In this lesson, students will begin by reviewing the product rule and quotient rule for exponents. Students will also review converting standard form to scientific notation. Students will learn how to multiply and divide in scientific notation by using what they already know about scientific notation and exponent rules. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students should review what they already know about exponent rules and scientific notation. For the exponent rules, you can let students know their answers can include negative exponents if needed.
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Students should be able to explain how they determined where to put the decimal place for the coefficient in scientific notation. Allow students to explain how they knew whether their exponent was positive or negative when converting to scientific notation. Check if students understand when their exponents will increase (moving the decimal to the left like #`3`) or decrease (moving the decimal to the right like #`4`).
Begin with a multiplication problem that does not need converting again into scientific notation. Let students brainstorm how they might approach solving this problem. Ideally, students will recognize that the only operation is multiplication, so the expression can be rearranged as needed.
If students need more scaffolding, ask students to group the numbers that are alike together to multiply them. This can help students recognize that they can multiply the coefficients and powers of `10` separately.
Once students multiply the values, they should determine if their answer is written in scientific notation. This can remind students that the coefficients in scientific notation must be between `1` and `10`.
The next example has one extra step. Encourage students to try this example on their own, and then check it with a partner. When students multiply the coefficients, they should recognize that the new coefficient is over `10`.
Some students may recognize that a coefficient of `29.302` is too large for scientific notation, but not recognize that they can move the decimal point and change the exponent accordingly. It can be beneficial to have students consider whether they would be adding or subtracting `1` from their exponent if they are moving the decimal to the right.
Make sure students notice that they now need to divide. Let students know they will use a similar strategy of grouping the coefficients and powers of `10` separately, but they should divide the values instead. It may help if students write fractions for the coefficients and powers of `10` separately.
With this example, students may only struggle with the powers of `10` because they need to subtract with negative exponents. For some students, it may help for them to write the powers of `10` as a fraction so that it is easier for them to recognize that they need to subtract.
Allow students an opportunity to try this problem and check it with a partner. At this point, students should be able to at least divide the coefficients and powers of `10` separately, although some may still struggle with what to do to write it in scientific notation.
In this case, the decimal has to move to the right in order for the coefficient to be between `1` and `10`. The most common error students will make is when they have to modify their exponent based on the movement of the decimal point. It may help to remind students of the warm up problems and when their exponents were positive or negative based on the direction they had to move the decimal place.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of mild, medium, and spicy practice problems for multiplying and dividing in scientific notation. Check out the online practice and assign to your students for classwork and/or homework!
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