Alpha Pig loves to eat Apples. Alpha Pig and Apples start with the letter A. Ask your child to find items at the grocery store that start with the first letter of their name, your names, or work your way through the alphabet.
As you find items while shopping, ask "What letter does pepper start with?" Now look for other items in the store that begin with this letter.
A is for Avocado. B is for? Can you and your child make it all the way through the alphabet using only items you can find in a grocery store?
Enlist your child to help you find items in the store. Instead of just telling them what to put in the cart, give them a rhyming word and have them figure it out. "I'm looking for something that rhymes with .... legs."
"I spy a cereal that starts with /c/."
"I spy a fruit that starts with the letter P."
Building memory skills helps with reading comprehension. Give your child a portion of your grocery list to memorize, say "A loaf of bread, a container of milk and a stick of butter" and have them pick out the groceries from memory.
As they get better at the game, make their lists longer, or have them find the groceries in reverse order.
Pick a treat in the grocery store that your child can have if they guess what the treat is in 20 questions or less. If they guess the treat you're thinking of, they can get it (or can choose a different one).
Start a rhyming game about the people you see. "Man in red, man in red, you have yellow hair on your head." Then start a rhyme and invite your child to finish. "Girl in blue, girl in blue, you have laces on your ..." Encourage your child to make more rhymes, even very silly ones.
Before you go shopping, have your child make their own shopping list with a few items. As they shop they need to find and cross off the items as they add them to the shopping cart.