Deeanna Golden, a teacher of 24 years at F.M. Golson Elementary
School in Marianna, Florida, is a beloved Illuminations lesson plan
writer. So we asked her, "Why do you think it is important to share resources?"
It’s not too hard to form the number 9 using three 3’s and any of the four standard
mathematical operations +, –, × and ÷. But can you come up with four different
solutions, each of which uses only one of the four operations? (Other standard
mathematical symbols can be used as needed.)
= 3 + 3 + 3
Which is bigger, or ?
Don’t even think about using
a calculator for this one.
is the smallest positive number with exactly ten positive integer divisors?
And what is the next one after that?
Ask a friend to pick a number from 1 through 1,000. After asking him
ten questions that can be answered yes or no, you tell him the number.
What kind of Questions?
A magic rectangle is an m× n array of the positive integers from 1 to m× n such
that the numbers in each row have a constant sum and the numbers in
each column have a constant sum (although the row sum need not equal the
column sum). Shown below is a 3 × 5 magic rectangle with the integers
Two of three arrays at left can be filled with the integers 1-24 to form a magic rectangle. Which one can't, and why not?
Wheels A, B, C, and D are connected with belts as shown. If wheel A starts to rotate clockwise as the arrow indicates, can all 4 wheels rotate? If so, which way does each wheel rotate?
Can all the wheels turn if all 4 belts are crossed? If 1 or 3 belts are crossed?
How do I love thee? Let me build the
a heart using any of the shapes in the PDF file. You can change their size, but you
cannot change their shape. And you can use a shape more than once.
you make a heart with just three shapes? What about five? Six? Ten? How many
different hearts can you make?
What is the sum of the following?
432 + 432 + 432 + 432 + 432 + 432 + 864 + 864
are 29 students in Miss Spelling’s class. As a special holiday gift, she bought
each of them chocolate letters with which they can spell their names.
Unfortunately, some letters cost more than others — for instance, the
letter A, which is in high demand, is rather pricey; whereas the letter Q,
which almost no one wants, is relatively inexpensive.
price of the chocolate letters for each student in her class is shown in the
AIDEN – 386
ARI – 209
ARIEL – 376
BLAIRE – 390
CHARLES – 457
CLARE – 334
DEAN – 317
EARL – 307
FRIDA – 273
GABRIEL – 410
IVY – 97
KOLE – 249
LEIA – 317
LEO – 242
MAVIS – 246
NADINE – 453
NED – 236
PAUL – 167
QASIM – 238
RACHEL – 394
RAFI – 231
SAM – 168
TIRA – 299
ULA – 148
VERA – 276
VIJAY – 179
WOLKE – 272
XAVIER – 346
ZERACH – 355
much would it cost to buy the letters in your
number 4 can be expressed as the sum of three positive integers in only one way:
4 = 1 + 1 + 2
the number 50 can be expressed as the sum of three positive integers in 200
in between, there is a number n that
can be expressed as the sum of three positive integers in precisely n ways. Can you find n?