Students often learn their multiplication facts without gaining any real understanding of their meaning or usefulness. So, as long as they encounter mainly problems that can be easily solved using skip counting or repeated addition, they fall back on the methods that have served them adequately in the past.

To break this self-reinforcing habit, students need to be challenged with problems that demand the use of multiplicative methods for reasons either of (i) efficiency or (ii) necessity.

A good place to start is helping students to understand the efficiency of multiplication as an alternative to counting or repeated addition. As part of this process, students need to understand that they can use multiplication only when they are working with groups of equal size.

Show the students three cups, each containing a different number of counters. Discuss why you need to use counting or adding rather than multiplication to find the total.

Show the student three cups, each containing the same number of counters. Discuss that counting, adding, or multiplying could be used to find the total. Have the student confirm that all three methods give the same result.

Next, discuss how you could solve a similar problem with cups containing the same number of counters but that this time there are 100 cups. Can you still use all three methods? Which method here is the most efficient?

In many situations, multiplicative strategies are not only more efficient (quicker and/or easier) than addition, they may be necessary to solve a problem. This is true when the numbers involved are large and when they are not whole numbers.

Demonstrate the need for multiplicative strategies through the use of appropriate examples. For example, skip counting can be used to find 16 x 3 or 5 x 25, but hardly to find 116 x 3 or 40 x 26. The latter requires the use of a multiplicative strategy such as doubling and halving (40 x 26 = 20 x 52 = 10 x 104 = 1040) or partitioning (40 x 20 = 800 and 40 x 6 = 240 so 40 x 26 = 800 + 240 = 1040), or a combination of the two. Many solution strategies will involve both multiplication and addition.

Asked to find the area of a rectangular room where the units are whole numbers (for example, 12 metres x 9 metres), students may count squares or even skip count. But to find the area of a room 12.5 metres x 8.9 metres (NZC level 4), they will need to use a multiplicative strategy.