Tasks | Early Adolescence | Investigating Powers

Tasks - Year 10

Investigating Powers   by Glenys Stade, Hampton Senior High School

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Symbols
Number	Reason About Number Patterns
Working Mathematically	Mathematical Strategies Reason Mathematically Apply and verify
Brief Description:	Looking for patterns in the units digit of powers.
Expected Outcomes:	Looking for patterns. Expressing these patterns in the appropriate form. Applying these patterns to answer questions.
Context:	Investigation originally used prior to introduction of graphic calculators for a Year 10 group. Updated and modified for a calculator inservice. Has not been trialed in its current form.
Learning Activities/ Experience:	Time Taken - 1 lesson : 1 week home activity What is the last (units) digit for 2671 ? A question like this could be posed and strategies developed for finding the answer or students could be given a structured worksheet like the ones attached. Of course the obvious strategy is to work with smaller numbers and look for a pattern. A graphics calculator or a spreadsheet can generate a table efficiently but the point can be made that it still can't answer the question. The student must look at the table that has been generated and look for patterns and try to generalise. The advantage of the technology is that more examples can be generated and checked before the numbers become too large.