The
8 × 8 grid at left represents an ocean with a hidden fleet of
ships. Ten ships are hidden within the grid — 1 battleship,
2 cruisers, 3 destroyers, and 4 submarines.

Each
ship may be oriented horizontally or vertically within the grid such that no
ship touches another ship, not even at a corner. The numbers along the right
and bottom of the grid show how many squares in each row and column are
occupied by ship segments. As a start, one square in the grid shows the
location of one end of a ship, and the X indicates a square that contains only water
(no ship).

Can
you determine the location of all 10 ships?

Problems

A problem encountered early in life by the great mathematician and
physicist Joseph Fourier was to draw 17 lines that intersect in
precisely 101 points. Can you find a way to do it?

(Fourier was able to find four families of solutions to this problem.)

Problems

A
grocery store sells brown rice in 3-pound bags and white rice in 5-pound bags.
Katrina bought a total of 22 pounds of rice. How many bags of rice did she buy?

Problems

Grades: 6th to 8th, 9th to 12th

Expression/Equation

Algebra

Analyze and solve linear equations and pairs of simultaneous linear equations.

Reasoning with Equations and Inequalities

Creating Equations

8.EE.C.8b, HSA-CED.A.3, HSA-REI.C.6, 8.EE.C.8c

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?

Problems

Grades: 6th to 8th, 9th to 12th

Ratio & Proportion

Functions

Stats & Probability

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Interpreting Functions

Investigate patterns of association in bivariate data.

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.A.1, 8.SP.A.1, HSF-IF.A.3, 7.RP.A.2a

Three puzzle competitors are
blindfolded. A white piece of paper is glued to each one’s forehead and they
are told that not all the pieces of paper are black. The blindfolds are removed
and the prize goes to the first man to deduce whether the paper on his forehead
is white or black.

All three announce white at
the same time. Why?

Problems