Explain that with standard algorithm multiplication you start by putting the numbers one under the other. You put the decimal number on top. Show that above each column there is a little box. In these boxes you can write down numbers that are regrouped to add them up with the other outcomes later on. In the intermediate step you can write down the outcomes of standard algorithm multiplication with tens and ones numbers. First imagine that the decimal point is not there and you are multiplying 2 whole numbers to each other. Explain that you begin with the lower number on the right. You multiply this number with the higher number in that column (5 × 2 = 10). From this 10 you write down the 0 under the line in the column. You can write the 1 (10) in the little box above the tens column. Now multiply the lower number from the ones column with the higher number from the tens column (5 × 3 =15). Emphasize that you shouldn't forget to add the 1 from the regrouping box to this (15 + 1 = 16). You write down this 16 under the line. This is the first outcome of the intermediate step. Next you multiply the lower number from the tens column with the higher number from the ones column (2 × 2 = 4). Then you multiply the lower number from the tens column with the higher number from the tens column (2 × 3 = 6). Now you add the numbers from the intermediate step together (160 + 640). The outcome of this is 800, but you still have to put the decimal point back. Explain that you see how many digits there are behind the decimal point in the problem, and this is how many should also be after the decimal point in the answer. Practice two problems together with the students that must be solve using the standard algorithm. The students may use scrap paper to write down their calculations. Explain that you can solve problems with multiple decimal places in the same way. Solve the problem 12.81 × 7 together with the students, step by step. The students solve the next two problems on their own.
Check whether the students can multiply using the standard algorithm with a decimal number by asking the following question:
- What steps do you take to solve the problem 15.26 × 7 using the standard algorithm?