Babies are starting to become ready to take solid food (other than milk) and often start needing the additional nutrients provided by these foods around 4-6 months of age. Typical foods to start with are rice cereal, or oat or barley cereal. Once these are tolerated for a few weeks, other pureed foods can be slowly introduced (usually waiting 3-5 days between introduction of new foods). Examples include cooked apple, pear or even prune (especially if constipated) purees, or ripe squashed bananas. Jarred foods such as squash or carrots can also be used. At 6-8 months, vegetables such as squashed peas, potatoes, and yams can be given. As the infant gets older, and teeth are evolving by 9-12 months, more chunky foods can be introduced in small pieces/strips. Allergens such as cow milk, egg white, shellfish, chocolate, and tomatoes should be avoided until after one year of age. Foods high in nitrates (beets, spinach, turnips) can cause methemoglobinemia and should be avoided in infants.
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According to this article from the US Department of Education, a baby might be ready at 4 months to eat solid foods. The article suggests some things to look for to determine whether or not your baby is ready to begin eating solid foods.
The article goes on to suggest foods such as rice, oatmeal or barley cereals (all of these being ground up) as being good things to start with.