iiinova — where your digital self keeps evolving

David Flynn @dpfl.bsky.social · 07/02/2025

I picked one of these up at a car boot sale a few years back with honest intentions to learn how it worked but never got round to it.

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David Flynn @dpfl.bsky.social · 03/02/2025

Though example 1 isn’t a particular good “e.g” in this case. Oh dear.

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David Flynn @dpfl.bsky.social · 03/02/2025

That’s a great question and something I completely overlooked. Derangements only seems like a necessary rule to make this question interest, but the first example doesn’t use that.

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David Flynn @dpfl.bsky.social · 09/01/2025

Honestly I can’t either anymore. I probably made a mistake but I’m gonna believe I had a moment of insight that’s just forever lost.

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David Flynn @dpfl.bsky.social · 09/01/2025

3/4? 3/9? 3/1? 1/5? This is cool.

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David Flynn @dpfl.bsky.social · 08/01/2025

This looks interesting. What are the common errors you’re referring to?

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David Flynn @dpfl.bsky.social · 24/12/2024

Maybe gradually removing parts and asking they think goes in the blanks.

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David Flynn @dpfl.bsky.social · 24/12/2024

Nice problem. I wonder if there is a way to keep this engaging for the kids after they’ve noticed the pattern.

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David Flynn @dpfl.bsky.social · 20/12/2024

Do you mind if I request access to this?

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David Flynn @dpfl.bsky.social · 20/12/2024

Storytelling about *learning* math is a lovely way to reframe perceptions of what is means to be a math person.

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David Flynn @dpfl.bsky.social · 19/12/2024

Is there something specific you’re talking about with number sense and fractions?

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David Flynn @dpfl.bsky.social · 19/12/2024

I think there’s also a lot with can do with digital representations that help strengthen conceptual understanding.

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David Flynn @dpfl.bsky.social · 19/12/2024

This is a good read! Looking forward to reading a few more responses on this one. #mtbos #iTeachMath

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David Flynn @dpfl.bsky.social · 19/12/2024

I think remainders in grade 4 can be really messy and not always done well. For example: 16 divided by 5 is 3 remainder 1 25 divided by 8 is 3 remainder 1 But 16 / 5 =/= 25 / 8 All in the same grade where students learn that 16/5 = 3 1/5.

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David Flynn @dpfl.bsky.social · 19/12/2024

That’s grade 3. There’s a lot of high impact stuff in Grade 3, particularly multiplication and fractions. A lot of struggles start if students are learning multiplication disconnected from addition, and fractions disconnected from integers.

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David Flynn @dpfl.bsky.social · 18/12/2024

The base 10 blocks play an important role. Altogether we have 182 blocks, but we can’t just make *any* rectangle with area 182 since the 100-piece won’t allow it.

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David Flynn @dpfl.bsky.social · 18/12/2024

What’s the max number and what’s the min number is a great prompting question for this. I wonder if aiming for a sum of 0 initially sounds like more of a challenge to students - when in practice it’s slightly simpler.

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David Flynn @dpfl.bsky.social · 15/12/2024

Nice question, started working on it before seeing the area of 2 condition so had to go back. I’m struggling to find the rhombus that isn’t a square.

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David Flynn @dpfl.bsky.social · 15/12/2024

That sounds pretty convincing. What about something like 32 and 55? 15 hundreds 25 tens 10 ones There are 2 different rectangles I can make with those blocks.

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David Flynn @dpfl.bsky.social · 14/12/2024

I meant giving “= 7/18” on F and “= 2/7” on G. It might shift the focus from evaluating the expressions to thinking more about the patterns - why sometimes the denominator changes and why sometimes the numerator changes ¯\_(ツ)_/¯ . But if the goal is evaluation - this’d make the task worse.

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David Flynn @dpfl.bsky.social · 14/12/2024

I absolutely love this task. But I wonder if it suggests we’re not allowed to say 7/9 = 3.5/9. Do you think the task gets better or worse if you changed from expressions to equations?

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David Flynn @dpfl.bsky.social · 14/12/2024

Maybe you could try some open number line stuff with division? And then revisit it when you get to fractions. I put together this task with 24 (which is nice for connecting to 3rd grade denominators!) You can use the first task during division, and then try a similar task during fractions.

24 divided by 2, 3, 4, 6, 8 on an open number line.
1/2, 1/3, 1/4, 1/6, 1/8 on an open number line.

