Archive of ‘math in real life’ category

Rational Functions and Jewelry Production

By Kristina

Math SL is a Diploma Programme (DP) course for grades 11 and 12, yet I’m unit planning in the IB Middle Years Programme (MYP) style since it’s consistent with our grades 6-10. MYP math has four criteria: A – Knowing and Understanding, B – Investigating Patterns, C – Communicating, and D – Applying Math in a Real-Life Context.

I’ve been racking my brain to come up with an authentic assessment (not a test) for my Rational Functions Unit. In this unit, we are focusing on the following objectives from the IB Math SL syllabus:
2.5 The reciprocal function x → 1/x, x ≠ 0, its graph and self-inverse nature. The rational function x → ax+b/cx +d and its graph. Vertical and horizontal asymptotes. Applying rational functions to real-life situations.

My statement of inquiry for the unit is “Representing change and equivalence in a variety of forms has helped humans apply our understanding of scientific principles.”  I’d been looking at population growth, water flow, and light (via Until Next Stop) after checking out the MTBoS, but couldn’t quite get the right assessment.

Then I found The Math Projects Journal Optimum Bait Company task and hint cards. This approach seemed great for scaffolding problems like this one, which students had had trouble with:

When printing out the Optimum Bait Company task, I ran into a coworker in the teachers’ lounge. We got to chatting about modeling production costs. She is an English teacher, but I feel like she’s my in-person MTBoS because she brings so many interesting approaches to teaching and problem-solving. We talked about the larger question “how do you know when to enter a market?” and concepts such as barrier to entry (overall cost of running a business, competition, willingness to buy), sunk cost, marginal cost, and bringing in investors.

This conversation led me to create my own task about my friend’s company (Winter Hill Jewelry), because the marginal cost of production of earrings seemed like it would be similar to the bait problems (and the problems from the textbook). I asked her what kind of printer she used and how much filament was needed for a pair of earrings. She replied “Flash Forge and on average, 3 grams of filament per pair of dangle earrings.”

I found pricing for fish hooks and PLA filament on Amazon, then found a few prices for FlashForge 3D printers. I recalled that Vanessa had space at Artisans Asylum, so I checked out their memberships and studio rental costs. I realized that Artisans provides 3D printer usage to members (at a cost of $0.10 per gram of PLA used), so I moved the “buy your own 3D printer” option to a homework problem.

I used the slides and task document linked at the bottom of this post to introduce the task and support students’ work. I started by asking “what questions could you ask about these earrings?” and “what do you notice?” Some students went right to “how much do they cost?” Some focused on geometric patterns in the designs. Others picked up on the fact that they were 3D printed (they’d done some 3D printing in summer enrichment).

I explained the origin story of Winter Hill Jewelry and then asked them to brainstorm what goes into the cost of making 3D printed earrings. Lots of great ideas came out in the groups: ads, URL, shipping, electricity, workspace/rent, labor, taxes, investors, and more. I showed them the monthly recurring costs (workspace, 3D printer PLA, and fish hooks), then explained that we were going to use hint cards to support their perseverance through longer independent work. The hint cards didn’t work as I had intended, so I changed strategy for the second class (offering more conversation when I noticed they were off versus holding to the “only thing I can offer is a hint card”). For example, when a student asked “am I right?” when proposing a per-unit cost of $652, I told him “I own three pairs of these earrings. Do you think it makes sense on a teacher’s salary to buy something that’s $652 before profit?”

We’ll finish out the task on Monday and revisit the traditional form of IB exam-style problems–I am curious to see if the students do better as a result of exploring problems like this one!

Winter Hill Jewelry Task and Slides.

Atlas Coffee Club and Math Projects

By Kristina

Disclaimer: I was sent a complimentary sample of Atlas Coffee in exchange for my thoughts on the product. I was not paid to write this post. All opinions are my own. There are no affiliate links in this post.

I’ve written about coffee math before and recently got inspired again after learning about Atlas Coffee Club. After my beginning of semester poll on “what would help you do better in math?” some of the students in my math enrichment class said “real-world projects!” I love doing those anyway, so I got to thinking about topics that are relevant to them. My first period 9th grade class doesn’t seem to have the same coffee addiction as my past 11th and 12th grade classes, but that may change for them in the future. In past years, my early morning 11th or 12th grade classes often looked like a Starbucks (minus the hipster clothing and MacBooks) because of the sheer number of Frappuccinos, iced passion teas, and coffees. The teachers, however, still come in with various types of coffee (homemade in a travel mug, Dunkin iced, Starbucks, or local cafe) and often go out for a mid-day coffee break or use the Keurig machine in the teachers’ lounge.

Thus is born my new project idea: Have students do “market research” and create a “make coffee at home” plan for teachers who spend way too much on buying coffee out. Atlas Coffee Club offers a wide variety of coffees from around the world along with subscription options that suit different frequencies of coffee drinking.

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1) Interview a teacher about their favorite type of coffee and their coffee habits. For example, if they like Ethiopian reserve coffees at Starbucks, they might like the Ethiopian Sidamo. For coffee habits, find how often they drink it, how much it costs per day, and their habits (e.g., are they always rushing in the morning? do they have to make coffee for a husband/wife/signficant other? do they have patience for using a Chemex? do they even know what a Chemex is?).
2) Find a coffee that matches their flavor preferences and coffee-making style (clearly explained by the Atlas coffee brewing guide)
3) Price out how much related equipment will cost if the teacher does not already own it (travel mug for taking to school, French press, Chemex).
4) Price out their subscription (including if they use the 5% lifetime discount).
5) Figure out when the teacher will break even given the cost of the equipment and subscription versus the daily purchase.
6) IB bonus: research the coffee industry in the country of origin of the chosen coffee.
7) Extension: find a k-cup brand and price out how much it would cost for the teacher to bring those to school to brew in the teachers’ lounge machine. Assess the environmental impact and time savings of this option.

