Weird Analogies: The Halloween Candy Tax
If you lot pass much fourth dimension inward my classroom at all, you lot volition chop-chop realize that I purpose lots of weird analogies. Some analogies I purpose 1 time as well as forget about. Other times I start analogies without truly thinking close them as well as destination upwards regretting my decision. And, sometimes, my analogies truly run as well as I destination upwards beingness able to purpose them to a greater extent than than once.
I don't recall the get-go fourth dimension I used this analogy, but I intend it must conduct keep been during my get-go yr of teaching. My students were struggling alongside factoring the GCF out of an expression. We were looking at problems similar this:
It didn't accept much convincing that nosotros should component an 8 out of both terms. But, my students were insistent that nosotros could exclusively component out 1 x as well as 1 y. Once I convinced them that it was okay to component out to a greater extent than than a unmarried variable, many of them defaulted to wanting to component out the release of variables from the get-go term. So, inward this example, they would desire to component out x to the 8th as well as y to the sixth. Telling them that nosotros wanted to component out the greatest release of things they had inward mutual didn't truly seem to help.
So, analogy fourth dimension it was. Be forewarned. I used this analogy alongside my students today, as well as it resulted inward 1 shape accusing me of beingness savage as well as cold-hearted. As long equally something helps my students encounter math to a greater extent than clearly, I'm okay alongside them thinking crazy things close me.
So, today, the shape is confused. Frustrated. Ready to compass up. Fixed mindset statements are beingness uttered at every turn. And, I'm pretty certainly most of my students would depict themselves equally beingness inward the panic zone. I sit down on overstep of an empty educatee desk, as well as I await around at my students. Eventually they seem to feel that I conduct keep something to say:
Okay, everyone. Listen up. From walking around as well as listening to your conversations, I tin tell that we're struggling. I'm going to tell you lot a story. Maybe it volition help. Maybe it won't. Maybe you'll become dwelling this evening as well as tell your parents what a crazy math instructor you lot have. But, maybe, merely maybe, it volition assist to shed some calorie-free on the problems we've been attempting to work.
Some twenty-four lx minutes catamenia you lot volition conduct keep children. [This controversy commonly gets their attention!] And, every yr you lot as well as your children volition participate inward this crazy tradition. October volition curlicue around, as well as you lot volition clothes upwards your trivial ones inward adorable or spooky costumes. Then, you'll become from door to door alongside cute, colorful pumpkin pails. The elementary human activeness of uttering 3 trivial words volition outcome inward candy beingness placed inward your kids' pails. After visiting a release of houses, pumpkin pails volition locomote overflowing, as well as you lot as well as your children volition provide home, excited to sort through the candy that has been amassed.
At this point, you lot explicate to your children that at that spot are certainly things inward life that...well...may non seem fair. But, life goes on, as well as things similar taxes must locomote paid. To assist your children acquire close the taxation system, a Halloween Candy Tax (HCT) volition locomote applied to the night's acquisitions. But, your children needn't worry also much because you lot volition locomote real fair inward collecting the tax.
The HCT requires that the candy must get-go locomote sorted past times type. Tootsie Rolls are placed alongside Tootsie Rolls. Butterfingers alongside Butterfingers. Twizzlers alongside Twizzlers. I intend you lot acquire the idea. The principal watch behind the taxation is that the same release of each variety of candy volition locomote taken from each of your children. If 1 kid has v lollipops as well as and your other kid has seven lollipops, the most lollipops you lot tin accept volition locomote v lollipops because that is the most that you lot tin accept from BOTH of your children. And, because you lot are greedy as well as jealous that you lot are at 1 time definitely also quondam to become fox or treating yourself, you lot volition ever accept the greatest possible release of candies from all of your children. Sure, you lot could merely accept 2 lollipops from each child, but your greed volition motility you lot to accept v lollipops from both children.
[At this indicate inward the story, my students are outraged. The 1 hapless kid at 1 time has cipher lollipops. Insert lots of comments close the injustice of the province of affairs as well as what a terrible someone I am. My promise is that if they're engaged inward the story, they'll locomote engaged inward how it relates to the work we're trying to solve.]
Imagine you lot conduct keep 2 kids. Billy as well as Sally.
Billy as well as Sally dump out their pumpkin pails to uncovering tootsie rolls, lollipops, jawbreakers, as well as a caramel apple. How many tootsie rolls volition you lot taxation your children if you lot desire to locomote fair but greedy? What close lollipops? Jawbreakers? What close that lonely caramel apple? Who gets it?
Eventually, you lot destination upwards alongside this:
The shape decides that Billy truly didn't destination upwards good inward this deal. Of course, they give-and-take it a fight to a greater extent than crudely than that.
Back to the problem:
We determine to permit the x's stand upwards for starbursts as well as the y's stand upwards for smarties. If 1 kid has 8 starburts as well as the other kid has ix starbursts, a greedy but fair nurture volition accept 8 starbursts from each child. And, the maximum release of smarties that tin locomote taken from both children would locomote 5. All of a sudden, lightbulbs start to come upwards on. Why didn't you lot explicate it this agency inward the get-go place?
