gistfile1.txt

class SearchBar extends React.Component {
  state = {
    searchTerm
  }

  onSearchTermChange = (data) => this.setState(...)

  handleSearch = () => ...
  handleClear = () => ...

  SearchField = () => <TextField onChange={this.onSearchTermChange} ></TextField>

  render () {
    return (
      {this.props.children({ searchTerm: this.state.searchTerm, SearchField })}
    )
  }
}

<SearchBar>
  {({ searchTerm, SearchField }) => (
    <Selector searchTerm={searchTerm} />
    <SearchField />
  )} 
</SearchBar>