Feedback | SoME

From Bananas to the Number Line: Why Does Minus Times Minus Give Plus?

Audience:

Tags: arithmeticmultiplicationnegative-numbersnumber-line

We go on a playful journey through one of the most famous — and mysterious — rules in maths: why multiplying two negatives gives a positive. Using examples with debts, colourful squares, and the number line, we visualise and explain the rule with intuitive activities. The aim is to show that maths rules are grounded in logic, balance, and symmetry — not just convention. The content is suitable for learners still mastering negative numbers, but encourages deeper questions for those interested in mathematical structure and reasoning. Recommended for curious readers, teachers, and anyone who enjoys a touch of monkey business in maths explanations.

https://tangenzialmente.com/blog/why-minus-times-minus-gives-plus/

Analytics

5.51 Overall score*

43 Rank

6 Votes

5 Comments

Comments

I liked your visuals.

Your explanation seemed like a statement with many words. The way I like to explain this topic is to define walking forwards and playing a video normally as positive, walking backwards and rewinding it as negative. Then set up the four cases:

walk forward and play normally=walking forward in video, ++=+ walk forward and rewind=walking backwards in video, +-=- walk backwards and play normally=walking backwards in video, -+=- walk backwards and rewind=walking forwards in video, —=+

Most students are able to visualize this and those that can’t believe it after seeing it. It’s also possible to present an algebraic proof:

https://mathsfromnothing.au/positive-and-negative-numbers/

but a maths level much higher than what a student has when we teach negative numbers is required to understand it, so it is almost never presented.

5.6

Adding a concrete example to understanding that negatives represent direction is useful, but I don’t see it explaining why that counts as multiplication.

6.5

Well made, but some use of complex terms that may confuse the target audience. The visuals were very good and the idea of flipping on the number line is nice, but the use of phrases such as “coherent and elegant” as well as terms such as “distributivity” are not well chosen for a younger audience.

I liked the entry and I think it fits the audience. I liked the interactive elements and the fact that there is also an exercise at the end, as well as the key questions between the chapters. Concerning the content, I did not find it fully intuitive to actually get bananas when I am in dept. When -3 x -5 erases my dept, I’d think I would end up with zero bananas, since my dept is payed, so to speak, even though it is true that I would need 15 bananas to pay my dept. The flipping however made sense! It also made sense when talking about adding and subtracting, since taking away -5 is as if adding 5. I also think as a sneak peak or so it would have been interesting to discuss the issue with the square root of negative numbers, since it is known that sqrt(-1) is not possible (at least with non-complex numbers), since what number multiplied by itself results in -1? I know complex numbers are “complex” at first and not for the respective audience but peaking into the topic could show that rules / logic (even though not random, as it is said) can also change for various reasons, e.g. context of other logical rules (e.g. concerning the appearance of the root of a negative number in the quadratic and specially cubic formula). Overall a nice entry! I will look into it again. <3

5.4

Clear explanations, and I liked the flipping animation. To me, some of the content reads like it’s AI-generated. Also, (-1) * x and -x seem to be used interchangeably, which might be confusing.