One of the hardest things to do in creating a math game is to come up with problems that relate at all to student interests. Textbook publishers try, and so do we. You see a lot of math problems that include baseball statistics or buying CDs. Of course, then no one buys CDs any more and the books are out of date.
We have two needs in what we are doing now. One is creating more problems that relate to the every day lives of rural communities. The nicest early Christmas present that I received so far was from a lovely woman who said she didn’t have a lot of money to sponsor games for kids so she decided to donate some math problems. You can read one of them below.
She even sent pictures of her cows to go along with the problems! How cool is that? If you have any ideas for math problems, I would love, love, love to hear from you.
Please post them in the comments below.
I have helped my father for five years hay and cube his cattle. My sister has helped on the farm all through the year.
Our hay season starts in the first week of October, and lasts through the winter. Where we live, spring usually begins in March. We herd the cows into a feeding pasture, and hay and cube them in troughs until the first week of March. We turn the cows out to graze until the next October.
How much more time has my sister worked than me?
First, I figure out how many months a season is.
1 season = six months.
Second, I multiply by the number of years 6 x 5 = 30 months
Third, I divide by the number of months in a year. 30/ 12 = 2 ½ years
Fourth, I subtract how much I have worked from how much my sister has worked. 5 – 2 ½ = 2 ½
My sister has worked 2 ½ years more than me.
What if we are dividing up the money we made from the cattle? We could divide how much she worked , 5/ 2 ½ and we would find that she worked two times as much as me so she should get twice as much money.
An even easier way to solve this would be to stop at step 1. How would you do that? You could say that I worked six months each year and there are 12 months in a year, so 12/6 = 2. She worked twice as much as me.
If you want to truly interest children in math, then I suggest thinking like a child. Geometry, like music, is a language we can all understand. Instead of posing problems to solve, I would give a kids a game where they can draw in digital sand, talk to each other, and be questioned by a teacher. Just give them a compass, a straight edge, and questions. Don’t tell them the answers! They can derive all of Euclid’s axioms. Just teach them logic and let them teach themselves everything else!
My degree is in Mathematics. I am an eternal child. My passions have always been learning and games. So, merry Christmas, how may I be of service?
You want problems? I need to know what concept you want to teach. I got 99 problems, but math ain’t one.
Hi, Daniel –
We are teaching statistics for grades 6-8. That being said, prerequisite information for statistics includes decimal, fractions, percentage, division. Statistics at the middle school grades includes measures of central tendency (mean, median, mode) and the concepts that distributions have a shape and center, and the concept of variability.
Sean grew up in a rural community, and had this to say: “Kids are kids first; make sure you don’t talk to them or assume they are backwards hicks. They still like pop culture and still like movies and music and hanging out with friends and stuff. Having said that, here’s some suggestions:
-Optimization problems (we have 4 buildings to build that must be near water/river — where should we put them? Have conflicting objectives that have to be compromised)
-We only have 36 feet of fence to protect our garden from rabbits. What’s the most area we can enclose with it? If you can let the kids draw it out on the property, they can “see” and it will be more intuitive than simply trying to answer.
-If x crop makes y dollars and z crop makes w dollars, but there’s only so much demand for z, how do I make the most money?
-I have to get to school every day. I can take the long, flat path on a bike, or the short, uphill, rocky path on foot. I can go x speed on my bike and y speed on foot. What is the quickest path?
-I have x dollars to spend in the candy store. Candy A is 25cents ea but I get one for free if I buy 4. Candy B is 20cents ea. Which candy do I buy if I want the most pieces of candy?
-My mom wants to make pies with her blueberries (regional fruit). She can sell as many as she can make, but she must make the pies within x time of the blueberry harvest. It takes her Y time to make each pie. How many pies can she make? She makes $5.00 profit per pie. How much profit will she make?
-Have a small map of town with various paths. What is the shortest distance you can travel and still go to points A B and C?
-I can bike x speed. I want to visit my friend’s house, but I need to be home before dark at 6:30. When do I have to leave my friend’s house. If I leave my house at noon, how long can I visit with my friend?
I absolutely agree with Sean. The issue we see is that nearly 100% of math problems kids encounter are things like the best cell phone plan and almost nothing addresses questions like how much fence do you need to enclose a pasture. That being said, we also include questions that every kid I ever met has (except only children) , like what is a fair way to divide up candy between me and my sister.
Thanks for the share Dr, Mars! The photo looks great! I’m hoping more people will send in math problems.
