If you have them, use base ten blocks to model multiplication problems: 6 x 8 and 8 x 6, for example.
Use coins, buttons, or other small objects to help your child discover associative and commutative properties for him/herself. For addition, lay a number of objects (perhaps 8-10 to start with) on the table and ask your child to arrange them in 2 groups. Write down the number sentence that you get (for example, with 8 items, the number sentences that are possible are 0+8=8, 1+7=8, 2 +6+8, 3+5=8, and 4+4=8. After that, we are repeating ourselves, because 3+5 is the same as 5+3, but children don’t automatically know this. Allow your child to reverse the order of the groups he/she laid out (the group of 3 and the group of 5 in this example change places) and see that the total is still 8. The child can then discover, with this same grouping that 8-5 is 3 and 8-3 is 5.
Make up a little story about number families. Each family has a grown-up and (for our purposes, for now) 2 children. If the family happens to only have 1 child, we’ll hold a place for the child that is “away visiting” and name that child “zero.” A family has to “prove” that it gets to be a family in this way: The number names of the children have to be equal to the sum (or product) of the grown-up. All families are named “the Add family” or “the Multiply family.” Now, let’s play. “Here are the children in the Add family. Their names are three (3) and (5). What’s the mommy’s (or daddy’s or grown-up’s) name?” Expect the answer “Eight.” When the child can do this confidently, change the question: “Here is the Add family. The mommy’s name is Eight and one of the children’s names is Five. What’s the name of the other child?” (It’s best if you say this in a sort of playful-“we’re pretending” fashion because while it’s a game that makes sense mathematically, it is just a game!) Soon your child will automatically think of these 3 numbers as having this special relationship. For the Multiply families, you could say, “Here is a Multiply family. The children are named Three and Five. What’s the daddy’s name?” Expect the child to answer “Twenty-four.” Eventually you can make this game harder with this question: “I see a Multiply Mommy! Her name is Twenty-four! Hi, Ms. Twenty-four? Where are your children today? Wait! Who ARE your children? The children, in a Multiply family, could be Twenty-four and One, they could be Twelve and Two, they could be Six and Four . . . you get the idea. This is a valuable game to play because when children begin to work with fractions later in their schoolwork they will need to find common denominators—a number that will allow several selected numbers to have a common division factor. When your child sees denominators of, say, 3, 4, and 6, a child who is good at playing “Number Families” will quickly think “12 is my common factor for these three numbers.”