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### Lesson plan

# Powers of 10

#### Learning Objectives

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

#### Introduction

*(5 minutes)*

- 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.,
**2**,^{2}= 2 x 2 = 4**5**,^{2}= 5 x 5 = 25**4**, and^{3}= 4 x 4 x 4 = 64**6**).^{3}= 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
**10**).^{3}= 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, 10
^{5}is ten times greater than 10^{4}. - 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? (10
^{4}) 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 10**and tell students that, since we know that 10^{2}= 500^{2}is 100, then**5 x 10**is equal to^{2}**5 x 100**. - Write another problem, like
**2 x 10**, and have students solve with a partner. Have students rewrite the power of ten as a number before solving (i.e.,^{3}**2 x 1,000**). Remind students to use their chart for help if needed. - Write another problem on the board, like
**3 x 10**, and have students solve it independently. Then, call on a student to share their answer and a justification (i.e., "10^{4}^{4}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 10^{4}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 10**,^{5}**12 x 10**,^{4}**98 x 10**,^{2}**134 x 10**, and^{6}**502 x 10**).^{3} - 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.

#### Differentiation

**Support:**

- 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 10**,^{4}**3 x 10**).^{1}

**Enrichment:**

- Have students apply the concept to decimals (see optional materials).

#### Assessment

*(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 10
^{4}). - 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 10**).^{4} - 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).