Ask them to move the item from one container to another and see if the new container is full, overflowing, or partly full. Ask them to think about the relative size of each container, if one holds more than the other or less. Then, have them fill a different container and ask them to estimate how much the other containers will get filled. Pour the contents into one and let them revise their estimates. For older kids, use a pen to mark the levels of water or other substance in each container and introduce the idea of fractions.
Young kids can test out their estimation skills without worrying about exact numbers.
First, while you're getting ready to go shopping, let your child create a shopping list with you, or create a separate list for a special meal. Have them estimate how many of each item will be needed for your family. Then, using the food section from a newspaper, have your child estimate how much it will cost to buy everything needed. While at the store, ask your child to estimate the relative weight of items, such as three apples and three tomatoes, and use the store's produce scales to verify their estimations. With younger kids, you might want to focus on estimating weights, while older kids can estimate prices.