Lesson plan

Powers of 10

Teach your students to recognise patterns of zeros when multiplying by powers of 10 with exponents.
Need extra help for EL students? Try thePowers of Ten PatternsPre-lesson.
EL Adjustments
GradeSubjectView aligned standards
Need extra help for EL students? Try thePowers of Ten PatternsPre-lesson.

Students will be able to multiply by powers of 10 with exponents.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
EL adjustments
(5 minutes)
  • Write 10 x 1 = 10, 10 x 10 = 100, 10 x 100 = 1,000, and 1 0x 1,000 = 10,000On 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).
(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, 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.
(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= 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.").
(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 maths 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 practise.
  • Provide additional practise with smaller numbers (i.e., 2 x 104, 3 x 101).


  • Have students apply the concept to decimals (see optional materials).
(10 minutes)
  • 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.
(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).

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