Fix the Math Clock!
First, I'll provide each of my students with a list of the expressions and equations already on the clock, and tell them that there's one that's not quite accurate. I'll ask them to simplify or solve each one (whichever word applies--a great time to review the difference between the two terms) to figure out which expression/equation doesn't correspond exactly to the number it's supposed to represent. Once they figure it out, I'll also lament loudly that the equations and expressions are way too easy for my students, and they deserve more of a challenge when they want to know what time it is.
Then I'll give each student circular piece of paper cut to fit my lovely clock, and a fistful of markers. Their job will be to create twelve equations, one for each clock number. These equations must take more than one step to solve, and they must require the use of the distributive property, combining like terms, or adding variable terms to both sides of the equation. Then they'll swap equations with a neighbor and check each other to make sure the solutions of these equations come out correctly. Once they're good to go, they'll create a new clock face featuring their equations along with any other creative touches they care to add.
The best one will replace the clock face that's already there!
Any thoughts to make this task richer?
Ryan, as (1/2*2) of your "wife's parents" (but I suppose that's too simple an equation!, for which I apologize), I am perturbed by the slight inaccuracy of the equation for 9:00 a.m. (I presume it could not, strictly speaking, be accurate or inaccurate for 21:00), so perhaps I should approach the other (2*1/2) of your "wife's parents" to address the logically-positivist question of the verifiability of the gift as a meaningful mercantile transaction. In short, did we get what we paid for? But with a flawed timepiece, however slight, ((1/2*2)+(2*1/2)) shall never be in sync, always phase-shifted a little in the space-time continuum (like a bit of underdone Star Trek), thus never quite meeting to simplify or resolve (whichever might apply to) the problem ....
ReplyDeleteYes, just as a stopped clock is right twice a day, this one is right a nanosecond or two after 9:00 and 21:00. And I'd say that if my students get a motivating lesson out of it, then you definitely get what you paid for, plus some!
DeleteBut what's truly disturbing, Ryan, are the time signatures for our posts!
DeleteWhat a great idea! I love the clock. Perhaps there is also an inaccuracy at 2 o'clock. Could it also be negative 2? You could extend the task to 24 hour clock but I do not think that is making it richer, just longer! I am not sure what to suggest in terms of richness. This is just a nice task that gives a chunk of practice in solving equations without it being a boring set of textbook questions.
ReplyDeleteTrue about 2:00. Now that you mention it, 7:00 and 8:00 have the same problem!
DeleteAs I understand it, the radical symbol only stands for the principal square root so I think that's probably okay. Though it would lead to a good discussion.
DeleteAndrew is correct here. We want the square root to be a function, so sort(4) is just 2.
DeleteI have the same clock (a gift from a student) and it is ticking away in my workroom right now.
A possible fix for 9 would be to use the greatest integer function for 3pi
One of my colleagues has a challenge (poster) to use four 4's and any mathematical operations to get all of the numbers from 1-100. The smaller answers are easier, but the bigger ones are pretty blank...
ReplyDeleteHow about bonus points for making equations for today's date, or something else that rotates on a daily basis? You might want to limit the input digits for something more challenging...
Thanks, I like that! Equations for different units of time. I could call it "Time for Math" or some such thing...
DeleteOooh! perhaps even stranger, make the same circular clock, but compensate for 24-hour time. The answer at the 7 has to be 7 and 19... (strange discussion for 0/12/24).
DeleteNow that IS a cool idea! A problem like that could be fun from algebra 1 on, and could be made more difficult depending on the level of the course and ability of the students. Thanks!
DeleteIn reading through the comments, it makes me think your students should just make their own clock. Clock parts cost like $4 at amazon and the board doesn't even have to be round. They could even make them out of paper plates at first and the class can vote on which one gets made into a real clock.
ReplyDeleteI have one of these clocks too, I got it from my grandmother. I LOVE the task that you have laid out here. Has it ever bothered you that the solution to 7 o'clock is technically 7 and -7? I've always wanted to replace that one with an equation with 7 and -5 as the solutions.
ReplyDeleteYES that has bothered me, but it didn't even occur to me to make it a solution modulo 12. I love that.
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