Wednesday, January 17, 2018

Word Chandeliers (A Word Game)

To play Word Chandeliers, I'll give you a starting word, which you can think of as the top level of a chandelier. Starting with the given word, your job is to create lower levels of the chandelier by discarding two letters at a time (any two letters) and rearranging the remaining letters to form shorter words.

In the example below, the top level is given as MUDDILY. The next level was created by striking the letters U and D from MUDDILY and rearranging the remaining letters to make DIMLY. Then, the next level was created by striking L and Y from DIMLY to make DIM. (Here it turns out no rearranging was necessary, but typically some rearranging is required at each step.)

The chandelier is complete when you reach a three-letter word.



Any chandelier is an accomplishment, but try to find a special one for which the letters you discarded along the way can be rearranged to form a bonus word. The above chandelier is special in this way:




Below are fifteen starting words; each is the top level of a chandelier. The starting words are in alphabetical order (not necessarily in difficulty order). Enjoy!

As usual in my word games, you should avoid proper nouns, foreign words, slang, contractions, hyphenated words, acronyms, and jargon.

CANVASS
CONFINE
CONTEXT
CRACKUP
ENTENTE
GREENER
HAMMOCK
JUGGLED
MERFOLK
PARKWAY
PIGMEAT
QUALITY
RHYMING
RUPTURE
WOESOME

Tuesday, January 16, 2018

A Twist On The Strike Two Word Game

A little while ago I received an email from reader Robert, who noticed something interesting about Strike Two, our most recent word game. Recall that in the example CONFUTE, we struck E and F then rearranged the remaining letters to form COUNT. What Robert noticed is that in some cases we can keep going and remove another alphabetically adjacent pair of letters. For example, removing N and O from COUNT, we obtain CUT.

That's a great catch! Here are words from the earlier post that allow a second iteration.

AUTOPSY → ? → ?

CONFUTE → COUNT → CUT

BOATFULS → ? → ?

PRICKLED → ? → ?

SANDWORT → ? → ?

WORTHIES → ? → ?

DAUGHTERLY → ? → ?

For each word in the list above, strike two letters from the word and rearrange the remaining letters to form a new word; then repeat the process once more. The letters you strike don't have to be adjacent in the word, but they do have to be consecutive in the alphabet.

Monday, January 15, 2018

A Six-Actor Diagram!

Improving on the known results for the 2017 Holiday Challenge, reader Joanie sends this diagram with six actors.

With so many actors and connections to show, Joanie provides a tabular display. The six actors in the table are Emma Thompson, Judi Dench, Michael Gambon, Colin Firth, Ralph Fiennes, and Helena Bonham Carter. For every pair of actors, a distinct acting credit is shown in the table.


(I checked all fifteen shared acting credits on IMDB. Note that Harry Potter and the Deathly Hallows refers to Part 2.)

Thanks for sending, Joanie!

Does a diagram exist with seven or more actors?

Saturday, January 13, 2018

Visit to the Lorraine Motel / National Civil Rights Museum

In November I drove with a friend from Kansas City to New Orleans, taking the long way around to visit the quiltmakers' collective in Gee's Bend, Alabama. It was my first time driving across "the flat south"—as distinguished from Appalachia, which is the South I'm more familiar with, and which is where my own Southern heritage lies. In past years I'd seen cities in this part of the country (Jackson, Monroe, Tallahassee, and others) but hadn't driven along rural byways with cotton fields stretching away to either side.




A day or two into our drive, we paid a visit to the National Civil Rights Museum in Memphis, on the site of the Lorraine Motel: where Martin Luther King, Jr. was assassinated on April 4, 1968.

A shrine in outward appearance, the motel turns out to have an extensively rebuilt interior. The design of the museum is a linear pathway that takes you through a series of high quality exhibits, some of them interactive. The museum helped me to integrate my disconnected knowledge of the civil rights movement. If you had asked me before my visit to fill in the blank in "Montgomery _____" or "Memphis _____", I would have supplied the answers "Bus Boycott" and "Sanitation Workers' Strike"; but I couldn't have told you which came first, or what the arc between them was. The museum tells the main story and includes some prior context, parallel narratives, and aftereffects.


The material presented is sobering, jarring, horrible, illuminating, and sometimes inspiring. Unfortunately, I can't say that the overall experience is anything but tragic, from the moment when you first glimpse the sadly beautiful funeral wreath on the motel balcony to the moment when, standing inside those glass doors, you try to measure all that was lost. Dr. King was taken from us at the age of 39.

