Comments on: Estimation Isn’t Just Calculating Badly On Purpose

By: Dan Meyer

Dan Meyer — Fri, 17 Jan 2020 04:36:31 +0000

In reply to Joel. Love it. That's exactly it!

By: Joel

Joel — Thu, 16 Jan 2020 19:52:04 +0000

Hello Dan,
I was working on an interactive estimation activity, when my wife sent me this post. The idea of sorting equation in the example above seemed to really get at the skill of estimation. After lots of design iterations I came up with this:

https://toytheater.com/apple-island/

Thanks,
Joel

By: Dan Meyer

Dan Meyer — Mon, 02 Dec 2019 02:51:59 +0000

In reply to Don Ostrow. Yep! It can be solved with that formula, with a spreadsheet, with sigma notation — through lots of means all of which depend on the student knowing information about the pyramid that isn’t evident from the photo. It has a square base. 40 layers. Each layer has 13 stacks. Etc.

By: Dan Meyer

Dan Meyer — Mon, 02 Dec 2019 02:48:28 +0000

In reply to Theresa M Clifford. That's fantastic. Including this in my next newsletter dispatch.

By: Don Ostrow

Don Ostrow — Wed, 27 Nov 2019 18:26:45 +0000

Hey Dan –
Can the Penny Pyramid problem be solved by computing the sum of consecutive squares from 1 to 40?
(2n + 1)n(n + 1)/6
(I found this formula on The Math Page: https://www.themathpage.com/Arith/asquares.htm#sum.)

Granted, solving this by mental math is out of reach of all but the few savants in the crowd, so estimation is by for the preferred approach.

I’m a longtime fan. Thanks for your work!
—Don

By: Theresa M Clifford

Theresa M Clifford — Tue, 26 Nov 2019 17:25:48 +0000

Featured Comment

At the beginning of the jar I fill 4 jars around the room. One with m&m's, one with eraser caps, one with cotton balls, one with paper clips. They are all allowed a guess for how many in each jar. They enter their answer and their name on a slip of paper and place it in a collection jar. Whenever we come to a question where I want them to estimate first, I remind them of what they did when they first looked at the jar. I don't tell them how many in each until the winter break - the suspense is awesome. Then in January I start with 4 new jars. Not sure what I'm doing in those ones yet so if anyone wants to suggest anything..... Thanks Dan for reminding us about estimating. It's so important and our kiddos are so afraid of it.

By: Jeremy

Jeremy — Tue, 26 Nov 2019 16:23:00 +0000

Estimation is also useful after an exact calculation has been performed. I often ask my students to perform a “sanity check.” For example, if you calculate a speed and get a number larger than the speed of light, your answer is insane and must be wrong.

By: Dan Meyer

Dan Meyer — Wed, 20 Nov 2019 05:07:40 +0000

In reply to Mr K. Nice reference here. Fermi problems seem to fall in the category of "tasks where estimation is the only possible method."

By: William Carey

William Carey — Tue, 19 Nov 2019 01:28:20 +0000

In reply to William Carey.

Sure – a couple that I do with students are recreating the method of exhaustion to approximate pi (where you know your estimate will be wrong, and in what way, but there’s literally nothing else to do). We also do the volume of a pyramid inscribed in a cube (with duplo at first, then via estimation, then analytically). First we estimate, then we approximate, then we refine.

I also run through a bunch of estimation and approximation techniques with the kids for data modeling in pre-calc. So, RANSAC, least sum of squares, and the like. Once we have tools to evaluate our estimates, they become much more powerful.

By: Sharing Diigo Links and Resources (weekly) | Another EducatorAl Blog

Sharing Diigo Links and Resources (weekly) | Another EducatorAl Blog — Mon, 18 Nov 2019 05:03:52 +0000

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