This activity starts with a problem to solve: Determine the number of cans in a stack, 30 rows high. Students use a range of visual and numerical representations of similar, related problems to build an understanding of associated algebraic formulas that can be used to solve this problem. The focus of the activity is on developing algebraic formulas with a fundamental understanding of their structure and therefore a deeper understanding of their meaning.
Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate - ACMNA239.
About the Lesson
The number of cans in a stack can be calculated using a relatively simple formula (quadratic), however building the formula using a range of strategies with corresponding visual aids is a much more powerful learning experience. Problem solving strategies such as “breaking the problem down into smaller parts” are employed to help students see how the algebraic expressions are formed. Tackling the problem from different angles helps students understand the different algebraic representations of the same formula.
See Also - Number Sums Extensions