This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

This lesson unit is intended to help teachers assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help teachers identify and assist students who have difficulties in: representing a constraint by shading the correct side of the inequality line; and understanding how combining inequalities affects a solution space.

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

This lesson unit is intended to help teachers assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to: find, from their equations, lines that are parallel and perpendicular; and identify and use intercepts. It also aims to encourage discussion on some common misconceptions about equations of lines.

This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the optimum case, checking it for confirmation; and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students are able to: recognize the differences between equations and identities; substitute numbers into algebraic statements in order to test their validity in special cases; resist common errors when manipulating expressions such as 2(x Đ 3) = 2x Đ 3; (x + 3)_ = x_ + 3_; and carry out correct algebraic manipulations. It also aims to encourage discussion on some common misconceptions about algebra.

This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

Although this task is quite straightforward, it has a couple of aspects designed to encourage students to attend to the structure of the equation and the meaning of the variables in it. It fosters flexibility in seeing the same equation in two different ways, and it requires students to attend to the meaning of the variables in the preamble and extract the values from the descriptions.