Tasks | Early Adolescence | Simultaneous Equations

Tasks - Early Adolescence

Simultaneous Equations   by Richard Grey, Curriculum Council

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Number	Reason about Number patterns
Working Mathematically	Mathematical Strategies
Algebra	Understand symbols Understand graphs
Brief Description:	Tabulate data gathered from car travel. Find graphical solutions when the cars pass each other.
Expected Outcomes:	Tabulate data from moving cars. Find difference patterns. Describe linear functions symbolically. Graph linear functions. Find points of intersection graphically
Context:	This activity is designed to be used as an activity for students who know and understand symbolically, write linear functions and graph the lines on a graphics calculator. The activity could be used to either introduce simultaneous equations or as an application.
Learning Activities/ Experience:	Time taken - 20 minute activity A car sets out from Ocean Reef Road travelling at a constant speed south on the freeway. Another car sets out from Forrest Road, 50 km from Ocean Reef Road, at the same time and travels north on the freeway at a constant speed. Time after car 1 leaves 0 min 5 min 10 min 15 min 20 min 25 min Distance from Ocean Reef of car 1 (y1) 0 km 7 km         First difference pattern for y1           Distance from Ocean Reef of car 2 (y2) 50 km           First difference pattern for y2           Complete the table showing the distances from Ocean Reef. Complete the first difference patterns. Work out the equations of the two journeys. Enter the two equations into the graphics calculator for 0 t 50 and 0 y 50, then find when and where the cars pass each other.