# Transformations of Trigonometric Functions

In this assessment, students work through scenarios of changing the function rule of the sine and cosine functions by addition and/or multiplication and see how such changes affects their graph. Students explore vertical/horizontal translation, reflection over the x-axis, and vertical/horizontal dilation. As they explore, students use their GDCs to graph functions, describe findings, suggest rules, and verify and justify their results.

Math Concepts: trigonometry functions transformation degree radian exact values sine cosine translation reflection dilation
MYP Related Concepts: models representation
MYP Key Concepts: relationships systems
MYP Global Context: Identities and Relationships

# Taxicab Geometry in NYC

In this assessment, students use a section of the map of New York City to describe routes recommended by Google Maps, analyze and identify rules and restrictions that applies to these routes, design (sketch and describe) a 4th route, and calculate estimates of distances travelled based on given values. Students are asked to describe their methods and explain their answers, providing the opportunity for them to reflect on the given information as well as their method(s) of calculations. As successful completion of this assessment does not require the knowledge of any specific mathematical concept, it is recommended as an introduction to MYP assessments at the beginning of grade 6 (or in the grade level a student first joins MYP).

Math Concepts: orientation maps distance routes estimation
MYP Related Concepts: models space systems
MYP Key Concepts: communication relationships
MYP Global Context: Orientation in Space and Time

# The Multiplexes of Pisa

In this assessment, students investigate possible combinations of housing units used to house different number of people. Students initially consider using only simplex units (that represent 1 single housing unit) and duplex units (that represent 2 attached housing unit under the same roof). At the end of the assessment task, students are guided to include triplex units (that represent 3 attached housing units under the same roof) in addition to simplex and duplex units. Throughout the investigation, students recognize patterns, state predictions, and use their findings to suggest and verify relationships as general rules.

Math Concepts: patterns Fibonacci sequence
MYP Related Concepts: patterns systems
MYP Key Concepts: logic relationships
MYP Global Context: Identities and Relationships

# Graceful Graphs

This assessment task introduces a concept in graph theory, focusing on nodes and edges and a few graphs that follow certain rules. Graphs that follow the two rules given are called graceful. Throughout the task, students are asked to find ways to gracefully label graphs, starting with simple paths, followed by graphs of two rows of nodes, and then finally by cycle graphs. This assessment task is based the Graceful Graphs activity available on the Julia Robinson Mathematics Festival’s website.

Math Concepts: patterns integers counting numbers graphs graph theory graceful graphs
MYP Related Concepts: models patterns
MYP Key Concepts: form relationships
MYP Global Context: Identities and Relationships

# Squarables and Triangulables

This assessment task is based on Dan Finkel’s Squarable Numbers task shared on Math for Love. In this task, students investigate patterns that can be used to find squarable numbers. We do this by taking a number of squares (of any size) and cover another square with them, without gaps or overlaps. The number of squares for which this is possible we call squarable numbers. Initially students investigate simple ways to find squarable numbers, following a simple pattern and thus finding a family of squarable numbers. Then, by following another pattern, another family of squarable numbers can be discovered. Finally, as an additional challenge, students explore triangulable numbers independently.

Math Concepts: squares triangles polygons patterns
MYP Related Concepts: models patterns
MYP Key Concepts: form relationships
MYP Global Context: Orientation in Space and Time