Unit 1 Sequences

Lesson 1

Learning Focus

Use variables to describe ways of seeing a pattern.

Lesson Summary

In this lesson, we found ways to see patterns in diagrams that help us to be efficient in counting. We modeled these patterns using variables to show how the pattern would work for any number of squares.

Lesson 2

Learning Focus

Describe a growing pattern with tables, graphs, and equations.

Lesson Summary

In this lesson, we modeled a pattern using tables, graphs, equations, and diagrams. We found that this type of relationship is called an arithmetic sequence. We used recursive and explicit ways of thinking about functions, and learned to describe the relationship between inputs and outputs using function notation.

Lesson 3

Learning Focus

Model a sequence of figures using tables, graphs, and equations.

Lesson Summary

In this lesson, we modeled a growing pattern using tables, graphs, and equations. We learned about a new type of function, a geometric sequence that has a common ratio between terms.

Lesson 4

Learning Focus

Model a sequence using a table, graph, and explicit and recursive equations.

Lesson Summary

In this lesson, we modeled a real-world situation with a table, graph, and equations, both explicit and recursive. We learned the mathematical notation for writing recursive equations and how to identify the common difference in each of the representations.

Lesson 5

Learning Focus

Represent a story context using tables, graphs, and equations.

Use function notation to write explicit and recursive equations.

Lesson Summary

In this lesson, we modeled a real-world situation with a table, graph, and equations, both explicit and recursive. We learned to use the mathematical notation for writing recursive equations for geometric sequences and how to identify the common ratio in each of the representations of a geometric sequence.

Lesson 6

Learning Focus

Understand the characteristics that make sequences decrease.

Compare decreasing arithmetic and geometric sequences.

Lesson Summary

In today’s lesson, we modeled a real context with arithmetic and geometric sequences. We found that some arithmetic and geometric sequences decrease. Whether a sequence increases or decreases depends on the common difference or common ratio between terms. Additionally, we used tables, equations, and graphs to compare the behavior of decreasing arithmetic and geometric sequences.

Lesson 7

Learning Focus

Determine if a sequence is geometric, arithmetic, or neither.

Write recursive and explicit equations for arithmetic and geometric sequences.

Lesson Summary

In this lesson, we described the pattern of growth for arithmetic and geometric sequences and wrote recursive and explicit equations to model the sequences. We learned to identify the first term and common difference or common ratio in both the explicit and recursive forms of equations, and we developed a process for writing equations for sequences.

Lesson 8

Learning Focus

Find missing terms in an arithmetic sequence.

Lesson Summary

In this lesson, we found missing terms in an arithmetic sequence using several methods. We developed a formula that allows us to find the common difference for any arithmetic sequence when two terms are known. We also found an equation that can be used to find any term in an arithmetic sequence.

Lesson 9

Learning Focus

Apply understanding of geometric sequences to find missing terms.

Lesson Summary

In this lesson, we found missing terms in a geometric sequence using several methods. We developed a process for finding the common ratio for any geometric sequence when two terms are known. We also found an equation that can be used to find the common ratio and any term in an arithmetic sequence.

Lesson 10

Learning Focus

Identify the type of sequence given any representation.

Find efficient strategies for representing sequences with tables, graphs, and equations, both explicit and recursive.

Lesson Summary

In this lesson, we found efficient strategies for identifying and representing arithmetic and geometric sequences, whatever information is given. We sharpened our skills in finding the first term and common difference or common ratio in any representation and how to use one representation to find another.