This afternoon I came across a tall stack of Lego® boxes stored in my son’s closet; they reminded me of a lesson.

(My son just turned 20 three days ago. I can still see him playing with his Lego sets for hours on end when he was younger. And when he ran out of floor space in his room, he took over our entire living room, and we were happy to let him.)

**Simple lesson **— (I was looking around and this site cited the Mathematics Teacher, Vol. 92, No. 2 February 1999 titled “Promote Systems of Linear Inequalities with Real-World Problems” as source for this problem.)

You own Funky Furniture, a store that makes tables and chairs out of Lego pieces to sell. A chair is made of one large and two small pieces. A table is made of two large and two small pieces.

Currently you have 8 small Lego pieces and 6 large ones. If the profit for a table is $16 and for a chair is $10, then **how many tables and chairs should you make to maximize profit for your Funky Furniture business?**

I know there are a ton of “systems of inequalities” problems out there, but playing with Lego pieces is just more fun. Students can see the “tables” and “chairs” as they build them. I have the kids work in pairs, so each pair gets a Ziploc bag of 8 small pieces and 6 large pieces. Nobody leaves my room until all the pieces are back into the baggies and returned.

If you don’t have Lego, maybe the kids can bring theirs in? There’s ebay. Or you can just use centimeter cubes and inch cubes, or dice and cubes, or Cuisenaire rods and round counters. Or you can just print small and large rectangles on construction paper for them to cut out — flat models are better than no models. Anything they can manipulate is fine.

We’ll be ready for this lesson next week as we just wrapped up systems of linear equations right before break.

And I just remember this fun problem about Mrs. Murphy’s Missing Laundry. Have you seen it? Here’s The_Case_of_the_Missing_Laundry1. There’s no manipulative involved, but kids like to solve mysteries too.

## 8 Comments

I can figure out the answer, but what about the mathematics behind this problem? I’m having a difficult time coming up with the constraints. Could you shed some light on them?

Thanks!

Hi Beth. The constraints are that you only have 6 large and 8 small Lego pieces. We can graph the various equations on an x-y coordinate, where x is the number of chairs and y the number of tables. Thus we have 2x + 2y < 8, and 2x + y < 6. We also have the profit equation of P = 10x + 16y. We can have kids create spreadsheets also: https://docs.google.com/spreadsheets/d/1uccK6RBuB_dC9-qTQhnplhCKqksUJdMcPsfDqfFztys/edit?usp=sharing

Hope this helps.

Sorry, the file you have requested has been deleted :-(

Hey, I love your stuff and I use it regularly. Just recently moved up to HS and am teaching Algebra II.

Was looking for an interesting and 3-act-able intro to feasible regions and linear optimization. This Lego stuff is great.

I made this movie to complement the lesson.

https://www.youtube.com/watch?v=ARXsMSLElz4

Just an FYI, I changed it to 12 small bricks and 8 large bricks. Thought I’d share.

This video is restricted. Try signing in with a Google Apps account :-(

can you make it visible?

I’ve got it set to public. Try searching YouTube for it by name: Lego Furniture Maker Guy.

Or there is another link to it here:

dyermath.wordpress.com

Greetings! I’ve been following your web site for a long time now and finally got

the courage to go ahead and give you a shout out from Dallas Tx!

Just wanted to mention keep up the great job!

Thank you, Kristen! Always great to hear that from readers. Much appreciated.

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[…] wrote about planning for this Legos lesson here. We really needed more pieces as a few of the students found the maximum profit within the first […]

[…] worked through Mrs. Murphy’s Laundry today, which is from from Fawn’s 180. For the first time this year I heard students talking about the problem on their way out the door […]

[…] -Lego Pieces by Fawn Nguyen […]

[…] to be honest, there are 1,000 things out there that are better than what I have. For example, Fawn’s Funky Furniture . It seems Steve had a similar idea and made a worksheet. Let’s all say hi to […]

Carpentry SquareLego Pieces and Feasible Region