The multiplication chart provides a visual of number family trios.
You might think that math is an immutable beast, unchanging from one generation to the next. However, textbook publishers and curriculum developers have created a whole new set of labels and explanations for many age-old mathematical processes. Parents everywhere can testify to the puzzle of helping their children with math homework that contains instructions and terminology they never met in their school days. A worksheet that asks the child to list the multiplication facts in "family groups," for instance, can frustrate well-meaning parents who only want to help their children do well in school.
Definitions
By one definition, a multiplication fact family is any fact that contains a given number that belongs in that number family. For example, 6 x 3 = 18, 6 x 8 = 48 and 6 x 12 = 72 all belong in the six family. A fact's two factors and the resulting product form another type of multiplication family group related by the commutative property and the inverse relationship of multiplication and division. In other words, the product remains the same regardless of the order of the factors in a multiplication fact; and because division and multiplication are opposites, one operation reverses the other. So the product divided by either factor equals the other factor. Case in point, the multiplication fact family for 7, 9 and 63 contains the following facts: 7 x 9 = 63, 9 x 7 = 63, 63 ÷ 7 = 9 and 63 ÷ 9 = 7.
Fact Family Cards
Make a set of multiplication fact family cards for independent practice. Cut out enough equilateral triangles for all the multiplication facts. On each triangle write the factors in two corners and the product in the third. Cover up one of the numbers and show the other two to your child, asking him to identify the missing member of the fact family. Alternatively, he can look at all three numbers and name all the multiplication and division facts associated with the number trio.
Egg Carton Multiplication
A couple of egg cartons and some dry beans provide an easy visual illustration of multiplication fact families. Explain to your child that multiplication is simply a way to count up things in groups. For example, 5 x 3 means you have five groups of three items each so you can put three beans in each of five egg cups and count by threes to get the total. If you add another group of three, you now have 6 x 3. Every cup still has three, so it remains in the same family.
You can also illustrate the commutative and inverse relationship family. Take a multiplication fact such as 4 x 5 = 20, drop four beans each in five cups, then switch it around to five beans each in four cups to show that the same amount of beans divides into equal groups either way. Show your child a multiplication fact family card and let her illustrate both groupings with the egg carton and beans.
Fact Family Go Fish
Make three cards for each multiplication fact. One for each factor and one for the product. Shuffle the cards, deal five to each player and leave the rest in the draw pile. Proceed with play as in Go Fish. Your goal is to collect number trios that form a fact family. Alternatively, you can try to collect all the facts in one family such as all the twos or fives. In this case, the winner would be the first player to succeed in collecting an entire fact family.
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