Variation Theory
Sequences of questions and examples where one thing changes at a time, so students can see what matters and think mathematically.
New My latest resources now live on mrbartonmaths.com ↓
Reflect, Expect, Check, Explain
I wrote this book to help teachers get the most out of the sequences on this site. It explains how to design a good sequence, and the classroom behaviours and teacher prompts that turn it into real mathematical thinking.
About this site
This site was my first attempt to put a small part of Variation Theory to work in maths lessons. Hold most things constant between one question or example and the next, change one thing, and students can see what that change does.
The sequences come in four activity types. Each one works best alongside a simple routine that I call Reflect, Expect, Check, Explain, with the teacher there to prompt and probe.
Every sequence is still here. Find them under Topics in the menu, or browse and search them below. New to the site? Start with the Introduction.
Reflect, Expect, Check, Explain
- 1ReflectWhat has changed from the last question?
- 2ExpectWhat effect will that change have on the answer?
- 3CheckWork it out. Was the prediction right?
- 4ExplainWhy did the change have that effect?
My new resources are on mrbartonmaths.com
I’m no longer adding to this site. Everything new I make using these ideas now lives on mrbartonmaths.com, where it is bigger, better organised and free. Here is where to go for each activity type.
Looking for the Pattern sequences? They are still here on variationtheory.com, under Activity type 3: Pattern.
Browse the original sequences
Hundreds of sequences, from primary to A level. Search, or pick a topic.
Supporting this site
I don’t make any money from this website. If you would like to support my work, and learn more about the ideas behind it, here are three ways.
More courses, including Explanations, modelling and worked examples, are in my online course store. Thanks so much for visiting. Craig