# Sums in a Square Grid

In this assessment, students investigate the sum of integers that are selected in a square grid of consecutive integers in a way that no two numbers are selected from either the same row or same column. Students begin the investigation by examining the 3 x 3 and the 4 x 4 grid, both with the starting number 1. Then, a closer look at the 3 x 3 grid (in Part B) and at the 4 x 4 grid (Part C) is concluded with discovering a general rule for the sum of the selected integers in the 3 x 3 and in the 4 x 4 grids. Finally, in Part D, to fully generalize the pattern, students examine the sum of selected integers in the k x k grid, with the starting number n.

Math Concepts: patterns sum sequence
MYP Related Concepts: change patterns
MYP Key Concepts: logic
MYP Global Context: Identities and Relationships

# The Metallic Means

"Along with π and e, the golden ratio is a numerical celebrity. It is the ratio of side lengths on a very special rectangle. If you take this rectangle and cut the largest square possible off of it, you are left with another rectangle with exactly the same side length ratios as the first one. This construction defines a unique relationship between the lengths of the sides, and any rectangle whose sides have that relationship is called a golden rectangle." (Scientific American) In this investigation, we will look into the exact and the approximate values of these metallic ratios (also called metallic means), starting with the golden ratio, followed by the silver ratio, bronze ratio, and other metallic ratios.

Math Concepts: golden ratio silver ratio bronze ratio
MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# Louvre Triangles Investigation

The glass pyramid of The Louvre is iconic and famous. However, this pyramid also contains mathematical patterns that this assessment explores. The rhombuses that form the sides of The Louvre can be divided into triangles, and in turn those triangles can come together to form even larger triangles. In this investigation students will look for relationships between the height (Part A) and the area (Part B) of these triangles and the number of rows needed to make those triangles. To problem solve students can use either trigonometric ratios or the Pythagorean Theorem.

Math Concepts: operations with radicals right angle triangle trigonometric ratios Pythagorean Theorem area of a triangle
MYP Related Concepts: patterns space
MYP Key Concepts: form
MYP Global Context: Personal and Cultural Expression

# Minimizing Wood for Birdhouse RLP

The context of this assessment place students in a grade-wide competition for designing a bird house. The be accepted into the competition though, students must find a way to minimize the amount of wood used in the design structure given certain constraints. There is one variable in the design and students must propose a value for it that would allow for the construction of the bird house to use the least amount of wood.

Math Concepts: right triangles Pythagorean Theorem
MYP Related Concepts: models space
MYP Key Concepts: logic
MYP Global Context: Orientation in Space and Time Globalization and Sustainability

# Dice Football RLP

This assessment looks at the fairness of a game involving the sum of two die. The game itself is unfair and the task asks students to first find out how it is unfair and then follow-up with proposing rule changes to make it fair. They will then need to explain the logic behind the changes. This assessment connects very well with the Probability Games Investigation found on The EdVaults website since both look into the fairness of games based on probability.

Math Concepts: addition rules for probability probability of independent events
MYP Related Concepts: models representation systems
MYP Key Concepts: logic
MYP Global Context: Fairness and Development