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David Flynn @dpfl.bsky.social · 14/12/2024

Another example of a unique solution: Put together 2 hundred-pieces 21 ten-pieces 27 one-pieces to make a rectangle. An example of a non-unique solution: Put together 1 hundred-piece 7 ten-pieces 10 one-pieces to make a rectangle. #MTBoS #iTeachMath

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David Flynn @dpfl.bsky.social · 14/12/2024

Puzzle for 4th Graders: Using Base 10 blocks, put together 1 hundred-piece 7 ten-pieces 12 one-pieces to make a rectangle. What are the side lengths of your rectangle? Puzzle for #iTeachMath #EduSky folks: What are the considerations in number choice that make these puzzles unique vs. non-unique?

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David Flynn @dpfl.bsky.social · 14/12/2024

What are the things that are most scary about teaching fractions? Are there things you find that students particularly struggle with?

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David Flynn @dpfl.bsky.social · 13/12/2024

Am I suppose to write a number in each arrow or square?

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David Flynn @dpfl.bsky.social · 13/12/2024

I thought impossible at first too. If A x B = A / B then has to be 1 (or so I thought). In which case both of the expressions are equal to A. In which case, A + B is A + 1 which doesn’t work. ☹️ Then I thought about whether B might be -1 🤔

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David Flynn @dpfl.bsky.social · 12/12/2024

I’m not sure what the best set of divisors are for this task. Including 5 and 9 definitely make the solution more interesting. But having 5 divisors make the task too cumbersome for primary school learners.

media.tenor.com

kermit the frog and miss piggy are kissing each other in a muppet show .

ALT: kermit the frog and miss piggy are kissing each other in a muppet show .

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David Flynn @dpfl.bsky.social · 12/12/2024

Nice. The elegance of that solution seemed to me that 335 must be the smallest number where we can max out the remainders. But 167 works similarly well.

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David Flynn @dpfl.bsky.social · 12/12/2024

🎵 "It's the Most Wonderful Time of the Year…”🎵

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David Flynn @dpfl.bsky.social · 12/12/2024

Glad I saw some other responses before wishing you a happy 76th 👀

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David Flynn @dpfl.bsky.social · 12/12/2024

Pick a 3 digit number. Divide the number by 6. Write down the remainder. Divide the number by 7. Write down the remainder. Divide the number by 8. Write down the remainder. Add the three remainders together. What starting number should you pick to get the greatest possible sum? #iTeachMath

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David Flynn @dpfl.bsky.social · 12/12/2024

Beast Academy is the ‘elementary’ wing of AoPS. But it covers a lot of middle school stuff. The Level 5 books get fairly advanced.

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David Flynn @dpfl.bsky.social · 11/12/2024

When students start estimating in grade 3, the standards ask them to do it with problems that can be solved exactly. It can feel contrived. Fermi problems are a great way to introduce estimation in a way that’s authentic, fun, and slightly divorced from all the arithmetic done throughout the grade.

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David Flynn @dpfl.bsky.social · 11/12/2024

This is also a great example of why number choice matters so much.

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David Flynn @dpfl.bsky.social · 04/12/2024

Left one: How many different sized squares can you see?

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David Flynn @dpfl.bsky.social · 04/12/2024

I think similar but slightly different question that I find interesting whether or not folks include the subject they teach when they’re asked what they work as. “I’m a teacher” Vs “I’m a maths teacher”

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David Flynn @dpfl.bsky.social · 02/12/2024

Wonderful set of tasks. Love seeing All Ten in there!

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David Flynn @dpfl.bsky.social · 28/11/2024

Yep, sorry! This oughta work:

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David Flynn @dpfl.bsky.social · 27/11/2024

It took a bit of trial and error to figure out if any area was uniquely solvable. I think/hope that it is.

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David Flynn @dpfl.bsky.social · 27/11/2024

As a follow up to this Dot Puzzles. I was thinking about how we can use this same set up with fractions in 3rd Grade. Here's a very rough mock up of a puzzle format: #iTeachMath #MTBoS #mathstoday

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David Flynn @dpfl.bsky.social · 27/11/2024

Let me know if you get an answer. I *think* there is only one unique solution.

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David Flynn @dpfl.bsky.social · 27/11/2024

More confusingly, they go by *both* names in the standards.

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David Flynn @dpfl.bsky.social · 27/11/2024

I like this! But I do wonder how natural the connection is from multi step word problems to order of ops. “Berkeley has 6 cookies on his plate. He gets another 3 plates with 5 cookies on each, how many cookies in all?” Answering this question? Sure 👌 Writing an expression? Yikes 😬

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David Flynn @dpfl.bsky.social · 27/11/2024

I don’t *think* it does. I remember cheesing a template on PowerPoint years ago when I wasn’t able to use the software, and I imagine a lot of people did the same thing.

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David Flynn @dpfl.bsky.social · 26/11/2024

These are lovely. It’s amazing how challenging problems can get with such a simple idea.

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David Flynn @dpfl.bsky.social · 26/11/2024

This is my slightly more ludicrous example.

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