Home → Curriculum Hub → Maths Lessons → Schemes of Work → Key Stage 3 → Patterns and Sequences
This Key Stage 3 Patterns and Sequences scheme of work brings together the lessons I use when I want students moving confidently from describing patterns and finding rules to working with position-to-term formulae and graphs. The page sets out what I expect students to bring from earlier algebra and number work, the ideas I keep coming back to in class, and how this unit fits the wider KS3 algebra strand.
Use it as a departmental reference: sequence the lessons below in the order that matches your scheme, adapt timings to your cohort, and cross-link to other units when you need extra practice on linear functions or substitution. Everything here describes the unit at a glance—the individual lesson pages hold the presentations, worksheets and tutorials.
For more schemes and topic routes across KS3, GCSE and A-Level, browse the Mr Mathematics Curriculum Hub.
Read the four summary cards first so you know the prior expectations and the language you want students to hear consistently. Then work through the lessons in the order below unless your department timetable needs you to split content across terms—if you do, keep term-to-term description and position-to-term rules clearly linked so students do not treat the nth term as a trick separate from the sequence itself. Jump straight to the lesson list when you are ready to open resources or set cover.
Presentations, worksheets, question generators and video tutorials for the lessons in this unit are available to members. Explore Mr Mathematics membership if you need full access to the library and schemes of work.
Students should arrive with these ideas secure enough to apply them when describing sequences and using formulae.
These are the ideas I keep explicit while teaching this unit.
How this unit supports fluency, reasoning and problem solving in Key Stage 3.
National curriculum links this unit supports at Key Stage 3 (Algebra).
Use it as the map, not the lesson. Check prerequisite knowledge with your classes, align the key concepts with your department’s vocabulary, then teach the lessons in the order that fits your timetable—opening each lesson from its own resource page when you need the presentation or worksheet.
They need to be comfortable with simple formulae, describing linear sequences in words, basic substitution and finding pairs that satisfy simple equations—so moving to nth-term rules and graphs is a development of structure, not a fresh start.
Each lesson in the list below has its own page on Mr Mathematics with downloadable resources and, where available, an online lesson and question generator—access depends on your membership level.
Yes, if your scheme requires it—keep an eye on dependency: students usually need fluent term-to-term description and a clear idea of position number before the nth term and graph work feel connected. If you reorder, re-check the key concepts card so term, rule and formula language stay consistent across the unit.
Lesson titles as listed on the scheme—open each from the site navigation or search when you are ready to teach.
Students learn to describe number patterns on a term-to-term basis.
As learning progresses, students tackle Fibonacci and geometric sequences.
Students learn how to find the nth term of an arithmetic sequence.
During the lesson, they are taught how to break a sequence down to find a position-to-term formula.
Students learn how how to generate terms of a sequence using a function machine.
Students progress from using function machines to the order of operations to write the first six terms of a sequence.
Students learn how to describe and continue a picture sequence.
During the lesson, students learn how to model a picture sequence using its numerical pattern.
Related Blog: nth term of picture sequences
Students learn how to plot a linear sequence on a grid.
As learning progresses they are challenged to work out the nth term of the sequence from the grid.
Additional practice working out the nth term of arithmetic sequences.
The problem-solving activity challenges students to model a picture sequence using the nth term.
Related Blog:
Additional practice generating quadratic sequences and finding the nth term of a quadratic sequence.
Later, as learning progresses, students create a quadratic sequence to find the number of matches played in a league.
Students revise how to derive the nth term of an arithmetic sequence.
As learning progresses, they use the nth term to find any sequence term when given its position.
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