Guided Lessons

# 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.

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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.
(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.

Support:

• 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).

Enrichment:

• 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).