To celebrate the Birthday of Martin Luther King, Jr., our family has made a small donation to this necessary museum via the website.

Wednesday, January 10, 2018

Strike Two (A Word Game)

For each word in the list below, strike two letters from the word and rearrange the remaining letters to form a new word. The letters you strike don't have to be adjacent in the given word, but they do have to be consecutive in the alphabet.

Example: given the word CONFUTE, strike the letters E and F, which are consecutive letters in the alphabet. The remaining letters are C, O, N, U, T. Rearrange these letters to form the word COUNT.

(It is not allowed to form the word FUTON by striking the letters C and E, because C and E are not consecutive in the alphabet.)

The words are listed in order from shortest to longest. However, for what it's worth I actually found some of the longer words easier to solve.

BLACK
DECAF
MOUNT
POUTS
SHIRT
CUBITS
GRUNTS
HOEING
SNOUTY
AUTOPSY
CONFUTE (solved as an example)
FIDGETY
PORTEND
BOATFULS
COMBINES
PRICKLED
QUESTION
SANDWORT
WORTHIES
ADVERSITY
FEUDALISM
DAUGHTERLY

Tuesday, January 9, 2018

A Tutoring Packet From Saturday School

Last month I observed my daughter drawing a complicated diagram to understand a fraction multiplication problem on her homework. The following Saturday, I made a tutoring packet that she and I could work on together. I wanted to show her some possible uses of tape diagrams, just as a tactical matter. (Also an area diagram.) But more fundamentally, I wanted to help her connect fraction products to her prior ideas about multiplication—in the process, altering to some extent her concept of multiplication itself.

Click here for the tutoring packet, in case useful or interesting.

The reason I stress that this is a tutoring packet, and not a worksheet, is that the problems and their sequencing are designed to stimulate new ideas and reshape old ideas in conversation; assigning the packet out of the blue as a worksheet would probably just create frustration. Even as a tutoring packet, it's pitched at a pretty high level.

If you look at the packet, you'll notice a few things:

   • The first problem is a prelude: not because it's easy (it isn't), but because it can be done using earlier fraction thinking. (It can also be answered in more sophisticated ways and probably rewards more than one look.)

   • The diagrams follow an arc. First, a diagram is given. Next, a diagram is given but incomplete. After that, the student is told to draw one. Then, space is left blank to draw a diagram if desired. 

   • The treatment becomes less visual and more symbolic as the packet proceeds, with diagrams eventually giving way altogether to "times as much" thinking. This includes redoing the diagrammatic problems from the perspective of "times as much" to see that everything comes out the same.

   • The last few problems show that a single way of thinking suffices to handle such initially diverse problems as 2/3 × 3/4, 2/3 × 5, 8 × 19/8, and 7 × 7.

The first time we worked through the packet, I tutored my daughter for a little over an hour. Then the next weekend, we worked through the packet again; this time it took probably 45 minutes. Both sessions were productive. What I might do next is write a "unit assessment" based on the packet and see what remains troublesome when she does the work by herself. In any case, the packet is obviously too much for a student to absorb during one session, which is why I have gone through it twice so far.

Sitting down to write the packet that Saturday morning, I opted to build general fraction products from products of unit fractions using "times as much" thinking, which I knew my daughter was already comfortable with. Actually, the movement from 1/b × 1/d to a/b × c/d involves two independent "times-as-much" iterations, which is one way to see why an area model works well. (Have a look at the problem of the alfalfa field.) It is the base case, 1/b × 1/d, that most challenges whole-number conceptions of multiplication. This product, which can also feel somehow simultaneously like a quotient, might be the most dramatic conceptual crisis in school mathematics.

Sunday, January 7, 2018

2017 Holiday Challenge: Results For Challenge 2, Rhyming Words

Below are the results of the second puzzle in the 2017 Holiday Challenge: find a pair of one-syllable words that rhyme despite having no letters in common. Readers came up with great answers—and a lot of them!

Something I didn't anticipate was that regional accents matter in this puzzle. When a friend from New York City submitted the words gore, slaw, it didn't make sense to me at first—then I imagined her saying the words, and I could hear the perfect rhyme. So if you see words below that don't rhyme when you say them, take into account that the submitter might be from a different part of the country.

