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?"
A 40‑inch straightedge
(without markings) is divided into four pieces. The length of each piece is an
integer number of inches. These four pieces, when used in tandem, can be used
to measure any integer length from 1 to 40 inches.
What are the lengths of the
The rectangle shown consists of eight squares. The length of each side of each
square is 1 unit. The length of the shortest path from A to C using the lines
shown is 6 units.
many different six-unit paths are there from A to C?
A Friedman number is a number that can be
represented with an expression that uses only the digits in the number. In
addition, the expression can include +, –, ×, ÷, exponents and parentheses, but
nothing else. For instance, 25 is a Friedman number because it can be
represented as 52. A nice
Friedman number is a Friedman number for which the digits occur in the same
order in the expression as they do in the original number.
So, 343 is a nice Friedman number, because it can be represented by an
expression with the digits 3, 4, and 3 in the same order:
343 = (3 + 4)3
seven nice Friedman numbers are 127, 343, 736, 1285, 2187, 2502, 2592. Can you
find an expression for each of them?
A 10 × 10 grid is painted
with three primary colors (red, yellow, and blue) and three secondary colors
(green, purple, and orange). The secondary colors are made by mixing equal
parts of the appropriate primary colors — that is, red and yellow are
mixed to make orange, red and blue to make purple, and yellow and blue to make
The figure at left shows
squares that were painted red and blue. No other squares were painted either
red or blue.
Suppose that each small
square requires a quart of paint. Altogether, 31 quarts of red paint, 40 quarts
of blue paint, and 29 quarts of yellow paint were used to paint the entire
10 × 10 grid.
Given this information, can
you determine if there were more yellow or purple squares? And how many more?
Tom was born on Thanksgiving Day.
On his seventh birthday, he noticed that Thanksgiving had never fallen on
his birthday. How old will he be when he finally has a Thanksgiving birthday?
Starting at 12:00 midnight, you wait a number of minutes that is a perfect square and
then look at a digital clock. The number you see (with the colon removed) is
also a perfect square.
is the first time after midnight that this happens?
“Mom, look at that license plate,” Will said.
about it?” his mother asked. It didn’t seem unusual to her. The plate consisted
of two sets of three digits, with the state logo between the sets.
Will said, “All six digits are different. And when you multiply the
first three digits, you get the same product as when you multiply the last
you do,” his mother said. “How many plates like that do you suppose there are?”
that’s the cool part,” Will replied. “The number of plates like that is equal
to the product of the first three digits.”
license plate might Will have seen?
In this multiplication example, P, E, and T represent different digits. What is the value of the three-digit
P E T
T T T
is a triangular number, because 10 objects can be neatly arranged in an
general, a triangular number is a number that can be represented as a triangle
with one object in the first row and each subsequent row contains one more
element than the previous row. (From the picture above, you might notice that
1, 3, and 6 are also triangular numbers.)
the digits 1 through 9 so that the sum of any two adjacent numbers is a triangular