I googled "third grade spelling words" and had many links that will assist you with your child's summer learning. Try some fun ways to help your child learn a word a day by using index cards in a scavenger hunt. Hide the cards and give extra points when the child can spelll the word and use it in a sentence.
Unlike the old days where everyone in the same school district uses the same spelling book. Nowadays, every teacher (even teacher within the same school) uses a different spelling list.
We have an information center on third grade vocabulary - which are words that third grader should know before advancing to fourth grade. Perhaps you could work on these worksheets with your child. In addition to doing the worksheet, you can have your child write sentences with the word. And if your child is up for the challenge, write a story/essay from the words on the worksheets. Below is the link to the third grade vocabulary portal.