Students learn how to solve quadratic identities by completing the square and equating terms. As learning progresses students are challenged to solve identities where the coefficient of b is odd and in the form a(x+b)^{2} + c.

At the start of the lesson students arrange six expressions written in the form (x + b)2 + c in order of their smallest possible value. In the plenary students are challenged to match a range of identities with their equal terms.

**Differentiated Learning Objectives**

- All students should be able to solve a quadratic identity in the form (x + b)
^{2}+ c by completing a square. - Most students should be able to solve a quadratic identity in the form (x + b)
^{2}+ c by completing a square and equating terms. - Some students should be able to solve a quadratic identity in the form a(x + b)
^{2}+ c.