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For younger learners

  • Early Years Foundation Stage

Staircase Sequences

Age 16 to 18
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
In playing around with the sequence you may well have asked some
questions.

Here are some questions we asked about these sequences that you might
like to think about, if you have not already considered them.

- What might this notation mean?

- Can I write these as more conventional fractions?  In other words, what do they equal?

- How do I expect the sequence to continue?

- Does the sequence have a last term?

- Can I predict what happens to the terms of the sequence a long way down the line?

- Are the terms in the sequence getting larger or smaller?

- Can I efficiently work out the value of each term of the sequence?

- Do I notice anything interesting about the numbers in the fractions?

You may also like

Powerful Quadratics

This comes in two parts, with the first being less fiendish than the second. It’s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.

Discriminating

You're invited to decide whether statements about the number of solutions of a quadratic equation are always, sometimes or never true.

Factorisable Quadratics

This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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