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.

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

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.

This is lovely.

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.

3/4?
3/9?
3/1?
1/5?

This is cool.

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

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

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

Thank you!!

Do you mind if I request access to this?

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

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

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

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

#mtbos #iTeachMath

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.

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.

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.

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.

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.

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.

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.

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?

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.

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.

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

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?

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

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

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 🤔

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 .

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.