I’m interested to see how this plays out with the kiddos. I like that this problem is open-ended and that they’ll have to apply the skill of “reaching out to an adult and actually speaking to them” as well as using linear equations and systems of equations in a context that’s not just a math problem that comes out to nice integer answers.

powerball

By Kristina

Powerball is all the rage right now. Despite knowing that I could have spent my $6 on something useful, I still gave in to the hype.

powerball

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“An Annuity Option means winners can choose to be paid in 30 graduated annuity payments made over a twenty-nine (29) year period. A Cash Option means winners can choose a one-time cash payment which will be (approximately) the cost of the annuity divided by the number of winning tickets. Note: If a winner fails to claim the jackpot and select a jackpot payment option within 60 days, the prize will be automatically paid as an annuity. All prizes must be claimed within one year of the drawing.”

My Facebook newsfeed has been hopping with erroneous applications of dividing the jackpot by the U.S. population as a “solution for poverty,” people making fun of the incorrect math, fun math discussion, and fun speculation of “what would you do if you won?” My friend Heather pointed out “So I tried to figure out a scam to win: if you need 292M permutations to win, at $2 a ticket you need a bankroll of $584M – the lump sum pay out is 62%, and that definitely puts you in the 39.6% income tax bracket… The take home is $487M (not counting the cost of the team of lawyers you now need to employ). Back to the drawing board.” Likewise, my friend Jonathan said “Also, isn’t the $1.3 billion mythical? In the sense that, if one elects a one-time payment, the payout is substantially less, and the $1.3 B number is only achieved by adding together 30 years of nominal payments of 1/30th of $1.3B. Of course, in 30 years, the last payment will be worth less than half its value in today’s dollars. In a real-life conversation, my friend Ashley said that she’d rather take the lump sum and invest it because she could get a better interest rate than with the annuity. I would love to examine the concepts of probability, expected value, inflation, annuity, and taxes with students (not to mention the social aspects of lottery winning). It would make good fodder for a math debate…

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I would also be interested in having students analyze the changes in the Powerball game structure:
“Powerball® Enriched: Starting Jackpots Double to $40 Million
In January 2012, Powerball® was redesigned to bring even more excitement and value to its players. Jackpots in the multi-state game now start at $40 million and grow faster overall. There are more chances to win a prize of at least $1 million cash and the overall odds of winning any prize in the game are also better. Beginning with the January 15, 2012 drawing, game tickets increased from $1 to $2 per wager.
The Power Play® add-on feature is also available for an extra $1 per play. For that extra $1, players have the chance to multiply their prize by as much as ten times. Just before each Powerball drawing, a multiplier number (2X, 3X, 4X, 5X and 10X) is randomly drawn. If a player purchased the Power Play option for an extra $1 per play, that randomly selected number is used to multiply any prizes won, with the exception the JACKPOT and the Match 5 prize (which increases from $1 million to a set $2 million with Power Play).

Powerball with Powerplay gets bigger!
October 4, 2015 – The multi-state Powerball lottery game changed the matrix which is designed to produce larger jackpots and add more winning experiences. In the new matrix, players will select 5 out of 69 white-ball numbers and 1 of 26 Powerball numbers. The overall odds of winning a prize in the game improves from 1 in 31.8 to 1 in 24.9.”

Questions
1) How would you approach this with your students?
2) What would you do first if you won the jackpot?

math in real life: blackout shades

By Kristina

I’m researching blackout shades for our nursery and started my design process by polling a few mom groups. One mom suggested Pottery Barn Kids.

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These Harper shades are lovely, on sale, and have been positively reviewed at Embrace My Space. However I realized that they wouldn’t work for our nursery upon seeing that all variations were 64″ long. Our windows are almost floor-to-ceiling.

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I went in to measure the window widths to see if curtains might work. A friend recommended these Koala Baby curtains, but they would be too short. These Harper curtains come in varying lengths that could potentially be tall enough. However, the smaller windows are approximately 22″ and the large window is approximately 58″. We’d need three 44″ panels to cover the span of the windows without leaving gaps.

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Perhaps wider curtains would work? My friend Heidi at This Bold Home recommended these, which are 52″ across. Two of those panels could work! The nursery foiled me again though. This weird ceiling dip also prevents a curtain rod from going all the away across the windows.

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Based on all of these constraints, I’m eyeing custom cordless cellular blackout shades that can be installed by the company.Blinds to Go cordless cellular thermal shades seem the most promising right now because the former owners of the unit two floors above ours also used these for their baby’s nursery (same room as Parker’s and same dimensions), so their shades would likely work well in our space. I feel like I *should* DIY and self-install, but I’m neither interested in nor good at it. I feel hypocritical saying “I’m not good at it” because I really dislike it when people say “I’m just not good at math” and give up on it. But, in comparison to something like cooking (which I enjoy and can do without lots of struggle), the time and effort spent on self-installation would far outweigh the cost. I recently had an Elfa closet installed, and the fee was well worth it. It only took the installer an hour to do (while it would have taken my husband or me much longer, and we would have had to have the other person watch Parker).

Other recommendations from fellow moms:
The Shade Store
Lowe’s – from the former owner of our unit, who installed plantation shutters in the living room and cellular shades in both bedrooms
Bed, Bath, and Beyond curtains
JC Penney cordless cellular blackout shades (install yourself) (though one mom pointed out that
Home Depot cordless cellular blackout shades