Connecting Rules

x = 3

y = 4

Find 20 rules connecting x and y

Eg. 5y - 17 = x

A Mathematics Lesson Starter Of The Day


Topics: Starter | Algebra

  • S Curtis, Brune Park CC
  • One of my more industrious students thought it clever to sequence it as follows:
    y-1 = x
    2y-5 = x
    3y-9 = x etc...
  • Heeley's Y7 brainboxes, Rawthorpe High, Huddersfield
  • We thought this was bare cushtie (this means very good)! we recognised that there are an infinite number of possibilities.
    Watch out for Mr Heeley on Teacher's TV on May 5th at 10pm. (Sky channel 880, Virgin 240).
    God bless you all at Transum
    Love Y7 xx
  • N. Cox, Woodbridge, Suffolk
  • Excellent open-ended starter which led to work with powers, brackets roots and many different types of equations.
  • Jules, Longton High School
  • 5. More like this please!
  • 7ab/M4 The Best Maths Class In KA's, King Alfred's College OXON
  • Some students in the class came up with these examples:
    Then we thought about squaring the values.
  • Luke, Savio Salesian College
  • My class were very good at this starter,i think you should make a similar one.
  • Transum,
  • This starter provides an open ended opportunity for pupils to demonstrate what they can remember about algebra. It is a suitable activity for most ability levels and a quick walk around the classroom to see what pupils are writing provides a quick assessment of their understanding and imagination.
  • Mr Anderson, Garth Hill College
  • This is a good warm up for any class.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.1 out of 5 based on 367 votes.

Previous Day | This starter is for 20 April | Next Day


There are of course no end of correct answers and here are some examples.

There is at least one mistake. Can you find the errors when x=3 and y=4?

\(x + y = 7\) \(x - y = -1\) \(y - x = 1\)
\(2x + 3y = 22\) \(5x - 2y = 7\) \(4y - x = 13\)
\(xy - 10 = 2\) \(180 - 2x + y = 178\) \(20x - 3xy = 33\)
\(x^2 + y = 13\) \(10x - y^2 = 14\) \(y^2 - x^2 = 7\)
\(x^2y + 13 = 49\) \(x^2y^2 - 2x = 138\) \(x^2y^2 = 576\)
\(x! + y = 10\) \(5(x + y) = 52\) \(3y \div x = 22\)
\(\frac{xy}{2}= 6\) \(\frac{84}{xy}= 7\) \(\frac{15y}{5x}= y\)

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.


Texas Instruments Nspire Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Click the images above to see all the details of these items and to buy them online.

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Here is the URL which will take them to a related student activity.

Student Activity


Extension Answers


©1997-2020 WWW.TRANSUM.ORG