ALEX Resources

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Learning Activities (3) Building blocks of a lesson plan that include before, during, and after strategies to actively engage students in learning a concept or skill. Classroom Resources (3)

ALEX Learning Activities  
   View Standards     Standard(s): [MA2019] FM-19 (9-12) 11 :
11. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Examples: fractals, population growth
Subject: Mathematics (9 - 12)
Title: Engaging Square Patterns
Description:

This is an activity used to introduce a lesson on explicit and recursive formulas for a sequence from a pattern. Students are asked to examine a pattern and find a formula to describe the sequence in the pattern. They will then determine if they wrote an equation that is recursive or explicit using the given definitions of both.  



   View Standards     Standard(s): [MA2019] FM-19 (9-12) 11 :
11. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Examples: fractals, population growth
Subject: Mathematics (9 - 12)
Title: Recursive and Explicit Equation Card Sort
Description:

This Desmos Activity will lead students to sort patterns and write formulas for each pattern.  They will then sort the formulas into either recursive formulas or explicit formulas. 



   View Standards     Standard(s): [MA2019] FM-19 (9-12) 11 :
11. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Examples: fractals, population growth
Subject: Mathematics (9 - 12)
Title: Recursive or Explicit, Why Not Both? Exit Ticket
Description:

This learning activity is an assessment activity that uses an exit ticket to ask students to write both a recursive and explicit formula for a simple application problem.



ALEX Learning Activities: 3

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ALEX Classroom Resources  
   View Standards     Standard(s): [MA2019] FM-19 (9-12) 11 :
11. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Examples: fractals, population growth
[MA2019] FM-19 (9-12) 12 :
12. Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.

Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.
Subject: Mathematics (9 - 12)
Title: The Fibonacci Sequence
URL: https://streaming.discoveryeducation.com/teacherCenter/lessonPlans/pdfs/9-12_Math_FibonacciSequence.pdf
Description:

In this lesson, students will:


   View Standards     Standard(s): [MA2019] FM-19 (9-12) 11 :
11. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Examples: fractals, population growth
[MA2019] FM-19 (9-12) 12 :
12. Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.

Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.
Subject: Mathematics (9 - 12)
Title: Recursive Formulas: Fibonacci Sequence
URL: https://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=MAT.CAL.500.3&questionId=54c2c962da2cfe7bd16cc05a&artifactID=2126993&conceptCollectionHandle=analysis-::-recursive-formulas&collectionCreatorID=3&plix_redirect=1
Description:

This interactive activity will challenge students' knowledge of the Fibonacci Sequence using the following scenario:

Recursive formulas describe sequences of numbers governed by a common pattern. Here a recursive pattern can be seen in the increasing side length of each square.

    • Use the two red points on the large orange and green squares to continue the pattern. 
    • Try to determine the recursive pattern that governs the side length of the set of squares.
    • Note that this recursive pattern expands from the smallest value to the largest.

Note: You will need to create a free account to access this resource.


   View Standards     Standard(s): [MA2019] FM-19 (9-12) 11 :
11. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Examples: fractals, population growth
[MA2019] FM-19 (9-12) 12 :
12. Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.

Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.
Subject: Mathematics (9 - 12)
Title: 12.1 Describing the Pattern and Writing a Recursive Rule For a Sequence
URL: https://flexbooks.ck12.org/cbook/ck-12-precalculus-concepts-2.0/section/12.1/related/lesson/describing-the-pattern-and-writing-a-recursive-rule-for-a-sequence-alg-ii/#
Description:

This informational material will introduce the concept of recursive sequences and explain how to write recursive formulas. The Fibonacci Sequence is introduced. Practice questions with a PDF answer key are provided


ALEX Classroom Resources: 3

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