRA 8 geometric arithmeticseq    Combination


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