Embedded Files
Lesson Video
Lesson Video
Focus Standards
Focus Standards
Learning Focus
Learning Focus
Additional Resources
Additional Resources
A Developing Understanding Task
Prepares students to model visual patterns with variables and to discuss math together.
Use variables to describe ways of seeing a pattern.
When I look at a pattern, how can I describe what’s changing and what’s staying the same?
Can seeing groups help in understanding diagrams?
How do variables express the way we see patterns?
A Develop Understanding Task
Introduces arithmetic sequences, recursive thinking, and common difference by modeling a pattern that starts with n = 0 with tables, graphs, and equations.
NC.M1.A-CED.2
NC.M1.A-SSE.1
NC.M1.A-SSE.1.a
NC.M1.A-SSE.1.b
NC.M1.F-BF.1
NC.M1.F-BF.1.a
NC.M1.F-BF.2
NC.M1.F-IF.2
Describe a growing pattern with tables, graphs, and equations.
How does the pattern change from one figure to the next?
How can I use a mathematical representation to show how I see a pattern?
A Develop Understanding Task
Introduces geometric sequences, recursive thinking, and common ratio by modeling a pattern that starts with n = 0 with tables, graphs, and equations.
NC.M1.A-CED.2
NC.M1.A-SSE.1
NC.M1.A-SSE.1.a
NC.M1.A-SSE.1.b
NC.M1.F-BF.1
NC.M1.F-BF.1.a
NC.M1.F-BF.2
NC.M1.F-IF.2
Model a sequence of figures using tables, graphs, and equations.
How can I label the diagram to show how I see the pattern?
How can I use mathematical representations to show how I see the pattern changing?
A Solidify Understanding Task
Solidifies common difference and extends recursive thinking to writing a recursive equation for an arithmetic sequence. Models a story context that begins with n = 1 with tables, graphs, and equations.
NC.M1.A-CED.2
NC.M1.A-SSE.1
NC.M1.A-SSE.1.a
NC.M1.A-SSE.1.b
NC.M1.F-BF.1
NC.M1.F-BF.1.a
NC.M1.F-BF.2
NC.M1.F-LE.1
Model a sequence using a table, graph, and explicit and recursive equations.
How do I see the change between figures in each representation?
How can I tell if a sequence is arithmetic, geometric, or neither?
How are explicit equations different than recursive equations?
What are the advantages of using an explicit equation versus a recursive equation?
A Solidifying Understanding Task
Solidifies common ratio and extends recursive thinking to writing a recursive equation for a geometric sequence. Models a story context that begins with n = 1 with tables, graphs, and equations.
NC.M1.A-CED.2
NC.M1.A-SSE.1
NC.M1.A-SSE.1.a
NC.M1.A-SSE.1.b
NC.M1.F-BF.1
NC.M1.F-BF.1.a
NC.M1.BF.2
Represent a story context using tables, graphs, and equations.
Use function notation to write explicit and recursive equations.
How can I find the pattern of growth in a story context?
How does the pattern of growth appear in each of the representations?
Lesson 6: Home on the Range
Lesson 6: Home on the Range
A Solidify Understanding Task
Extends conceptual understanding of arithmetic and geometric sequences, including decreasing sequences of both types. Extends skill in writing equations for geometric sequences by using a percent decrease.
Understand the characteristics that make sequences decrease.
Compare decreasing arithmetic and geometric sequences.
What makes an arithmetic sequence decrease?
How can a geometric sequence be decreasing?
How are equations of decreasing sequences different than increasing sequences?
A Practice Understanding Task
Builds fluency in distinguishing between arithmetic and geometric sequences and in using tables to write recursive and explicit equations.
Determine if a sequence is geometric, arithmetic, or neither.
Write recursive and explicit equations for arithmetic and geometric sequences.
How can I efficiently use the information in a table to write formulas for arithmetic and geometric sequences?
A Solidify Understanding Task
Solidifies understanding of common difference by finding missing terms in an arithmetic sequence.
Find missing terms in an arithmetic sequence.
What patterns do I recognize in arithmetic sequences that can help to find missing terms?
A Solidify Understanding Task
Solidifies understanding of common ratio by finding missing terms in a geometric sequence.
Apply understanding of geometric sequences to find missing terms.
How can I find missing terms in a geometric sequence?
What equations can help find missing terms in a geometric sequence?
A Practice Understanding Task
Builds fluency and flexibility in distinguishing between arithmetic and geometric sequences, using all representations and finding missing terms. Contains all skills and conceptual understanding in the unit.
Identify the type of sequence given any representation.
Find efficient strategies for representing sequences with tables, graphs, and equations, both explicit and recursive.
What conclusions can be drawn about a sequence, given just a few pieces of information?
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