This series of pages includes many favourite Underground Maths resources.
The Underground Maths series is now easily accessible from the top menu.
- Introduction
- Underground Maths: A Level Mapping
- How to Guide
- Building Blocks
- Review Questions GCSE 9-1
- Coordinate Geometry
- Save & Organise Favourite Resources
The A Level Mapping page includes some review questions mapped to the A Level specification.
A few more favourite resources…
- Scary Sum
- Divide it up – polynomial division
- To log or not to log
- Powerful Quadratics
- Circles & Teddy Bears
- Can we show that these four points lie on a circle?
- Three Algebra problems
- Gradient Match
Categories on Underground Maths
I have so many favourites on Underground Maths, here’s one – Scary Sum!
Following on from an area model for multiplication, for your older students, try Divide it up from Underground Maths, a resource designed to help students to make links between multiplication and division of polynomials using multiplication grids. The problem is presented in the image here, but also provided is a warm-up activity and further notes
See the related post, which includes this resource – Factorisation of Quadratic Expressions.
To log or not to log – Underground Maths
A favourite Underground Maths resource I have used many times – To log or not to log? This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. I have always found that in addition to working on indices and logarithms this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!
This problem is classified as a Problem Requiring Decisions.
Students are often used to problems being posed in such a way that they have all the information that they require in order to start, and no more. Problems (especially from the real world) are very often not like this, and so resources of this type will give students the opportunity to develop the skills needed to deal with this. Some problems might not contain enough information, so students may need to decide on classifications, make assumptions or approximations, or do some research in order to move forward. Some problems might contain too much data, so that part of the challenge is to identify the useful information.
Here’s what my students said:
Powerful quadratics, will certainly give your students food for thought, as the authors state:
When students are familiar with concepts and ideas they often benefit from exploring them further to improve their understanding. These problems aim to allow this further exploration, and for example, might bring different techniques together, highlight interesting or unusual cases, or probe the definition of mathematical terms.
A resource I found very useful for the matching functions with their gradient functions is Gradient Match which can be used interactively online. See this post on introducing gradients at GCSE. Note that you can simplify the task by giving students the set of six functions and the six gradient functions separately.
Identify the equations of the circles.
I rather like this review question on circles:
Can we show that these four points lie on a circle?
Good for A level mathematicians – also for my Year 11 Level 2 Further Maths Students.
And of course – Desmos to illustrate.
This diagram could make a rather nice starter…
Underground Maths has many Proof resources; perhaps try these proof sorts, Proving the laws of logarithms or Proving the quadratic formula. Or try this review question…
Can we fully factorise x4+4y4?
Starts with a Show that….
And then we factorise and will need to recall the difference of two squares.
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.
Can we simplify these algebraic fractions?
Review algebraic fractions, simplifcation including the difference of two squares and quadratic equations. We could of course also talk about functions (including domain and range.
Can we simplify these simultaneous equations of degree 1 and 2?
Solve simultaneous equations, we’ll need simplification of algebraic fractions again and we can talk about the graphical solution of equations. We will also need to factorise a quadratic, 3y2−y−80 with a coefficient which is not 1 for the square term. (See Factorisation of Quadratic Expressions)
