Step 6 Objective

Show understanding of situations by describing them mathematically making correct use of symbols, words, diagrams, tables and graphs.

Examples of what pupils should know and be able to do

a diagram with a two by two grid and a two by three grid

Shading Squares
There are six different ways to shade two squares in this shape. Can you find them all?

 

What about this shape?

How many ways are there?

Try using different rectangles made up of more squares.

Try shading three squares.

Examples drawn from Shading Squares

Develops and uses a procedure which guarantees to produce all the ways of shading two squares in a given number of squares.

A procedure which guarantees to produce all the ways of shading two squares in a given number of squares.

Probing questions

What is happening here?

What is this diagram, table, graph showing you?

How have you expressed this mathematically?

What if pupils find this a barrier?

diagram showing three lines crossing

Line Crossings

  • Draw three straight lines (line segments) so that some cross over each other.
  • How many crossings are there?
  • Try different arrangements of the lines. What is the maximum number of possible crossings?
  • Try using more lines.
  • Is there a rule for the maximum for any number of lines? If so, write it down.

Use the problem Line Crossings.

You have drawn a lot of diagrams.

  • Can you show the results for different numbers of lines together?
  • What information would you put into a table of results? Can you draw this table?