Lesson 29 Straight line graphs

# Straight line graphs

Overview Resources
An activity on the basic ideas that underlie the use of graphs and related algebraic notation. it allows pupils to handle and reflect on these ideas in advance of their later use as conventions in formal mathematics. The formal treatment will be seen then as giving the most economical and precise descriptions of actual patterns of relationships. Worksheets 1 and 2, Large sheets of paper. Worksheet 3 (optional). Graphical calculators (optional)
Exploring conceptual foundations for graphs.
• Graphs of linear functions,
• Tangent and intercept,
• Use of graphical calculators.
• EPISODE 1
Reinventing the coordinate system
Pupils work through a concrete context to ‘reinvent’ the coordinate system in a way accessible to all pupils. The aim here is to link their natural language descriptions of locations and line patterns on a plane with formal mathematical use of axes and algebra. Pupils move from describing single points to the lines that they lie on.
EPISODE 2
Patterns in slanting lines
Now pupils describe lines using both axes. As they do they realise that they need to describe two values: a value for the crossing point at the y-axis and a value for the slope. Here the gradient and intercept notions of linear relations are explored.The actual algebraic notations are only developed to the extent the teacher judges these to be accessible to their classes.
EPISODE 3 (optional)
Writing the paths of moving objects
This part of the lesson emphasises the link between verbal descriptions and visual available mathematical cues. Some pupils will link the intersections, arrived at via trial and error, to precise calculations and the graphical calculator with solving simultaneous equations. Others will use the time to explore simultaneous linear and quadratic functions.