Learning one fact actually means learning two facts as the commutative property demonstrates. Students should be directed to state that while 2 x 4 = 8, 4 x 2 also equals 8. This cuts down the amount of facts that students need to learn. In addition, seeing all four facts in a family reinforces the inverse relation of division to multiplication. The related division fact starts with the answer to the multiplication fact, increasing exposure to the related numbers.
Seeing patterns in facts provides an opportunity for students to develop reasoning skills. By placing the two times, four times and eight times tables next to each other, students can see how the answer doubles as the factor doubles. For example, since 2 x 3 = 6, 4 x 3 = 12 and 8 x 3 = 24 as the answers double across the factors. This also works with the three times and six times tables. Hundred charts are another visual aid in reinforcing facts. Students can explore how certain multiples form diagonal or vertical lines on the chart as they increase.
Arrays, or rectangular arrangements, help students visualize factor pairs. Students can be instructed to make rectangular arrays for a given number, such as 24. By creating arrangements such as 2 by 12, 3 by 8 and 4 by 6, students begin to see how many different factors a number like 24 has. This can be compared to arrays for the numbers 7, 17 and 23, which have only a single row of tiles. By studying facts by starting with the multiples, students will master facts in groups rather than one fact at a time.
Finding and observing real-world examples of factors helps reinforce fact mastery. Using pairs of socks to see the two times tables, triangle sides for the threes and tires on a car for the fours are all examples of real-world applications. Students can start with skip counting and progress to multiplying as a quicker way to find the total.