An easy math activity that utilizes a wide variety of math skills is the use of ten frames. You can download and print out a ten frame or just draw one out on a sheet of paper.
Provide your child with 10 or less items (goldfish, coins, Lego blocks, LOL figures anything your child would enjoy counting). Have him/her count the items. This initial counting works on one-to-one correspondence, the matching of the number word to the number of items you are counting. Make sure you child touches/points to each item and only says one number for each item touched. Many children count 1,2, 3, 4, 5, etc but might skip items in the group or say 1,2 then move their finger. The goal is to touch and count at the same time.
Next have your child place the items onto the ten frame. This works another level of one-to-one correspondence. They need to place one item in each square. (one item, one space). Have them count to check.
You could then have your child practice writing the corresponding numeral one to three times.
Now change out the number of items your child is counting. I would have your child do 4-6 sets before moving onto a different task.
What do I do if my child is struggling? First reduce the number of items try having him/her count 3 or 4 items and see if they are able to count and point with a smaller number. Show your child to line up the items into a line or into rows/columns this will limit recounting the same item multiple times. Provide items that are all different colors or types to help them remember which ones they have already counted.
What do I do if this is too easy? Have your child compare groups. Do you have more red goldfish or green? Add in the concept of adding more. How many would you have if you added 3 more? Go beyond 10 by adding a second ten frame.