Story and role driven elements seem well geared towards providing a suitable backdrop for educational games. A detective, architect, engineer or other job based role might have numerous problems to solve that fall outside the ordinary everyday experience of most people. If students play a game from the storyline perspective of a detective that could provide expositionary background for them solving crimes & passing levels using math and critical thinking skills.
From a storyline perspective, their character could be a man or woman who is an engineer/architect/detective who plans to get married & they have to raise money for their wedding or some other type of social cause. To raise the funds they must successfully complete a number of missions where they use basic math and problem solving. Having some type of virtual incentive to learn and pass missions with some comic relief and plot twists thrown in.
It might also be possible to use mixed martial arts or judo as a backdrop. Where students play a game from the perspective of an mma fighter or mma trainer/manager. They use basic math to figure out which MMA trainers offer the best cost per value. What number of days their virtual mma fighter should train in a week to be healthy and how much training would constitute overtraining or burning themselves out. Which mma promotions offer the best contracts per value. How many meals they should eat in a day of what type of nutritional foods, how much water they should consume to cut weight. There’s a lot of math and science in sports.
I love some of these ideas I have read! I was thinking about how every user has unique math problems in their lives. This is why I encourage everyone who reads this to donate their problems, art, and photos. This way, the company can have a donation pool of problems to dip into should they get close to deadline on a game. I was thinking the middle school age users would have some very interesting problems ideas, and a contest for users to donate ideas would make for a great research study. During start up, I like to think the donation pool would be a great way to have free help, and get users already consuming involved. I think the tourist visa program is great to have, in that you can not only have game testers, but you can also be like hey we are close to deadline, and need this kind of art, or need input help on problems. I feel on developing quality games that stand the test of time, you have to have love, and many sets of eyes that share in that love.
What I like the most about the current 7generation games is how every one teaches unique native history. Each game reveals accurate stories with input from actual tribal members the games are for. This inspires me to double check the game, to see if the game has actual elders, and warriors depicted in the game! Each game, establishes another tribe on the virtual map, and in time, as each game is developed, the virtual map comes alive. In time, after input and feedback, as each phase goal is met, the virtual map can be put into future server. The native world is global, and each tribe has unique history and stories. I am looking forward to Aztech, for example, in that I am guessing we will learn more truth about the actual history of the Aztec tribe. I find at times I am excited on this one, to see how the art will look, and how the math is presented.
I was thinking when I apply math, most of the time, I honestly use math the most on figuring out animal feed. Granted, I do use math to pay my bills, and keep gas in my car. I just work this other math on autopilot. What I scratch my head on is gee hmm how much food did I really feed the animals I cared for?
Here are more math problems for the calves. When that photo was taken, they were getting weaned from their mothers. The babies are now pretty much weaned, and are eating wheat and rye grass in a five acre hay patch. The weather is currently warm at the ranch, so we only feed the calves once a day, in the mornings, one five gallon bucket of sweet feed. The main herd is fed 2 fifty pound sacks of cattle cubes every other day. Due to warm weather, we have the main herd of mama cows in another wheat and rye grass hay patch. This saves us from using up our winter hay bales so fast.
We were having to keep them separated, and bring them 4 five gallon buckets of water, which filled a foo tub of water. How many gallons is that? Me and my Dad factor in splash factor and say about 18 gallons of water a session. We watered them three times a day, so that meant 18 * 3 = 54 gallons, figured on splash factor.
The babies during the time of the photo was eating two buckets of sweet lot feed, or crushed up corn products, three times a day. I figure two five gallon buckets is 10 gallons with allowing one gallon off the top. We never fill the buckets all the way to top, so I figure 8 gallons of feed. We fed the babies three times a day, and that would be 8 * 3 = 24 gallons of sweet feed.
To guess how much per cow we were feeding, one sack of feed is 50 lbs, so divided by 12, with screw up factor, we say that the calves actually are getting 48 lbs of feed from the sack. 12 calves + 48 = 4 lb average a day.
I am thinking this is just one set of problems from one aspect of my daily life. I wonder what about everyone else’s lives? I think it is a given we all do math problems daily. Some problems are just easier than other problems.
Merry Christmas everyone!
