The purpose of this multi-level task is to engage students in an algebraic investigation of a practical problem.
The background knowledge presumed for this task is outlined in the diagram below:
The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.
The arithmetic approach (show more)
- The student forms algebraic equations as a description of the steps taken in calculations. They calculate with numbers first, enabling them to focus on the steps they took as they generalise with algebra.
Prompts from the teacher could be:Consider the case that this rectangle has all four sides of equal length (ie, is a square).
- Try all the possibilities for a solution using numbers.
- Show how you found your successful solution using x for the length of a side of the square.
The procedural algebraic approach (show more)
- The student carries out directed calculations that will lead them to form and use a quadratic equation to solve a problem.
Prompts from the teacher could be:
- Sketch a variety of possibilities. Label the sides x, and/or a multiple of x.
- For each of these rectangles, form equations to solve for x.
- Find as many solutions as possible.
The conceptual algebraic approach (show more)
- The student carries out an exhaustive algebraic investigation where they to form and use algebraic equations, including quadratics, to solve a problem.