germinalmaths.bsky.social
I teach maths in a Scottish state-sector secondary school.
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197 followers
247 following
Getting Started
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Down a “square grid” rabbit hole.
#MathArtMarch
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To be honest, I can’t remember. A pupil had come up with the basic idea of connecting dots on a square grid and showed me his pattern. The ones her are my playing with the idea. I believe we did it on mathsbot geoboard. @studymaths.bsky.social
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1/2 hour = 30 minutes
1&1/4 hours = 75 minutes
Same units so fraction is
30/75 = 2/5
Or,
1/2 hour = 2 x (1/4 hour), ie 2 units
1&1/4 hours = 5 x (1/4 hour), ie 5 units
Fraction is 2/5
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Scale both numerator and denminator equally to obtain the smallest possible two whole numbers. This requires a scale factor of 4, giving 2/5.
Alternatively, scale to make numerator whole (giving 1/(2&1/2)); repeat to make denominator whole (giving 2/5).
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I’m sure your adult learners remember it well.
“£1.56, £1.58, £1.60;
£1.80, £2.00;
£3.00, £5.00”
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Agreed. Your strategy of simply multiplying the whole fraction by 11 (or 7) then comparing is much more efficient than my numerator-only scaling. Thank you.
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The gradient of each line corresponds to the reciprocal of each fraction. This illustrates another numerical strategy that is sometimes useful when comparing two fractions a and b. If 1/a > 1/b, then a < b and vice versa. Not really helpful in this case (the picture is, though).
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But 5/7 of 11 is 55/7.
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This is not quite my thinking. What you have done, though is essentially to divide 8/11 by 5/7.
This is another general strategy for comparing two fractions a and b: if a/b > 1 then a > b and vice versa.
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Regarding your written example, I would find 5/7 of 11 and compare it with 8. Alternatively, find 8/11 of 7 and compare with 5.
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I hadn’t thought that far ahead. What you describe is very much ratio-based thinking. Starting with x, you’re creating the fraction 3x/7x. I think you could get a really nice lesson out of that which would help develop a ratio-based (rational!) conceptual understanding
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A simple example based on my understanding. My S1 class were finding fractions equivalent to 1/2. They chose a random numerator and doubled it to find the denominator. They seemed to find this much more intuitive than “multiplying the numerator and denominator by …”,
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Yes, as here perhaps
satisfry.blogspot.com/2024/09/fra0...
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For me, building fraction sense, as you put it, is vital. Extending the ways in which we understand and work with fractions and how those relate to our existing number sense.
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Agreed on all points. One is more than 1/2, the other less. I chose that fraction pair as Segar had used it earlier. I also wanted to widen the initial discussion on “units” to include comparison of numerators as well as denominators.
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Actually your strategy of equating numerators then comparing denominators is a valid way to compare any two fractions. We can incorporate ratio here: eg In your earlier example, scaling both parts of 5/13 to obtain 7/(91/5). Since 91/5 > 11, 7/11 > 7/(91/5), ie 7/11 > 5/13.
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Reminds me of the apocryphal student who wrote
sinx/n = six = 6.
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How about incorporating sinx^2 + cosx^2 ….?
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Establishing truth?
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Would this be useful?
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Compare times for 42 laps.
C must take > 102.6 minutes which, in turn, is longer than the 96.6 minutes taken by B.
A must travel a further 7 laps, one-fifth more than 35 laps. One-fifth is two-tenths, so this would take 84 + 2 x 8.4 = 100.8 minutes, also longer than B.
B is fastest over 42 laps.
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Would either or both of the following add value to the task?
The blue circles/green pentagons.
The red sector/orange hexagon.
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No.
No.
No.
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I asked a class (S3, mostly 14yo) on Monday for the square root of 2025. No one could do it without support.
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Some equal areas - quarters.
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I enjoyed this - thank you, Segar!
Here’s my solution, involving two copies of the diagram for clarity. Capital letters represent areas.
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What changed my mind was seeing 1200 not as an instant in time but a time interval: 1200 <= t < 1201. Midday (meridiem) is, in contrast, an instant. Every value of t other than 1200 is pm.
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That was my long-held view - until earlier today.
What about 1 second later?
0. 1 seconds later?
0. 0…1?
How much of the time represented by 1200 is midday and how much post?
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Further thoughts. 1200 represents a period of time lasting one minute, rather than an instant in time. Most of that minute (arguably all of it) is after midday and is, therefore best represented as 1200pm. Likewise the minute represented by 0000 is earlier in the same day, so 1200am.
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Fair point regarding the redundancy of the 00 when specifying noon or midnight.
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Written 12 midnight (or 2400), it is the end of the old day, therefore pm. By this reasoning one 12 o’clock is neither am nor pm while the other can be either. I agree they should be written as 1200 noon and 1200 midnight to avoid ambiguity.
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Here’s my take on this, for what it’s worth. The m in am and pm stands for meridiem - Latin for midday. Precisely 1200 is neither before (ante) nor after (post) midday. 0000 is more problematic. As written it is clearly the beginning of the new day, therefore am.
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Close to 60/44 = 15/11 = 1 and 4/11.
I know 1/11 is 0.0909… so 4/11 =0.3636…
So my (under)estimate is £1.3636… per litre.
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I wonder if it would be possible to get beyond 50 per set. Seems to me it would. Might give it a try …
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I love that idea of just getting a little better every time you do something. I often ask pupils if they think they could improve their exam scores by a few percentage points every time they do a past paper as an incentive to do lots of them in a purposeful way over a suitable time period.
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I’m reminded of this passage from the book, “Holes”
www.stpeterscatholicprimary.com/_site/data/f...
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Major achievement - well done!
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366 consecutive?
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And it was fun to do!
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Correction
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I’m reminded of doing this with some pupils for a @atmmathematics.bsky.social #beingmathematical task on Twitter a few years ago. As you can see, our supply of Cuisenaire rods wasn’t quite up to reaching 2025 and beyond.
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I hope he sends you a photo if he’s back there after 27 December.
I’m eager to find out how much two will cost when the offer ends.
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Me too!
I was sure I’d followed you a couple of weeks back. I’m finding I often need to do things twice here.
Btw, your previous reply had me thinking:
6 half-houses
6 half-dogs
6 half-burgers …
and …
6 half-sevenths.