Powers of 10
Students will be able to multiply by powers of 10 with exponents.
- Write 10 x 1 = 10, 10 x 10 = 100, 10 x 100 = 1,000, and 1 0x 1,000 = 10,000 on the board. (Note: write each new equation above the previous one, making sure to align the equal signs)
- Ask students to look for patterns and discuss with a partner.
- Discuss patterns as a class (i.e., each equation is ten times greater than the one before; each equation has the same number of zeros in the product as in the two factors). Guide the discussion as needed.
- Tell students that today they will be studying powers of ten (10 multiplied by itself a certain number of times).
Explicit Instruction/Teacher modeling(15 minutes)
- Introduce exponents. (The exponent of a number says how many times to use that number in multiplication, for example 4 to the third power would be 4 x 4 x 4.)
- Provide a few examples (i.e., 22 = 2 x 2 = 4, 52 = 5 x 5 = 25, 43 = 4 x 4 x 4 = 64, and 63 = 6 x 6 x 6 = 216).
- Explain that powers of ten are numbers that are a result of 10 being multiplied by itself a certain number of times. Therefore, we can use exponents to express various powers of ten.
- Hand out the Growing by Powers of Ten Chart printout, and guide students through it, filling in blanks as a whole class.
- When the worksheet is completed, have students look for patterns and discuss with a partner. Then, as a class, discuss the patterns (i.e., each power of ten has one zero more than the previous; each power of ten has the same number of zeros as the exponent, for example 103 = 1,000).
- Explain that each power of ten has a value ten times greater than the previous power of ten, because it is multiplied by an additional 10. For example, 105 is ten times greater than 104.
- Point out the pattern of added zeros on the worksheet and tell students that each additional zero represents a place value that has been added.
- Write 10,000 on the board and ask students: What power of ten is this? (104) Call on a student to give an answer and justification.
Guided Practice(10 minutes)
- Write a multiplication problem on the board that includes a power of ten (i.e., 5 x 100 = 500).
- Explain: we can rewrite this problem with a power of ten.
- Under the first problem, write 5 x 102= 500 and tell students that, since we know that 102 is 100, then 5 x 102 is equal to 5 x 100.
- Write another problem, like 2 x 103, and have students solve with a partner. Have students rewrite the power of ten as a number before solving (i.e., 2 x 1,000). Remind students to use their chart for help if needed.
- Write another problem on the board, like 3 x 104, and have students solve it independently. Then, call on a student to share their answer and a justification (i.e., "104 is 10,000 and when you multiply that by 3, you get 30,000. The pattern of zeros helped me because I know that the product of 104 will have four zeros.").
Independent working time(15 minutes)
- Write five problems on the board and have students solve them independently (i.e., 6 x 105, 12 x 104, 98 x 102, 134 x 106, and 502 x 103).
- Hand out scratch paper for student work or have students work in a math notebook.
- Circulate as students work and offer support as needed.
- Go over the problems as a class.
- Encourage students to use their completed Growing by Powers of Ten chart as a support during independent practice.
- Provide additional practice with smaller numbers (i.e., 2 x 104, 3 x 101).
- Have students apply the concept to decimals (see optional materials).
- Pass out a sticky note and one die per student (multiple students can share a die if needed).
- Instruct students to roll the die and use the number to write a power of ten on their sticky note (i.e., if a 4 was rolled, the student would write 104).
- Instruct students to roll the die again. Have them use this second number to multiply by their power of ten (i.e., if the second number rolled was a 2, the student would write and solve this equation: 2 x 104).
- Collect as an exit card and check for understanding.
Review and closing(5 minutes)
- Ask students: How can the problems we solved today (multiplying by powers of ten) help us understand and solve bigger multiplication problems?
- Discuss as a class (i.e., we can solve big problems in our head by counting zeros; we know that a digit in one place represents ten times what it represents in the place to its right).