For Stats & Pre-requisite:
Create a game play like Duck Hunt, Big Buck Hunter or fishing which requires students to solve simple math problems in ever more limited time with proficiency difficulty and complexity as they progress which are the pre-requisite to calculating stats (repeated challenges/trips throughout the game for data collection and comparison for stats per trip and overall). Then have them play this game play throughout the game, continuing to collect data on their math proficiency growing as they go. So they can calculate the mean, median and mode based on their results, bell shaped curve to their proficiency of accuracy and speed as well as their variability. Also could escalate the difficulty into various levels to compare apples to apples with some cross over so kids are building to better proficiency with difficulty, starting with the most basic to far beyond the expected grade level so they have something greater to aim for, while using proper progression to highlight to simplicity hidden in the seemingly impossible complexity they feel at first, so give them an early peek at high difficulty then revert to simple and let them build, that way, they are constantly reminded of their progress, what first seemed hard will become easy, and so on.
Also for mean, median and mode, come up with simple number collects with different answers for each. Like 1,1,2,5,6 = Mean is the average 3, Mode is most common 1, median is the middle 2. and so on, because mental math is fun math and keeping it simple allows the concepts to shine through and be understand so they can apply to more difficult data with mastery. Starting with whole numbers for answers than working into simple fractions or decimals like the first 5 numbers kids should be competent in with fractions…
1 = 0, 1
2 = 0, .5 & 1
3 = 0, .333 , .667 & 1
4 = 0, .25, .5, .75 & 1
5 = 0, .2, .4, .6, .8 & 1
also 6 is good because it’s basically simplified to 3s and 2s with slight additional.
6 = 0, .167, .333, .5, .667, .833 & 1
Odd numbers get a bit messy for mental math after that but converting or highlighting some larger even numbers reduce nicely will help them see patterns, like 8 & 10, even 12 similar to 6s.
as well as their fraction form and simplifying their fractions, so if someone catches (solves) 8 out of 10 fish, then they can reduce to 4 out of 5 as well, while percentage stays the same, so using basics to apply decimal, fractions and percentages all with simple mental math proficiency which can then be applied with more complexity as well as aid with calculator competency.
Don’t rush to over complicate with word problems, (focus on simplified progression training), use them to highlight the function visually and real life application, like dividing the food with their family after the hunt/catch which is the same as the mean, etc. And using Mode & mean together to create expectations, but no guarantee to each foresight hunt/catch, to try to plan accordingly. Lead time it takes to build tools might be more predictable, or processing food and skins afterwards as well as shelf life expiration date so they know to conserve reinforcing not to take more than they need to waste, so they develop a pattern of hunting and gathering according to use, as waste on a trail becomes more of a burden than a blessing (besides using it as bait for further hunting perhaps, like attracting bear maybe.)
Word problems should help teach the concepts more universally, but creating a game play which applies will build mastery, so they can then develop their own word problems or apply concepts to their own lives accordingly, with teacher & students, so word problems should shine light on the start of those useful applications but focus on developing mastery with progression training so they can understand fully and apply freely or purposefully to their own circumstance, knowing when, how & why is best use.
Merry Christmas & Happy Holidays to All!
Also, chore or task optimization, calculating mean for time or cost of goods sold or work efficiency analysis, etc.
For example, watering plants by hand with bucket and walking trips:
Compare bucket which waters one plant at time with one trip each,
Compared to a bucket which waters two plants at a time with one trip together,
Compared to two buckets, one per hand which water 4 plants using only one trip, etc. etc.
– Which reduces number of trips which could be time consuming/saving while also optimizing bucket fill and plant pour times as well.
– Could calculate time or task as fractions or decimals, and use percentage for supply and demand limits or chore completion, etc. Getting more complex comparing price points in market to optimize your return, whether it’s plants, games, any product or service with limiting market constraints.
Could them turn this into business modeling and scaling with constraints, if a bucket that waters 4 plants at once costs far more, let’s say 10x a two plant bucket costs and you are just starting out with small scale sale or use and finances are limited, you might prefer to use less effort efficient but more money efficient method, however, once scaled large for mass production, you’d want to optimize effort and time as much as possible within supply and demand means and financial constraints, to optimize unit cost or cost of goods sold. (Example of bad buy: buying custom car rims with nonstandard sizes, simply a could inches more but carrying far higher cost/price with little to no added benefit, this is a foolish fad and how gullible people get conned.)
Can apply this optimization to anything, movement, math, work; promoting efficiency like a fish in sea. Working smarter & harder if it makes sense to get more done due to stress-less success with less fatigue per unit output. Sometimes slowing things down to simplify & optimize form, focused on fundamentals to reduce waste actually allows one to speed things up, like solving a Rubix cube for speed or learning martial arts or any learning curve progression slow to build then exponential growth until diminishing returns, like mass production in manufacturing, etc. Understanding learning curve & progression while reducing waste.
With basic competency pursuing mastery, kids could apply this to anything in life.
These are GREAT. Thank you so much.