- Represent repeated multiplication with exponents:
- Describe how powers represent repeated multiplication: powers are used when a number is multiplied by itself more than once. It’s an easier way to write repeated multiplication.
- Demonstrate the difference between the exponent and the base by building models a given power, such as
and
:
- Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication:
- Evaluate powers with integral bases (excluding 0) and whole number exponents:
- Explain the role of parentheses in powers by evaluating a given set of numbers such as
,
and
:
In the first and second examples the difference is that with the parentheses surrounding the negative number with the exponent outside means that the negative base is multiplied by itself as many times as the exponent says, but when the parentheses surrounds the negative base and the exponent it indicates that there is only one negative and the rest of the base numbers are positive. In the second and third example the parentheses don’t change anything. - Explain the exponent laws for multiplying and dividing powers with the same base:
Exponent law for multiplying powers with same base is to keep the base, add exponents and multiply the coefficients. Exponent law for dividing powers with the same base is to keep the base, subtract exponents and divide the coefficients. - Explain the exponent laws for raising a product and a quotient to an exponent:
Exponent law for raising a product and a quotient to an exponent is to keep the base and multiply the exponents - Explain the law for powers with an exponent of zero: Any power with the exponent of zero (except zero) equals one.
- Use patterns to show that a power with the exponent of zero is equal to one:
(Divides by the number of the base) - Explain the law for powers with negative exponents: The law for a power with a negative exponent is to reciprocal the base (with the exponent) and make the exponent positive.
- Use patterns to explain the negative exponent law:
- I can apply the exponent laws to powers with both integral and variable bases:
- I can identify the error in a simplification of an expression involving powers:
- Use the order of operations on expressions with powers:
- Determine the sum and difference of of two powers:
There is no fast way to do addition and subtraction, you have to use BEDMAS - Identify the error in applying the order of operations in an incorrect solution:
If you don’t follow BEDMAS, then you will end up with a completely different answer. - Use powers to solve a measurement problem: Lily wants to paint the walls of her room, which are five meters by five meters. She has a window that is two meters by two meters. How much paint does she need to paint the four walls of her room?
- Use power problems to solve a growth problem: There are twenty people in an office building. The number of people doubles every hour. How many people will there be after 1 hour, 3 hours and 8 hours?
- Applying the order of operations on expressions with powers involving negative exponents and variable bases:
- Anything else I know about exponents: Any base with the exponent of 1 equals the base number. 1 with the exponent of anything equals 1
November 12, 2016 at 7:18 am
Hi Shannon, Overall I think you did a great job on your blog. You provided excellent examples, put in the time and effort, and demonstrated all the learning outcomes. However I think you may want to add more detailed explanations explaining all your steps and actions. In question five I think you may want to add a question such as
to explain how to evaluate powers with integral bases. Although it isn’t required I think you may want to add anything else you know about exponents such as any base with an exponent of one, is always equal to the base or anything else you think might be necessary. Excellent job on the assignment. Keep up the good work Shannon.
November 13, 2016 at 4:39 am
Looks very well done. Very neat and organized.
November 17, 2016 at 12:31 am
Good Job Shannon, check your OneNote for more specific feedback.