Copyright © University of Cambridge. All rights reserved.

## 'Interactive Number Patterns' printed from http://nrich.maths.org/

This problem, and the Excel interactivities, have been created to
deepen students' understanding of the 'difference method'.

The Hints section contains additional direction for students
engaging with this task.

Students often possess the method but without any sense of why
it's valid. Hopefully this activity will not only help them to
explore this method's validity but will also encourage in them a
questioning attitude and a desire to establish the validity of
other common methods as they meet them.

It may be valuable to notice that the quadratic expression and the
red values can be set on either sheet and will then automatically
update on the other.

There are a large number of values displayed on the sheet called
'Patterns with differences' (see the tab at the bottom of the work
area on Interactive Number Patterns 2). Students need to be given
the time to understand all parts of the display.

The following may be one useful way to use this resource with a
class.

Below the formula box are three rows. These display the values
of the quadratic, linear and constant terms respectively. Change
the terms in the formula box to help students grasp what each row
shows, and verify that the three values added together match the
blue values. In the two rows of differences above the formula box
and verify that the data showing is the correct difference for the
blue values, and use the slider to change the red values, allowing
students to verify the new values displayed within the sheet.

Draw attention to the first difference which changes, and the
second difference which does not. Why is that?

The constant term contributes nothing to the first difference,
the linear term contributes to the first difference but not the
second, and the coefficient, or multiple, of the quadratic term is
the only coefficient which influences the second difference.