Fact families are groups of related numbers that help reinforce numbers and relationships. For example, the addition fact 3 + 1 = 4 is related to the subtraction fact 4 - 1 = 3. By showing that subtraction is the inverse, or opposite of addition, students understand the link between the two operations. Students can learn four facts using the same set of numbers. Fact families can also be used to show related multiplication and division facts, reinforcing that division undoes multiplication.
While tables can be used for all four sets of facts, they are typically used to display multiplication facts. Tables consist of rows and columns of numbers, with the facts displayed along the top and left side of the tables. The answers are placed where the rows and columns intersect. Multiplication tables can be used to show the order property of multiplication, square numbers and other number patterns. Students can highlight the facts that are known and identify the facts that have not been mastered and need reinforcement.
Arrays are visual representations of multiplication and division facts using symbols arranged in rows and columns. Students can create the arrays, placing the symbols in rows while using repeated addition to model multiplication. Division can be modeled by using arrays to show how the total number of objects can be placed in groups or take away groups using repeated subtraction. Showing how some numbers can be arranged in many different groups leads to an understanding of prime and composite numbers.
Number lines can be used to model all four operations. Addition and subtraction can be modeled by starting with an initial number and either adding to or taking away from the number. Multiplication can be modeled showing skip counting, or repeated addition. Division can be represented by showing repeated subtraction. Students can begin to understand how addition and subtraction facts move numbers minimally while multiplication and division move numbers further. This leads to an understanding of the magnitude of numbers and operations.