Engaging Square Patterns
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This learning activity provided by:
Author:
Lorie White
System: Lauderdale County School: Rogers High School
General Activity Information
Activity ID:
2899
Title: Engaging Square Patterns
Digital Tool/Resource:
Web Address – URL:
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.
Associated Standards and Objectives
Content Standard(s):
Mathematics 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
Unpacked Content
Evidence Of Student Attainment:
Students:
-Use inductive counting methods to find recursive patterns and explicit formulas. Teacher 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. Diverse Learning Needs:
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.
Strategies, Preparations and Variations
Phase: Before/Engage
Activity:
The teacher will direct students to the Desmos Activity Engaging Square Patterns.
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.
As the students complete the table, the teacher should monitor students' progress to identify problems or gaps in learning.
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.
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.
Advanced Preparation: Prior to the lesson the teacher should:
have an internet connection (WiFi).
have a classroom set of computers, iPads, or smart devices. (If allowed, students can use their devices.)
create a code and assign the Engaging Square Patterns Desmos student activity.
become familiar with the Engaging Square Patterns Desmos student activity to be prepared to address student questions.
Variation Tips (optional): 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.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
Arithmetic Sequences, Explicit Formulas, Patterns, Recursive Formulas, Sequences