Congratulations to prizewinners Marsha, Jeff, and Joanie—a copy of Word Games for Kids is on its way to you!

That wraps up the 2017 Holiday Challenge. Thanks for participating this year! My best wishes to everyone for a happy and healthy 2018.

------------------------

The list is sorted more or less by the combined size of the pair. Qualifying pairs of words aren't easy to come by…possibly we've unearthed many of the best cases that exist. Asterisks in the list highlight pairs of words that end in a consonant sound.

One entry worthy of a special note: crypt|sniffed was the longest pair submitted, though it rhymes in a way that isn't quite simple. 

beaux|throws*
flew|through
slew|through
beaux|grows
beaux|flows
chic|streak*
cough|dwarf*
stray|weigh
neigh|stray
bricks|pyx*
buys|prize*
like|psych*
beaux|rows*
spry|thigh
faux|throw
beau|throw
flaw|shore
claw|shore
chore|slaw
chore|flaw
balk|toque*
tray|weigh
neigh|tray
flay|weigh
flay|neigh
clay|weigh
clay|neigh
pugh|view
grew|shoo
flue|shoo
flew|shoo
crew|shoo
clue|shoo
blue|shoo
rye|thigh
high|stye
high|spry
fly|thigh
eye|thigh
dye|thigh
dry|thigh
cry|thigh
chai|stye
chai|spry
bye|thigh
buy|thigh
faux|show
beau|show
pour|slaw
paw|shore
moor|slaw
law|shore
jaw|shore
gore|slaw
four|slaw
fore|slaw
flaw|sure
flaw|pour
flaw|moor
flaw|gore
core|slaw
core|flaw
claw|sure
claw|pour
claw|moor
claw|gore
claw|four
claw|fore
chore|saw
chore|paw
chore|law
chore|jaw
view|you
phew|you
few|pugh
ewe|pugh
stew|zoo
slew|zoo
slew|too
moo|stew
moo|slew
grew|zoo
grew|too
grew|moo
gnu|stew
gnu|slew
gnu|shoo
flue|zoo
flue|woo
flue|who
flue|two
flue|too
flue|moo
flu|stew
flu|shoo
flu|grew
flew|zoo
flew|too
flew|moo
flew|gnu
crew|zoo
crew|too
crew|moo
crew|gnu
crew|flu
clue|zoo
clue|woo
clue|who
clue|two
clue|too
clue|moo
chew|zoo
chew|too
chew|moo
chew|gnu
chew|flu
blue|zoo
blue|woo
blue|who
blue|two
blue|too
blue|moo
spry|vie
spry|tie
rye|sigh
lie|spry
high|sty
high|rye
fly|sigh
fly|high
eye|sigh
eye|high
dye|sigh
dye|high
dry|sigh
dry|high
die|spry
cry|sigh
cry|high
chai|sty
chai|rye
chai|guy
chai|fly
chai|eye
chai|dye
chai|dry
bye|sigh
bye|high
bye|chai
buy|sigh
buy|high
buy|chai
faux|sew
pour|saw
paw|sure
moor|saw
moor|paw
law|sure
law|pour
law|moor
jaw|sure
jaw|pour
jaw|moor
gore|saw
gore|paw
gore|law
gore|jaw
four|saw
four|paw
four|law
four|jaw
fore|saw
fore|paw
fore|law
fore|jaw
core|saw
core|paw
core|law
core|jaw
awe|pour
awe|moor
awe|four
few|you
ewe|you
gnu|zoo
gnu|woo
gnu|who
gnu|two
gnu|too
gnu|moo
flu|zoo
flu|woo
flu|who
flu|two
flu|too
flu|moo
do|stew
do|slew
do|grew
do|flue
do|flew
crew|do
clue|do
chew|do
blue|do
vie|why
tie|why
sty|vie
shy|vie
shy|tie
pie|why
pie|sty
pie|shy
lie|why
lie|sty
lie|shy
guy|vie
guy|tie
guy|pie
guy|lie
fly|vie
fly|tie
fly|pie
dry|vie
dry|tie
dry|pie
dry|lie
die|why
die|sty
die|shy
die|guy
die|fly
cry|vie
cry|tie
cry|pie
cry|lie
cry|die
buy|vie
buy|tie
buy|pie
buy|lie
buy|die
faux|oh
beau|oh
pee|ski
do|gnu
do|flu
oh|sew