For addition activities, begin with small numbers. If you are using blocks, for example, place one block on one side of the table and one block on the other side. Help the child count each block. Then, bring the blocks together, saying, "One plus one makes..." and count the outcome with the child. Do as many variations as you can as long as the child is still interested. At some point, ask the child to start setting up her own addition problems with the blocks. You can advance this activity further by adding three groups of blocks or more.
Subtraction activities are fun with manipulatives that the child can eat, such as jellybeans or Cheerios. Begin with a single group of Cheerios, or whatever you choose to use, and ask the child to count them. For example, you might start with five Cheerios. Once the child has counted all five and arrived at the correct amount, ask him what happens if he takes away one. Help him verbalize the concept by saying, "Five minus one leaves..." Let him eat one of the Cheerios and then count the new total to find the answer. Again, repetition and varying the starting number and the amount you take away will help to solidify the concept of subtraction.
Multiplication is a difficult concept for some children to grasp at first, but using manipulatives can make it much easier. Begin with the "ones" multiplication table. Place one item like a button in front of the child, or in one cup of a muffin tray. Ask her how many buttons she has if she counts one, one time. She can count the single button for the answer of one. Put a second button on the table so it is separate from the first, or into a second cup of the muffin tray. Ask how many she has if she counts one, two times. She can count to find that one times two is two. Continue up through one, 10 times. Then move up to two buttons per group and repeat the process.
Manipulatives can help a child to understand place values better. For this activity use pencils or crayons. Bundle a group of 10 pencils together in a rubber band. Let the child count the tips of the bundled pencils to see that there are 10 pencils in the one bundle. Place the bundle on the table in front of him and then place one pencil to the right of the bundle from his perspective. Ask him how many pencils there are if he adds the one to the bundle of ten. When he answers 11, show him how the bundle of pencils is like a one in the tens place and the one pencil is like a one in the ones place. Repeat this activity using different numbers and multiple bundles of pencils.