# Trapezoids in Triangles

This assessment builds on and extends the content of the chapter. Students are guided through a process to find the number of trapezoids (of different size) in a series of nested equilateral triangles. Such nested triangles usually appear in mathematical puzzles, asking for the number of triangles that appear in them. However, counting the number of trapezoids might reveal a completely different number patter.

Math Concepts: triangles trapezoids patterns triangular numbers
MYP Related Concepts: patterns systems
MYP Key Concepts: form relationships
MYP Global Context: Orientation in Space and Time

# Odds in Squares, Cubes, and Beyond

In this assessment, students investigate patterns between sums of consecutive odd numbers and square numbers, cube numbers, and numbers raised to the 4th and 5th powers. Patterns for numbers raised to the 2nd and 4th power are easier and are for achievement levels 1-4. Students might already be familiar with these from their studies. However, patterns for numbers raised to the 3rd and 5th power are more challenging and are for achievement levels 5-8. It is very unlikely that students have encountered these patterns previously.

Math Concepts: odd numbers squares cubes 4th power 5th power consecutive numbers number patterns
MYP Related Concepts: patterns
MYP Key Concepts: relationships
MYP Global Context: Identities and Relationships

# The Maths Behind Biorhythm

In this assessment, students explore the pseudoscientific concept of Biorhythm Theory, developed in the late 19th century and popularized in the 1970s. The theory is based on different cycles modeled by sine functions with different periods. Students explore these sine curves, their properties (mostly their periods) and the properties of combined sine functions. In order to successfully work through this task, students also need to know how to calculate the LCM of two or three numbers.

Math Concepts: LCM least common multiple period amplitude sine curve composite function
MYP Related Concepts: models patterns
MYP Key Concepts: logic relationships
MYP Global Context: Identities and Relationships

# A Sea of Squares

In this assessment, students investigate an ever-expanding pattern of squares, called "Sea of Squares", for patterns in the side length and the number of squares, as well as the perimeter and area at different stages. Initially, students draw earlier stages of the Sea of Squares to recognize simple patterns, which they are asked to describe. Then, students are asked to find mathematical formulas for different patterns for a general stage (Stage n), which they are asked to verify. At the end of the task, for Achievement Level 7-8, students are asked to investigate more complex patterns, and write formulas for and verify these patterns.

Math Concepts: patterns formula exponents algebraic expressions
MYP Related Concepts: patterns representation
MYP Key Concepts: form relationships
MYP Global Context: Identities and Relationships

# Trucks Through a Tunnel

In this assessment, students work through an initial and then an updated proposal for a tunnel, identifying points that represent the edge of lanes and finding the width of lanes. Then, given the dimensions (width and height) of four vehicles, students are asked to find whether these vehicles are able to use the outer lanes of the tunnel, if they drive extremely closely to the inner edge of the outer lane. For the Tesla Semi (or the Tantra Dump Truck in the extended version of the task), it is not possible, as shown. However, is it possible for the other vehicles? – this is the question to answer in Achievement Level 7-8.

Math Concepts: quadratic functions x-intercepts system of equations Desmos graphing point of intersection
MYP Related Concepts: models space
MYP Key Concepts: logic relationships
MYP Global Context: Orientation in Space and Time