Engaging Square Patterns

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

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.  

Phase

Before/Engage
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.11

Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

UP:MA19.FM.11

Vocabulary

  • Difference equation
  • Recursive process
  • Recursive formula
  • Sequences
  • Series

Knowledge

Students know:

  • How to use inductive counting methods such as lists.

Skills

Students are able to:

  • Use inductive counting methods to collect data for conjecturing.
  • Find recursive formulas from collected data.
  • Develop explicit formulas.

Body

  1. 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

Learning Objectives

The student will be able to identify a pattern from a set of blocks arranged in rectangles and produce a formula to model the pattern.

Activity Details

  1. The teacher will direct students to the Desmos Activity Engaging Square Patterns.
  2. Instruct the students to work through the activity.  Students will examine the patterns and count the number of white squares.  They will use the number of squares to complete a table.  From the table, they will write a formula for the arithmetic sequence. 
  3. As the students complete the table, the teacher should monitor students' progress to identify problems or gaps in learning.
  4. Student formulas will be shared with the class. This will allow students to compare their results. It is possible that some students will write explicit formulas and some will write recursive formulas. They will be given the definition for each type of formula and will be asked to identify the type of formula they produced. 
  5. This activity will be used before a lesson on finding a pattern from an application and using the pattern to produce either a recursive or explicit formula.

Assessment Strategies

Student responses will be shared with classmates and will allow them to self-assess their work. Teachers should also check student work using the Desmos Teacher Dashboard and correct any misconceptions or mistakes. 

Variation Tips

Students could work in pairs if there are not enough devices.

The Desmos activity could also be displayed for the entire class and could be worked as a whole group activity.

This activity can be used to refresh student knowledge on finding formulas from patterns or tables. Students can work independently or in pairs to find the formulas.

Background / Preparation

Prior to the lesson the teacher should:

    1. have an internet connection (WiFi).
    2. have a classroom set of computers, iPads, or smart devices. (If allowed, students can use their devices.)
    3. create a code and assign the Engaging Square Patterns  Desmos student activity.
    4. become familiar with the Engaging Square Patterns  Desmos student activity to be prepared to address student questions.

Learning Activity (Before)

Engaging Square Patterns

Learning Activity (During)

Recursive and Explicit Equation Card Sort

Learning Activity (After)

Recursive or Explicit, Why Not Both? Exit Ticket
Engaging Square Patterns Desmos Activity
https://teacher.desmos.com/activitybuilder/custom/62c231eb437cdf0529044935#prev…

Approved Date

Owner (Author)

mrswhite
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