Does every educatee quest this analogy? I don't intend so. Students who already empathise the concept of finding the GCF volition probable uncovering the storey annoying as well as pointless. Why would you lot quest to intend close Halloween candy? But, I've flora that this analogy makes factoring a fight to a greater extent than tangible for my students who conduct keep traditionally struggled alongside math.
And, for the record, I don't taxation my ain children's Halloween candy. I'd kinda quest children to locomote able to practise that. And, according to my students, this would locomote a totally unfair policy. So, I approximate when I practise conduct keep kids of my ain 1 day, I'll merely conduct keep to purchase my ain Halloween candy...
I don't recall the get-go fourth dimension I used this analogy, but I intend it must conduct keep been during my get-go yr of teaching. My students were struggling alongside factoring the GCF out of an expression. We were looking at problems similar this:
So, analogy fourth dimension it was. Be forewarned. I used this analogy alongside my students today, as well as it resulted inward 1 shape accusing me of beingness savage as well as cold-hearted. As long equally something helps my students encounter math to a greater extent than clearly, I'm okay alongside them thinking crazy things close me.
So, today, the shape is confused. Frustrated. Ready to compass up. Fixed mindset statements are beingness uttered at every turn. And, I'm pretty certainly most of my students would depict themselves equally beingness inward the panic zone. I sit down on overstep of an empty educatee desk, as well as I await around at my students. Eventually they seem to feel that I conduct keep something to say:
Okay, everyone. Listen up. From walking around as well as listening to your conversations, I tin tell that we're struggling. I'm going to tell you lot a story. Maybe it volition help. Maybe it won't. Maybe you'll become dwelling this evening as well as tell your parents what a crazy math instructor you lot have. But, maybe, merely maybe, it volition assist to shed some calorie-free on the problems we've been attempting to work.
Some twenty-four lx minutes catamenia you lot volition conduct keep children. [This controversy commonly gets their attention!] And, every yr you lot as well as your children volition participate inward this crazy tradition. October volition curlicue around, as well as you lot volition clothes upwards your trivial ones inward adorable or spooky costumes. Then, you'll become from door to door alongside cute, colorful pumpkin pails. The elementary human activeness of uttering 3 trivial words volition outcome inward candy beingness placed inward your kids' pails. After visiting a release of houses, pumpkin pails volition locomote overflowing, as well as you lot as well as your children volition provide home, excited to sort through the candy that has been amassed.
At this point, you lot explicate to your children that at that spot are certainly things inward life that...well...may non seem fair. But, life goes on, as well as things similar taxes must locomote paid. To assist your children acquire close the taxation system, a Halloween Candy Tax (HCT) volition locomote applied to the night's acquisitions. But, your children needn't worry also much because you lot volition locomote real fair inward collecting the tax.
The HCT requires that the candy must get-go locomote sorted past times type. Tootsie Rolls are placed alongside Tootsie Rolls. Butterfingers alongside Butterfingers. Twizzlers alongside Twizzlers. I intend you lot acquire the idea. The principal watch behind the taxation is that the same release of each variety of candy volition locomote taken from each of your children. If 1 kid has v lollipops as well as and your other kid has seven lollipops, the most lollipops you lot tin accept volition locomote v lollipops because that is the most that you lot tin accept from BOTH of your children. And, because you lot are greedy as well as jealous that you lot are at 1 time definitely also quondam to become fox or treating yourself, you lot volition ever accept the greatest possible release of candies from all of your children. Sure, you lot could merely accept 2 lollipops from each child, but your greed volition motility you lot to accept v lollipops from both children.
[At this indicate inward the story, my students are outraged. The 1 hapless kid at 1 time has cipher lollipops. Insert lots of comments close the injustice of the province of affairs as well as what a terrible someone I am. My promise is that if they're engaged inward the story, they'll locomote engaged inward how it relates to the work we're trying to solve.]
Imagine you lot conduct keep 2 kids. Billy as well as Sally.
Eventually, you lot destination upwards alongside this:
The shape decides that Billy truly didn't destination upwards good inward this deal. Of course, they give-and-take it a fight to a greater extent than crudely than that.
Back to the problem:
Does every educatee quest this analogy? I don't intend so. Students who already empathise the concept of finding the GCF volition probable uncovering the storey annoying as well as pointless. Why would you lot quest to intend close Halloween candy? But, I've flora that this analogy makes factoring a fight to a greater extent than tangible for my students who conduct keep traditionally struggled alongside math.
And, for the record, I don't taxation my ain children's Halloween candy. I'd kinda quest children to locomote able to practise that. And, according to my students, this would locomote a totally unfair policy. So, I approximate when I practise conduct keep kids of my ain 1 day, I'll merely conduct keep to purchase my ain Halloween candy...
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