Equations and identities

This is an activity that intends to focus attention on distinguishing between algebraic statements of truth (identities) and equations in x. Learners are given cards such as, for example below (Figure 1). On each card is an equation in x. Some of these are identities, and are ‘Always true’ (e.g. 2x + 3x = 5x). Some can be solved for x and are ‘Sometimes true’ (e.g. x + 2 = 5) and some are incorrect and ‘Never true’ (e.g. x + 3 = x). In one version some of the cards require the students to multiply out brackets first, and in another version all the cards require this.

In the classroom activity, students work in pairs to place the cards on a poster in one of three columns labelled ‘Always true’, ‘Sometimes true’ and ‘Never true’.

Figure 1: Learners working with the small cards
Figure 1: Learners working with the small cards

Towards the end of the lesson the teacher hands out big versions of the cards and asks learners to come to the board and put the cards into the columns on the board. Figure 2 shows one learner doing this.

Figure 2: A student places one of the cards in the 'Almost True' column
Figure 2: A student places one of the cards in the ‘Almost True’ column

Figure 3 shows one of the teachers discussing a card match with the class.

Figure 3: Jonathan discusses one of the card matches with the class
Figure 3: Jonathan discusses one of the card matches with the class

Download the card set for the first version here: Equations and identities cards for printing

Download the card set for the second version here: Equations and identities small cards version 2

Download the outline lesson plan here: Equations and Identities lesson plan