Algebra – powers of ten and exponents

Algebra – Powers of Ten and Exponents STANDARD 5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying it by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-­‐number exponents to denote powers of 10.

OBJECTIVE. I can write and evaluate repeated factors in exponent form.

ASSESSMENT Students will show understanding by completing the exit slip questions.

OPENING How will you communicate what is about to happen? How will you communicate its importance? How will you communicate connections to previous lessons? How will you engage students and capture their interest?

Routines

MATERIALS 10 min

1. Check homework from lesson 1.3 2. Problem of the Day: A museum guide provides 10 brochures to each group who visits. If 12 groups visited the museum today, how many brochures did the guide hand out? (Answer: 120 brochures) 3. Making connections: Refresh students memories on place value: -How could you represent the number in the 10s place as a multiplication problem? (# x 10) -How does this relationship apply to other place values?

-How can you express 100 as a product of 10s? (10 x 10) INTRODUCTION OF NEW MATERIAL How will you explain/demonstrate all knowledge/skills required of the objective, so that students begin to actively internalize key points?

10 min

Introduce new vocabulary: -­‐Base: The number that is used as the repeated factor -­‐Exponent: The number that tells how many times the base will be used as a factor

Instead of writing out the problem 10 x 10 x 10, there is a way we can represent that same multiplication problem in more simple terms using base and exponent.

For example, we notice that the repeating factor is 10. That factor would be our base.

The number of times that 10 is multiplied would be our exponent: 3. Thus that multiplication problem could be simplified as 103 .

When we read numbers in exponent form, we read the exponent as an ordinal number.

In this case we would say 10 to the third power.

Think about base ten blocks. How could we show base ten blocks using 10 as our base in exponent form?

One unit is represented as 100 (1) Rod: 101 (10)

Flat: 102 (100) Cube: 103 (1000) What do you notice about the relationship to the exponents and the number of zeros in the number when you have 10 as the base?

GUIDED PRACTICE How will students practice all knowledge/skills required of the objective, with your support, such that they continue to internalize the key points?

Using the problem on page 24, determine the average speed of the hummingbirds wings per minute.

If the average hummingbird flaps its wings at 3 X 103 a minute how many times is that written as a whole number?

Multiply by powers of ten to find your answer: 3 x 100 = 3 3 x 101 = 30 3 x 102 = 300 3 x 103 = 3,000

The average hummingbird flaps its wings 3,000 times a minute!

What pattern do you notice? (For each power of 10 the number of zeros written after the whole number is the same number as the exponent) INDEPENDENT PRACTICE (Ongoing Learning & Practice) How will students attempt independent mastery of all knowledge and/or skills required of the objective, such that they solidify their internalization of the key points?

15 min

35min

Students will begin working on pages 24 and 25 (AOL: numbers 2 and 4). Once pages are

complete and checked for accuracy, move onto centers with any time remaining.

Intervention Group: Practice multiplying whole numbers by 10, 100, 1,000 6 x 10 = 60 6 x 100= 600 6 x 1000 = 6,000 Now let’s show how we can express 10 in exponent form, how many times do we multiply 10 to get 10? (Once) So our exponent form would be 101. Think about 100, how many times do we multiply 10 to get to 100? (Twice 10 x 10) so our exponent is 102. Continue this with 1,000, what is the pattern you see?

Centers/Activities: -­‐ Powers of 10 Matching Game -­‐ Multiplication Relay -­‐ Enrichment sheet

CLOSING 5 min How will students summarize and state the significance of what they learned?

If the independent practice did not serve as an assessment, how will students attempt independent mastery of the knowledge and/or skills introduced and practiced above?

Exit ticket questions:

4 1. Write 10 x 10 x 10 x 10 in exponent form (10 ) 2. Write the 3 x 10 x 10 x 10 in exponent word form (3 times the third power of 10) 3. Find the value of 4 x102