Nothing fiber-related to share today — with the partial exception of Whinnie’s dress in these photos. I knitted that for her earlier this year when she requested a ‘yellow dress.’Β Yes, I completely and totally geek out when she chooses to wear one of the (many) items I’ve hand knit for her…I admit it freely. π

In the above photo the ‘learning stuff’ happened because of a child’s natural impulse to climb — and the wisdom of ‘interpretive history’ planners who understood. At the back end of this ‘old covered wagon without its cover’ is a small step ladder.

No matter what you think you understand there is an element of the real and tactile and tangible that transforms one’s knowing. Being IN this little space and considering how all of a whole family’s possessions would have to fit into it for a long, hard trek across the land — that was something. Theo (rather wisely) observed that it might only ‘just’ hold his Lego collection. π

Whinnie in the one-room schoolhouse

…listening to the ‘teacher’…

…talk about this…

As I told Nic later, I have been reading for 42 years. I have long been passionate about reading and learning and researching. I’ve been a homeschooling mama for nearly a decade. And I’ve been to this interpretive history center many times. And yet, with all of that, I’ve never, ever encountered the above photographed math triangle. And I was gobsmacked by its perfection of form, symmetry and use.

As the teacher showed us, it can be used for all 4 main math functions: addition, subtraction, multiplication and division. And one can continue the numbers on infinitely (given enough space.)

Ok, so how DOES it work?

1st — multiplication

Look at the 6 row.

Take the row number of 6 look at the first set of numbers 1 over 6.

…then say 6 times 1 equals 6

…next set, 2 over 12 — 6 times 2 equals 12

…next set, 3 over 18 — 6 times 3 equals 18

See?

The sets of numbers give you the answers.

For division, reverse that order:

…18 divided by 3 equals 6

…12 divided by 2 equals 6

…6 divided by 1 equals 6

Cool, huh? π

Addition and subtraction, oddly enough, are a bit more abstract for me to explain in this format…but I will give it a go. π

Give a look at the 5 and 6 rows.

Next to the row-starter 5 you’ll see 1 over 5 (they look like fractions, no? yes! we’ll get to that later…)

Then look sort of right below that 1 over 5 and see 1 over 6.

Ignore the 1 in 1 over 6. Now say: 1 plus 5 equals 6 and see that play out before you.

Move over one set to the right on the same rows:

2 plus 10 equals 12

Again….

3 plus 15 equals 18

Again…

4 plus 20 equals 24

See?

Subtraction?

As with division, just reverse what you did in addition…

24 minus 20 equals 4 — and so on

Ok — back to fractions…

Look at each row and you’ll see a perfect set of equivalent fractions π

Look at the ‘denominator’ of each row and you see the multiples of the number as well as a counting aid for those learning to count by 2’s or 5’s or whatever…

Numbers are beautiful.

Math is beautiful.

There is such a perfect symmetry and beauty in math.

I wish that math had been offered to me as a child as something beautiful and logical.

If this math triangle had been shown to me, it would have been one of those ‘angels singing’ moments and I mightn’t have spent years thinking I wasn’t ‘good at math.’

I intend to make one of these with the boys (if they wish to help) and make it as large as I can. For me the fun in this is exploring whether or not it can be continued infinitely. I do believe it can — but as with the coverless wagon above — it is the doing, the touching that true understanding transforms.

Heaz

said:ZOMG, I love this! I started noticing a few of the applications when you shared this photo elsewhere, but the explanation…wowser. I’m going to make one for myself! How cool; thanks for sharing. β€

melissa

said:thanks for sharingthetriangle! its lovely…

attachlings

said:My pleasure!

Claire

said:Cool!

I’ve made one up to 16, it does work π

I’ts really cool for multiplying and dividing and fraction π

It only has some occurences of additions and substractions though… I do get the very cool diagonal patterns, as in 16+4=20 +4=24 +4=28… (and the reverse suibstractions). But I don’t see how you could use it to add 7 to 4 for exemple (Or 16 +9 …). Is there a way and I am just missing it?

attachlings

said:I’m not sure. I’ll have to do another one and see. π