Lightnews — Scholar-powered news

Karen Campe @karencampe.bsky.social · 18h

Hello #iTeachMath #MathsToday folks... these Yohaku puzzles from Mike are an excellent thinking task for students at many levels. Enjoy!

Mike Jacobs @mikejacobs.bsky.social · 22h

Start your day with this #yohaku. Fill in cells with 9 different factors of 384 to get totals shown in each row/column. #mathsky #iTeachMath

Use 9 different factors of 384 in a 3 by 3 grid. The numbers in the top row add to 34. The numbers in the middle row add to 121. The numbers in the bottom row add to 13. The numbers in the left column add to 32. The numbers in the middle column add to 120. The numbers in the right column add to 16.

4

Karen Campe @karencampe.bsky.social · 18h

This is a lovely puzzle to find a second "solution" by letting some factors repeat.

Karen Campe @karencampe.bsky.social · 18h

What lovely powers today! Can you see where the odd factors of 384 have to go?

2

Reposted by Karen Campe

Shelby Strong 💗💜💙 @sneffleupagus.bsky.social · 1d

"When we are so solution focused, students are afraid to be wrong... And I wonder how that applies to voters. How can we ever feel safe to change our minds?"

When @cluzniak.bsky.social speaks, I am seated and listening and learning. #NCSMRiseUp #NCSM2025

2 6

Karen Campe @karencampe.bsky.social · 1d

Ok if there are 15 students, for each of them to have a diff nonzero number of candles, you'd need 120 candles (sum of 1,2,3,...15 = 120)
If 16 students, you'd need 136.
Therefore you don't have enough candles for each student to have a unique number. QED.

1 3

Karen Campe @karencampe.bsky.social · 1d

A week of school (5 days) or a calendar week? Did you have 85 candles or 119 to distribute?

1 1

Karen Campe @karencampe.bsky.social · 2d

6 miles/5 minutes multiply by 6/6 -->
36 miles/30 minutes

7 miles/6 minutes mult by 5/5 -->
35 miles/30 minutes

So 6 mi/5 min is faster!

#MathStratChat
#MentalMathMonday
#iTeachMath

2

Karen Campe @karencampe.bsky.social · 2d

Students will do either, whichever they find more accessible. Some don't remember exterior angle theorem, but triangle sum and linear pairs still works!
(More than one path to solve many angle-chase problems 😊

1 1

Karen Campe @karencampe.bsky.social · 3d

Have a great time, will look forward to seeing what you share here.

1

Karen Campe @karencampe.bsky.social · 3d

Wish I could be there, sadly not coming to conference. Be sure to post for those of us playing along from home!

{are you coming to ATMNE October 30-31?}

1 2

Karen Campe @karencampe.bsky.social · 6d

Ask @mnmmath.bsky.social she knows!
{I won't be at nctm}

1

Karen Campe @karencampe.bsky.social · 6d

Oh dear...

a south park cartoon shows a woman and a boy and the caption he seems to get worse every day

ALT: a south park cartoon shows a woman and a boy and the caption he seems to get worse every day

media.tenor.com

Karen Campe @karencampe.bsky.social · 7d

I used 3 ideas:
-Right triangle with hypotenuse = 10
-Geometric mean** of the 2 parts of diameter
-the question asks for area, not the dimensions separately

**thanks to @howiehua.bsky.social I've had the different means on my mind.
In marked diagram --> y is geometric mean of w and x.

Semicircle and rectangle, with base of rectangle along diameter of semicircle, and top edge of rectangle tangent to semicircle.

Left side of rectangle divides diameter of semicircle into two parts, labeled w and x.
Let y be the part of the left side of rectangle from bottom corner up to semicircle intersection.

Then y is geometric mean of w and x:
w/y = y/x

1

Karen Campe @karencampe.bsky.social · 7d

Why thank you... 😊

1

Karen Campe @karencampe.bsky.social · 7d

Cool!!
My usual approach (w/out technology) is rational root theorem and use the remainder theorem to help P(root) = 0 so can do some easy tests with 1, -1, 2 etc.

1 1

Karen Campe @karencampe.bsky.social · 7d

Yes, that's typical phrasing in US.

1

Karen Campe @karencampe.bsky.social · 7d

🤣

1

Karen Campe @karencampe.bsky.social · 7d

And here's the full post "One Big Rule to Rule Them All"

#iTeachMath #MathsToday #UKMathsChat

karendcampe.wordpress.com/2023/10/13/o...

One “Big Rule” To Rule Them All

We were talking online1 recently about parallel lines that are intersected by a transversal, and that there are multiple ways a student could justify that two particular angles were congruent. Sinc…

karendcampe.wordpress.com

2

Karen Campe @karencampe.bsky.social · 7d

The marked angle is half the sum of the intercepted arcs, so (1/2)•(50+110) --> (1/2)•160 = 80°

This is one of 7 angle-arc cases that can be boiled down to "one big rule"

#iTeachMath #MathsToday #UKMathsChat

Big Rule: Identify the location of the angle’s vertex, which gives the relationship of the angle measure to the intercepted arc(s):

At center: angle = arc
On circle: angle = (1/2)•arc
Inside circle: angle = (1/2)•(arc 1 + arc 2)
Outside circle: angle = (1/2)•(arc 1 – arc 2)

Notes: This condenses 7 rules into 4 rules. Use these varied situations to practice circle vocabulary. In class, I would pantomime an “intercepted arc” with my two arms, as if I were a football player making an interception.

3 2

Karen Campe @karencampe.bsky.social · 7d

Nicely done, David.
At first glance, cubic not easily factored.
Did you use rational root theorem or a graphing calculator to help finding that factorization... or other ideas??
Would love to hear more about your thinking.
#iTeachMath #ProblemSolving

Karen Campe @karencampe.bsky.social · 7d

Yes the harmonic mean is good for average rates, such as rate of work or rate of speed.
I am waiting for Howie's next video explainer to see if it is also the "average" of divisors or something like that...

1

Karen Campe @karencampe.bsky.social · 7d

Dislike... hang in there.

Karen Campe @karencampe.bsky.social · 7d

Howie, this is absolute gold! Love these explainers of what the different means *mean*
...
So, the arithmetic mean is the average of addends, the geometric mean is the "average" of scale factors, then the harmonic mean must be ... ?
#iTeachMath

1

Karen Campe @karencampe.bsky.social · 8d

Follow the link from here to get to the printable models.
cc: @mathhappens.bsky.social

#MathsToday #iTeachMath

www.mathhappens.org/conic-sectio...

Conic Section Models - MathHappens

www.mathhappens.org

1 9

Karen Campe @karencampe.bsky.social · 8d

Number of diagonals? Or diagonals that are bisected/ congruent/ etc.

3