Powers of 10

Explicit Instruction/Teacher modeling

• 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, 10⁵Is 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 practise

• 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= 500And tell students that, since we know that 10²Is 100, then 5 x 10²Is 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., "10⁴Is 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 10⁴Will have four zeros.").

Independent working time

• 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 maths notebook.
• Circulate as students work and offer support as needed.
• Go over the problems as a class.