Examining Exponents

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Objective

SWBAT understand place value to multiply & divide by powers of ten.

Big Idea

Learn how place value patterns help you multiply & divide by powers of ten.

Warm Up

5 minutes

To review exponents, we use this website, Math Games 4 Children, Pirate Exponents. We virtually roll the dice, and our ship is moved the corresponding number of spaces. My students each have white boards and markers, and hold up their answer, on my count, to the problem that comes up on the screen after we've moved our spaces.

Guided Practice

15 minutes

In this lesson, students will use whole number exponents to denote powers of 10. Using this notation will help students recognize patterns when multiplying and dividing powers of 10. Students can practice describing powers of 10 using the terms: base, exponent, factor, and to the power of. I write these terms on the weekly vocabulary wall. I'm sure to point out that because multiplying 4 by 10 the fifth power is the same as multiplying by five factors of 10, the product is 4 followed by five zeros.

You may wish to extend the concept by providing multiplication expressions and having students write a power of 10, such as 10 x 10 x 10 x 10 x 10= 10 to the fifth power.

Students should be able to describe the multiplication pattern. When a whole number is multiplied by a power of 10, the exponent determines the number of places each digit in the first factor is shifted to the left in the product.Some students may incorrectly think that the number of zeros in the product is the same as the exponent. This is true only if the first factor doesn't contain a 0. Give an example such as 20 x 10 to the first power =200. Students should be very precise in their language.

Students should be able to describe the division pattern as well. When a whole number is divided by a power of 10, the exponent determines the number of places each digit in the first factor is shifted to the right in the quotient. If students have trouble understanding how the digits shift when a number is divided by a power of 10, use larger whole numbers, such as 370 or 3,700 as the dividends.

This presentation will help students extend what they know about multiplying and dividing whole numbers by powers of 10 to multiplying and dividing decimals by powers of 10. Be sure that students understand the placement of decimal points in whole numbers. For example, 7 can be written as 7.0 without changing its value.

Independent Practice

15 minutes

I provide my students with an array of seven different types of relatively simple problems, including one word problem. I use numbers 1, 2, and 3 for a Think-Pair-Share with table partners. For #3, students construct viable arguments and critique the reasoning of others. More specifically, students construct an argument based on place value patterns.

For #4, I encourage students to look at the nonzero digit in the known factor and in the product, and then determine how many places that digit shifts. This shows students which power of 10 is the unknown factor.

For #5, I encourage students to look at the nonzero digit in the dividend and in the quotient and then determine how many places that digit shifts. This will tell them which power of 10 is the divisor.

For #6, some students will benefit by rewriting 30.05 as 30.050, so that both numbers have the same numbers understand that you can write a zero to the right of the last digit in a decimal number without changing the value.

Closure

10 minutes

Using cold calling, pairs of students explain their thinking for the Think-Pair-Share in #3. I use individual cold calling to review the answers for the rest of the problems.