The problem of teaching arithmetic to a backward class in a secondary modern school is necessarily a complex one. The children will probably have been drawn from a number of junior schools and will have been taught by different methods. The children are often dispirited and feel that they are failures, having no inclination to try the work at which they have so often failed. Ability will be mainly low in a backward class but there may be a retarded child with higher ability. Record cards usually give results of intelligence tests; when averaged over several years these give a good enough idea to work on. Mental exercises help the children to listen, especially if, after the first few, each sum is given only once. Backward children need an arithmetic lesson of not more than thirty minutes each day.