What makes a word easy to learn? Early-learned words are frequent and tend to name concrete referents. But words typically do not occur in isolation. Some words are predictable from their contexts; others are less so. Here, we investigate whether predictability relates to when children start producing different words (age of acquisition; AoA). We operationalized predictability in terms of a word's surprisal in child-directed speech, computed using n-gram and long-short-term-memory (LSTM) language models. Predictability derived from LSTMs was generally a better predictor than predictability derived from n-gram models. Across five languages, average surprisal was positively correlated with the AoA of predicates and function words but not nouns. Controlling for concreteness and word frequency, more predictable predicates and function words were learned earlier. Differences in predictability between languages were associated with cross-linguistic differences in AoA: the same word (when it was a predicate) was produced earlier in languages where the word was more predictable.