In this series of lessons, students learn mathematical reasoning strategies to facilitate learning the basic multiplication facts.
In this lesson, students learn a strategy for the basic facts for multiplying by 2. They learn that multiplying a number by 2 is the same as adding the number to itself.
In earlier lessons, students learned to make tens from ones and to count by tens.
In this lesson, students learn a strategy for the basic facts for multiplying by 5 and 10. They learn that multiplying by ten is the same thing as counting by ten as many times as the other factor.
Multiplying 5 by an even number is illustrated using arrays, and the students knowledge of the distributive property of multiplication. When 5 is multiplied by a number, an array is displayed, for the multiplication, then it is subdivided to show groups of ten. The number of groups is half the number multiplied by 5.
Multiplying 5 by an odd number is illustrated as first decreasing the number by 1, multiplying that number by 5, then adding 5 to the result.
In this lesson, students learn a strategy for the basic facts for multiplying by 0 and 1. When a number and zero are multiplied, the result is always zero. When a number and 1 are multiplied, the number stays the same.
In this lesson, students learn a strategy for the basic facts for multiplying by 3 and 4. When a number is multiplied by 3, the result is two times the number plus the number.
When a number is multiplied by 4, the result is the same as doubling the number, then doubling the result.
In this lesson, students learn a strategy for the basic facts for multiplying by 9. They learn that to multiply a number by 9 is the same thing as multiplying by 10 and subtracting the number.
The way to use this is to recognize the pattern that results when the digits 2 through 9 are multiplied by 9. In each case, the result can be found in two steps. First, reduce the number by one to get the first digit of the result. The first digit of the result is then subtracted from nine to get the second digit.
In this lesson, students learn a strategy for the basic facts for multiplying by 6, 7, and 8.
When 6 is multiplied by an even number, the first digit of the result is always half the number. The second digit is the same as the number. When 6 is multiplied by an odd number, the result is 6 times one less than the number plus 6.
A general strategy for multiplying by 8 is not taught. There are two facts using 8 that can’t be solved using a strategy for one of the other digits. One is 7 times 8. A heuristic is taught to help remember this fact. Seven times 8 is 56, which results in the sequence 5678.
There are two remaining facts, 7 times 7, and 8 times 8. Since no strategy is taught for these facts, students must rely on memory. However, these are easier to learn because they only remembering two numbers, not three.
In this lesson, students practice multiplying using all the basic facts to facilitate automatic recall.