What is Interweaving?

Excellent question…

Interweaving (and interleaving) are terms that different people seem to use to mean different things.

This is my interpretation.

  • There are a number of benefits to be gained by using questions and tasks that bring together multiple different topics from mathematics (i.e. interweaving those topics).
  • For example, if you are currently teaching how to find the 𝑛th term rule of arithmetic sequences, then having fractions in those sequences:
    • gives pupils practice of subtracting, adding and multiplying fractions,
    • forces pupils to understand the process for finding the 𝑛th term rule of a sequence, without the simple numbers that can lead to routine thoughtless calculation,
    • helps pupils to appreciate the fundamental interconnectedness of all things mathematical. To see the solution to each problem as being detectable in the pattern and web of the whole (to borrow a line from Douglas Adams),
    • allows you to explore interesting patterns and ideas in both topics that are revealed through their connection with the other.
      For instance, reversing the terms of a geometric sequence makes the common ratio the reciprocal of what it was before.
  • Similarly, having pupils form and solve equations from angles in parallel lines:
    • gives pupils practice of solving different forms of linear equation, of substituting back in solutions, and of forming equations in context,
    • makes the use of facts about angles in parallel lines less obvious than when all the angles are either 70° or 110°!
    • helps pupils see an, albeit contrived, application of equations for solving problems, and with semi-self-checking solutions.
  • The more that such tasks are used with pupils, I feel, the more they will appreciate maths as a wonderful subject full of connections and structures, all underpinned by powerful ideas and concepts. They will also get to review different topics, gaining fluency and long-term recall, and the ability to apply ideas in new contexts and situations. In short, they will become better mathematicians.

That’s why I’ve made this site. Creating interwoven tasks is quite laborious, so I’m hoping that a repository of thought-through tasks covering a variety of different intersecting topics will be helpful! All the tasks have editable PowerPoints that you can use/adapt/improve as you wish.

I’d love to have others contribute too. If that would interest you, please see the ‘Submit Your Own!‘ page.

For more details, feel free to reach out to me @nathanday314.