Explain the 3rd grade Math lesson multiplying by multiples of 10

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Welcome to our lesson on multiplying by multiples of 10! When we multiply by numbers like 10, 20, or 30, we can use a special pattern to make it easier. Let's start with a basic multiplication fact that we already know: 3 times 2 equals 6. We can see this visually with these 6 blocks arranged in 3 rows of 2. Now, let's try multiplying by a multiple of 10, like 3 times 20. Here's the pattern we can use: First, multiply the non-zero digits. 3 times 2 equals 6. Then, look at the multiple of 10, which is 20. It has one zero. So we put that zero at the end of our product from the first step. 6 becomes 60. So 3 times 20 equals 60. We can think of this as 3 times 2, which is 6, and then multiplying by 10, which gives us 60. Look at how we can group our blocks into 10 groups of 6, giving us 60 blocks total. Let's try another example: 4 times 50. Using our pattern, first we multiply the non-zero digits. 4 times 5 equals 20. Then, we look at the multiple of 10, which is 50. It has one zero. So we put that zero at the end of our product from the first step. 20 becomes 200. So 4 times 50 equals 200. We can visualize this as jumping by 50 four times on a number line, starting at zero and ending at 200. The rule is: When multiplying by a multiple of 10, multiply the non-zero digits first, then add the zeros from the multiple of 10. Let's understand why this pattern works. When we multiply by a multiple of 10, like 20 or 50, we're really multiplying by a number and then by 10. For example, 3 times 20 is the same as 3 times 2 times 10. Multiplying by 10 has a special effect: it shifts all digits one place to the left in our place value system. Look at what happens when we multiply 6 by 10. The 6 moves from the ones place to the tens place, and a zero fills the ones place. So 6 becomes 60. This is why we add a zero when multiplying by 10, two zeros when multiplying by 100, and so on. Understanding place value helps us see why this pattern works! Let's summarize what we've learned about multiplying by multiples of 10. Multiples of 10 are numbers like 10, 20, 30, 40, and 50. To multiply by a multiple of 10, first multiply the non-zero digits, then add the zeros from the multiple of 10. For example, 3 times 20 equals 60, 4 times 50 equals 200, and 7 times 30 equals 210. This pattern works because multiplying by 10 shifts digits one place to the left in our place value system. Now try these problems on your own: 6 times 40 and 9 times 70. Remember to use the pattern we learned: multiply the non-zero digits first, then add the zero!