Divisors and Dividends

Hi folks!

Thank you to everyone for signing up over the last few weeks! If you like what you see, share it with your colleagues! I would love to find out how you are implementing language in your classrooms, whether you were doing it before or since these posts.

So, to the matter at hand. The official terminology for parts of a calculation are often grounds for speculating what children do or do not ‘need’ to know. That a Key Stage 1 pupil must memorise minuends and subtrahends is often the maths teaching equivalent of ‘PC gone mad’ for commentators, both outside the field or teachers of non-mathematical subjects.

To some extent, I agree. There are many instances where such knowledge is sub-optimal, particularly if working under the presumption that attention and memory are limited. However, I want to explore them, and help present the case as to whether some of these terms can help offer clarity and specificity when explaining some concepts to our learners.

For those who need a refresher, here are the basics:

· addend + addend = sum

· minuend – subtrahend = difference

· multiplicand x multiplier = product

· dividend ÷ divisor = quotient

Now, on the face of it, I agree that a Key Stage 1 student does not need to know each of these by heart. However, from late KS2 onwards, I would argue that several of these can come in handy:

· addend + addend = sum

· minuend – subtrahend = difference

· multiplicand x multiplier = product

· dividend ÷ divisor = quotient

The two least important, to me, are minuend and multiplicand. Subtraction and multiplication are often less required to atomise, and I find that both of these are very easily called ‘the original number’, both without evading exam words and without getting tongue-tied in unnecessary language or overly long ‘simplifications’.

Those in bold are the ones I deem most valuable. We know about sum, difference and product. All are prone to being asked without context, so to avoid these words for ‘easier’ ones makes a mockery of the task at hand. I would drill these words constantly, and often feature at least one of them in every retrieval starter.

You may be more surprised (other than the title of this post, obviously), to see dividend and divisor in the high importance list. To explain this, I want you to take a moment, particularly is you can use a pad or Notes app, and write down any topics you can think of involving division. When you realise the sheer number, you see how scrutinised division is as a topic. Now think about how often you are calculating different parts of the puzzle, rather than always just the product. The anatomy of division is spoken about constantly, and so having distinct descriptors for the different parts can be very helpful. All the talk of real-life maths, we can explain how dividends are the pot of profit that companies divide among their shareholders, so equated to ‘what you’re dividing by’. With divisor, it’s all about the suffix. When there’s a noun ending in either -er or -or, it’s responsible for an action (employer, realtor etc). Therefore the divisor is the thing doing the dividing (what you’re dividing by).

Those in italics have lesser or questionable importance. For this, I would like your help! I will pose some questions, and I’d love for you to respond to them, either as a reply or via Bluesky.

1. Does multiplier have enough importance in other topics to be used more frequently for any multiplication discussion?

2. If we deem that important, do addends and subtrahends have a claim, particularly when discussing number bonds and fact families?

3. Quotient is the one resultant word that we don’t use in GCSE, but becomes far more important at A Level. Do we introduce this early on, or is it pure clutter?

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As always, see you next week!