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This work is devoted to the numerical approximation of the shallow water Exner system. We investigate three different numerical strategies to discretize the Exner equation which expresses the evolution in time of the bed sediment. The numerical schemes are all based on the Lagrange‐projection formalism which consists in splitting the mathematical model into the acoustic and transport system. In particular, the Exner equation is taken into account either in the acoustic and transport steps, or only at the acoustic or transport level. The methods and their second‐order extensions are designed in such a way to satisfy the well‐balanced property, namely the “lake at rest” and the “constant bed slope” steady states. Numerical evidences are given to validate the numerical schemes.