Light Up the Pattern: Finding the nth Term

About This Resource

A complete Grade 6 math pack on linear sequences with a festive lights theme: describing growing patterns, finding the common difference, writing the nth-term rule (such as 3n + 1), using the rule to find any term, deciding whether a number is in a sequence and finding which term has a given value. Includes slides with worked examples, a lesson plan, worksheet, quiz, homework, flashcards, a rubric and answer keys.

Overview

Students explore growing patterns of festive lights and learn to describe them with algebra. A string of lights that starts with 4 bulbs and adds 3 each time makes the sequence 4, 7, 10, 13… The common difference, 3, tells us the rule starts with 3n; comparing 3n with the sequence shows we need to add 1, giving the nth term 3n + 1. Students use nth-term rules to find the 10th, 50th or 100th term without listing every term, test whether a number belongs to a sequence and work backwards to find which term has a given value.

Resource Details

Subject: Math
Topic: Christmas Light Patterns: Finding the nth Term
Category: Number Sense
File Type: PDF
File Size: 288 KB
Published: 11 Nov 2026
Downloads: 0

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Grade 6 math (ages 11–12) 55 minutes Algebra sequences generalizing reasoning problem solving

Learning Objectives

Find the common difference of a linear sequence.
Write the nth-term rule of a linear sequence.
Use the nth-term rule to find terms and to decide whether a number is in a sequence.

How to Use This Resource

Start with the slides: show light patterns of 4, 7 and 10 bulbs and ask how many bulbs pattern 10 will have.
Teach the nth-term method with the worked examples, then do worksheet activities 1 and 2 together.
Students complete activities 3 to 6, then use the quiz and send the homework page home.

Classroom Activity Ideas

Build the pattern: students make light patterns with counters and record the number in each pattern.
Rule detectives: one student writes a secret nth-term rule and gives three terms; the class finds the rule.
Is it in the sequence? Call out numbers; students decide yes or no using the rule.

Differentiation

Support: use a table with columns n, 3n and term, and keep differences small. Challenge: students find the nth term of decreasing sequences and create a pattern of their own with a rule.

Assessment

Use the worksheet and quiz to check finding and using nth-term rules. Use the rubric to assess the homework pattern design.

Teacher Tips

Students often write n + 3 for a sequence that goes up by 3. Compare the 3 times table (3, 6, 9, 12) with the sequence (4, 7, 10, 13) to show that the rule is 3n, adjusted by adding 1.

What's Included

10-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (6 words with meanings and examples)
Student worksheet (6 activities)
Quiz / assessment (4 parts)
Homework practice page
Printable flashcards: 6 A5 picture cards (separate PDF)
Assessment rubric (4 levels)
Lesson slides (editable PowerPoint)
Editable Word version of all student pages
Complete answer key (also as a separate PDF)