# Visiting the Statue of Liberty

In this assessment, students apply their knowledge of right-angled trigonometry (and in the Extended version also the Pythagorean theorem and non right-angled trigonometry) to calculate the measure of angles through which Tom the Tourist looks at the replica of the Statue of Liberty. Throughout the task, students calculate angles using inverse trigonometric ratios and comment on the accuracy of their findings. At the end, students are asked to use their GDC to graph a function that can be used to find the optimal distance from the statue where Tom should stand in order to take the photo through the largest possible angle.

Math Concepts: trigonometry SOHCAHTOA sine rule cosine rule optimization maximum point
MYP Related Concepts: models
MYP Key Concepts: logic
MYP Global Context: Orientation in Space and Time

In this assessment, students investigate non-zero integer triples (called Addition Triples), in which (1) all three numbers are different non-zero integers, and (2) the first two numbers add up to the third number. For example, the number triple (2, 3, 5) form an Addition Triple as none of the three numbers are equal (i.e. they are all different), none of the three numbers are zeroes, and 2 + 3 = 5. Some other Addition Triples are (5, 6, 11) or (2, 5, 7). In this investigation, we are looking at the Total Number of Addition Triples that we can make from a list of n integers, considering whether n is an odd or even number.

MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# Sum and Product of Quadratic Roots

In this assessment, students investigate the sum and the product of the roots of quadratic equations. While Parts A and B of the investigation provide guidance to finding the general formula for the sum of the roots, in Part C students are asked to conduct an independent investigation into the product of the roots of quadratic equations.

Math Concepts: quadratic equations quadratic formula roots sum of roots product of roots
MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# Polygonal Numbers

The concept of polygonal numbers is closely related to regular polygons. Namely, polygonal numbers are numbers that are represented by dots arranged in a shape of regular polygons. In this investigation, students discover patterns for polygonal numbers (starting with triangular numbers and then square numbers, pentagonal numbers, and so on), derive explicit formulas for them, and combine their findings to verify and justify an explicit formula for one of the polygonal numbers.

Math Concepts: triangular numbers square numbers pentagonal numbers hexagonal numbers polygonal numbers quadratic sequence
MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# The Leibniz Triangle

In this assessment task, students investigate the terms in the Leibniz triangle in connection to a similar triangle they are already familiar with: Pascal’s triangle. In the first parts of the investigation, students observe the terms in the Leibniz triangle and state their predictions for the terms in its 5th row. Then, students work with binomial coefficients to discover their use for Pascal’s triangle. Finally, students bring all of their findings together to find, verify, and justify an explicit formula for any term in the Leibniz Triangle.

Math Concepts: unit fraction Pascal's triangle Leibniz triangle binomial coefficient unit fractions
MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships