The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even.
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 provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable.
This 3-minute video lesson introduces the concept of abolute value.
This 8-minute video lesson continues to look at absolute inequalities.
This 6-minute video lesson looks at absolute value and number lines.
This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.
This task is a somewhat more complicated version of "Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly. Instead, students have to combine the algebraic techniques with some additional problem-solving (numerical reasoning, informed guess-and-check, etc.)
This 8-minute video lesson continues to look at absolute inequalities.
An introduction to adding, subtracting and multiplying complex numbers. [Algebra: Lesson 34 of 86]
This 5-minute video lesson looks at adding and simplifying radicals.
A demonstration of the use of algebra for more advanced ratio problems.
This lesson introduces the use of algebra for solving age word problems.
This lesson continues the explanation for the use of algebra to solve age word problems.
A demonstration of using algebra to solve age word problems.
This 4-minute video lesson continues to demonstrate how to solve radical equations.
A demonstration of how to divide one polynomial into another polynomial.
This demonstration presents an alternate solution to the advanced ration problem for algebra in the previous lesson.
This algebra lesson is an introduction to functions.
