# Patterns in Intersections

In this assessment, students investigate systems of equations and whether a pattern in the coefficients/constants of equations graphed simultaneously results in anything noteworthy with regards to the coordinates of the point at which the graphs of the equations intersect. Students initially use given values of A, B, and C for equations in the form of Ax+By=C, then apply their pattern to find specific values of A, B, and C that provides the same result. In the final part of the investigation, students are to verify that their general rule works and briefly justify why it does.

Math Concepts: simultaneous equations system of equations equations graphs linear graphs linear equations
MYP Related Concepts: patterns systems
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# Predicting Forest Fires

In this assessment task students explore a fire index developed in Sweden and known for its simplicity: the Angström index. After identifying factors relevant to determining the likelihood of fire, students explore weather data of Canberra, Australia, where bushfires caused severe damage in January of 2003, and explore what level of air temperature and relative air humidity we need to look out for in order to be able to predict the likelihood of fire occurring.

Math Concepts: data linear function modeling gradient slope intercept statistics data analysis
MYP Related Concepts: models
MYP Key Concepts: relationships
MYP Global Context: Scientific and Technical Innovation

# Painting Towers

In this assessment students are asked to draw the next stages following an established pattern and use their drawings to recognize different patters: in the number of blocks at each stage, in the surface area at each stage, and in the number of blocks with different number of painted faces at each stage. Students are to recognize and describe these patterns and derive mathematical formulas to find values for Stage n, which then need to be verified and justified.

Math Concepts: patterns quadratic sequence isometric drawing formulae
MYP Related Concepts: models patterns
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# Window Panes

In this assessment, students start by working through a simple process to find patterns for the number of different types of panes used in a simple window design, called The Edgy. Then, once they manage to work through the pattern in that design, they use a method of their own to find a mathematical expression for the number of different types of connectors used in a different, slightly more complex, window design, called The Griddy. At the end of the assessment task, students are asked to describe their patterns, verify, and briefly justify their findings.

Math Concepts: patterns formulae number sequence sequence
MYP Related Concepts: models patterns
MYP Key Concepts: form relationships
MYP Global Context: Orientation in Space and Time

# Discovering Triples

In this assessment, students investigate generating Pythagorean triples and work on discovering patterns that help finding primitive Pythagorean triples (ones that cannot be reduced by a common factor). In the process of exploring this topic, students also learn about the importance of co-primes and their roles in finding those primitive Pythagorean triples. This is a fairly long assessment, which likely requires more than 120 minutes to complete.

Math Concepts: Pythagorean theorem Pythagorean triples Pythagoras co-prime relative prime pattern formulae
MYP Related Concepts: patterns systems
MYP Key Concepts: logic relationships
MYP Global Context: Identities and Relationships