The interactive Paper Pool game provides an opportunity for students to
develop their understanding of ratio, proportion, greatest common factor
and least common multiple.
In this investigation, students are asked to play a game called Paper
Pool. The game is played on rectangular grids made of congruent
The Paper Pool unit was adapted with
permission and guidance from the Connected Mathematics Project.
Which is bigger, or ?
Don’t even think about using
a calculator for this one.
The number groups below are the last five digits of the fifth powers
of the numbers 31 through 39. However, the groups aren't in the right
order to represent the fifth powers of 31 through 39 sequentially. Using
only these digits, and without using a calculator, can you place the
groups in the correct order?
A plywood sheet is 45 by 45
inches. What is the approximate diameter of the log the sheet was made from?
The diameter d of a circle equals ,
where C is the circumference, but
please do not make a mistake. The diameter of the log is not .
The Fibonacci sequence is shown below, with each term equal to the
sum of the previous two terms. If you take the ratios of successive
terms, you get 1, 2,
, and so on. But as you proceed through the sequence, these ratios get
closer and closer to a fixed number, known as the Golden Ratio.
1, 1, 2, 3, 5, 8, 13, …
Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?
The triangle at left lies on a flat surface and is pushed at the top vertex. The
length of the congruent sides does not change, but the angle between the two
congruent sides will increase, and the base will stretch. Initially, the area
of the triangle will increase, but eventually the area will decrease,
continuing until the triangle collapses.
is the maximum area achieved during this process? And, what is the length of
the base when this process is used to create a different triangle whose area is
the same as the triangle above?
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?
Label the ten points in the grid shown with the letters A-J so that
AB < BC < CD < … < HI < IJ.
Look at the panel of
elevator buttons shown. Can you find a set of three buttons whose centers
form the vertices of a right triangle and whose numbers are the side lengths of
a right triangle? (The classic 3-4-5 right triangle doesn’t work, because the
3, 4, and 5 buttons don’t form a right triangle on the elevator panel.)
And after you’ve found one
set, can you find another?