Mathematics Lesson: The Power of a Ten 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Essential Question( How do the powers of ten impact the size of a decimal number?

Exploring Power of 10 Evaluate 10 x 1 = 10 101 10 x 10 = 100 102 103 10 x 10 x 10 x 10 = 10,000 104 10 x 10 x 10 x 10 x 10 = 100,000 105 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 106 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 107

Describe any patterns you see in the “Evaluate” column. I notice that when you multiply 10 x 10, the 1 in the tens place moves one place to the left and has a value of one hundred now This same idea can be applied to the rest of the equations. I also notice that each time I multiply by another 10, there is one more zero in the product. This makes sense based on what I’ve learned about place value. I realize that each time I move down a row, I’m multiplying the previous product by 10 (since I have just one more ten to multiply by each time I move down in the chart). Multiplying by ten means each digit will shift one place value to the left since ten in one place value makes one in the place value to its left.

Describe what you notice about the exponents in the “Power of 10” column. Students should reason that the exponent above the 10 tells how many tens they are multiplying (or how many times ten is being used as a factor). They should also notice that the exponent above the ten is the same as the number of zeros in the product. For example, in 105 the exponent is 5 and in the product there are 5 zeros (100,000). Multiplying by ten one time shifts each digit to the left one place. So if they multiply by ten more than one time, each digit with shift that many places to the left.

Exploring Multiplying by a Power of 10 with Whole Numbers Evaluate 25 x 101 = 25 x 10 = 250 25 x 102 = 25 x 10 x 10 = 25 x 100 = 2,500 25 x 103 = 25 x 10 x 10 x 10 = 25 x 1,000 = 25,000 25 x 104 = 25 x 10 x 10 x 10 x 10 = 25 x 10,000 = 250,000 25 x 105 = 25 x 10 x 10 x 10 x 10 x 10 = 25 x 100,000 = 2,500,000

Identify and describe any patterns you see. I noticed that every time I multiplied by 10 there was one more zero on the end of the product. That makes sense because each digit’s value became 10 times larger. To make a digit 10 times larger, I have to move it one place value to the left. When I multiplied 25 by 10, the 20 became 200. The 5 became 50 or the 25 became 250. So I had to place a zero at the end to have the 2 represent 2 one- hundreds (instead of 2 tens) and the 5 represents 5 tens (instead of 5 ones).