This is the second of two lessons focusing on polynomial identities. In the previous lesson, students learned what identities are and in this lesson students practice determining when an equation is an identity.
The warm-up is meant to help students make sense of the following activity (MP1), where they investigate an identity that can generate Pythagorean Triples. This lesson includes an optional activity to use if students need additional practice proving algebraically that an equation is an identity. In the last activity, students prove identities involving rational equations as they learn about Egyptian fractions and consider different ways to rewrite a fraction as the sum of unit fractions.
- Create expressions to represent a mathematical situation and justify an identity about them.
- Justify (in writing) general relationships by using identities.
- Let’s explore some other identities.
- I can justify why identities are true.
An equation which is true for all values of the variables in it.