Down Syndrome (DS) is caused by trisomy of chromosome 21 (Hsa21) and results in a spectrum of phenotypes including learning and memory deficits, and motor dysfunction. It has been hypothesized that an additional copy of a few Hsa21 dosage-sensitive genes causes these phenotypes, but this has been challenged by observations that aneuploidy can cause phenotypes by the mass action of large numbers of genes, with undetectable contributions from individual sequences. The motor abnormalities in DS are relatively understudied—the identity of causative dosage-sensitive genes and the mechanism underpinning the phenotypes are unknown. Using a panel of mouse strains with duplications of regions of mouse chromosomes orthologous to Hsa21 we show that increased dosage of small numbers of genes causes locomotor dysfunction and, moreover, that the Dyrk1a gene is required in three copies to cause the phenotype. Furthermore, we show for the first time a new DS phenotype: loss of motor neurons both in mouse models and, importantly, in humans with DS, that may contribute to locomotor dysfunction.