Making Work Rate Math Problems Interesting
Making Work Rate Math Problems Interesting
February 18, 2020
The Work Rate Problem
Math formulas are tools to help us understand a situation. I see a lot of content dedicated to showing the operation of various formulas, but few about why and when to use tools.
Stories are a time proven vector for shuttling information into the brain. It’s one of the reasons fables, myths and legends are often the longest lasting remnants of long-past cultures. We remember and repeat the stories, and the lessons there in, ad-infinitum. The challenge than is to add x amount of sugar to the medicinal knowledge, in order to raise the probability that more people will learn, remember and use the information they spend years memorizing in school.
Formulas that are able to model interesting situations seem the most likely to succeed at telling a good story. One with potential is the work-rate formula, which is applied to situations where several entities all work together on some work at different rates.
That this formula is regularly applied to working people, makes it possible to tell some relatable stories. However, there were some very noteable patterns in the work-rate problems I came across in my brief refresher. Usually, the problem would ask how long it would take 2 or 3 workers to complete exciting tasks like painting rooms, cleaning and picking fruit. Some creative ones included water pumps and conveyor belts. The trouble is, I’ve never met or heard of any kids with even the vaguest of interests in these topics.
So what might make a situation interesting? A quick glance at any age groups popular media helps answer this question. Given that word rate problems tend to pop up around grade 8, we’ll look at the interests of 13 year olds. What is, or has been, popular with this age group? This list is definitely not exhaustive, it’s showing just how much sugar may be needed to make the medicine palatable.
- Harry Potter
- toy cars/pistols
- Wriggling out of adults boring schedules and plans
This list is feeble but it is also illustrative, most kids aren’t interested in studying or self-optimization, they’re interested in having fun. If you’ve met a kid with an interest in Fortnite, even things tangentially related will get them talking for hours. Hours of utterly wasted firing and wiring neurons. Not that Fortnite is any worse than the hobbies most of us occupy ourselves with.
If we can connect things we need to know, to things we want to know, then education may stop being a distraction from real life, and start being useful. It may well be impossible to make work rate problems genuinely interesting to most people, especially kids, but we’ll never know unless we try. So here’s an attempt.
I think the first step should be to understand what questions these problems enable us to answer. So, what are the variables in a work-rate equation?
We have two or more work rates, and total time to get the work done. Only one variable can be unknown at a time, so most of the work rates must be known in any situation. A fictional reason will need to be given as to why we can’t just measure the unknown entity completing a job on its own, and instead must mingle their work with others. Perhaps the other workers have some specialized skills necessary for the job. Perhaps we only have data on the person, so can’t conduct any specific experiments. Whatever it is, it partially explains why this formula is important in some situations.
So what questions can this formula answer? Why would we need them?
Why would we need to know exactly how long a set of workers will take to complete a task?
- A client needs to know when they can pick up a product
- Two or more chemical reactions need to trigger at the same time
- We need to crank out the right amount of energy for a machine, without burning it out.
- We want to appease some angry deities with offerings at some specific alignment of the stars
Why would we need to know the precise rate someone can work at?
- A new employee has arrived and we want to know their stats
- A new machine has arrived, and we want to know how efficiently it can work.
- We need to create a shift roster for some shared important item
- We need to know at present weight loss rates, how long it will take someone to lose their share of weight
Questions the formula cannot answer
What happens if you’re wrong about the time to complete a task? Is it catastrophic? Or is faster always better? As math is about precision, care must be taken to avoid situations where more is always better, as this doesn’t actually require skill to get the best outcome. A better problem is one where there are consequences for too little and too much.
So what events could this model, of several entities joining forces for a task, apply to?
- Training cats to do tricks
- Crafting items/potions/cakes/clothes for clients
- Basic survival tasks in a zombie outbreak
- Farming and plant growing
- Saving up for a coveted item
- Levelling up animals/characters in a game
- Hatching/Feeding/Caring for animals
- charging electronics with human powered motors
- Harry Potter antics, in making wizardy products with the Weasly twins
- Batman antics in having arkham inmates send Joker-power laced letters to Gotham
- Searching rooms for secret items
- Having kids write their own work rate problems about their peer groups could be socially catty, but would probably shuttle that information very successfully
Although it is unknown how popular IPs, like Batman or Harry Potter, would respond to fan-educational-exercises, it doesn’t change the fact that kids would probably love it.
It is also unknown if contextualizing a formula in an environment where it’s answers actually matter, would be beneficial or disruptive to learning. Would the ability to converse with characters about how fast they can each work, or why the task they’re all contributing to is important, help the brain remember why and how this formula can be used? Or would stories and characters prove distracting? Would they overload the brains working memory with unnecessary information? It’s a question worth exploring.
As a quick example, a math problem based in the Batman universe already has substantial anchors in many kids imaginations. A little story about the Joker orchestrating a nefarious event with insane inmates shows, rather than tells, why its important to know precisely how fast people can work, so deadlines can be planned. Such a story, however silly, would have more meaning to some children than any example about businesses operations or using machine conveyor belts.
I built a little math based game engine explicitly to explore the possibilities of contextualizing math in stories and simulations, that show the answers importance. I’ll next be focusing on writing a problem focusing on the work rate formula, and the very human problems it relates to. I haven’t decided exactly which topic best fits at the moment, but I particularly like the idea of a group of people using hand cranks to generate electricity for something sensitive.
Poll Question: When was the last time you did math voluntarily?
- Never, more than a year ago, more than a month ago, more than a week ago, more than an hour ago
- How beneficial do you think it would be to contextualize a math formula in a story?
- Do you think it would be possible for a story to make a math formula genuinly interesting to you?
- Which scenario do you think would best characterize the work-rate formula?
More information about these reports can be found here