1 Exponential Thinking

Last updated almost 6 years ago

19 questions

Note from the author:

This lesson is a review of evaluating exponential values and a precursor to solving exponential equations.

1 Exponential Thinking

Last updated almost 6 years ago

19 questions

Note from the author:

This lesson is a review of evaluating exponential values and a precursor to solving exponential equations.

Watch the following video. It is a clip of a Vi Hart video, and the link is also in today's lesson plans.
Stop after watching the first minute, and answer the following question.
How is multiplication similar to counting by addition? Write 1-2 full sentences and give an example.

Since division is the inverse operation of multiplication, it is related when you count by adding. State one item you have noticed or wondered in the first minute and forty five seconds of this video.

Explain how counting in exponentiation is different than counting by multiplication or addition(around 2 minutes in). Please write 1-2 sentences.

Use the number line to show what four to the power of four looks like.

Answer the following problems with what the result would be.  You can use any method you prefer, but do it without a calculator.

Evaluate

What happens when our exponent is zero?

Evaluate.

What happens to our base when the exponent is negative?

If

Evaluate.

Evaluate.

Evaluate. Remember that this means a half count of multiplication to 9.

Evaluate. Remember that this means a fourth count of multiplication to 9.

Evaluate. Remember that this means a 3/4 count of multiplication to 9.

You will remember that the base of an exponential expression is the big number we are multiplying by. What happens when the base is a fraction?

Evaluate.

Find the missing part of the following exponential equation

Explain in a sentence how you came up with your answer to the problem before this. If you just guessed, why did the answer you guess work?

What is the best food you have eaten since you have been at home?

The following are some videos reviewing some of the concepts in this formative. They are completely optional.

1 Exponential Thinking

1 Exponential Thinking

Watch the following video. It is a clip of a Vi Hart video, and the link is also in today's lesson plans.Stop after watching the first minute, and answer the following question.How is multiplication similar to counting by addition? Write 1-2 full sentences and give an example.

Since division is the inverse operation of multiplication, it is related when you count by adding. State one item you have noticed or wondered in the first minute and forty five seconds of this video.

Explain how counting in exponentiation is different than counting by multiplication or addition(around 2 minutes in). Please write 1-2 sentences.

Use the number line to show what four to the power of four looks like.

Evaluate

Evaluate

What happens when our exponent is zero?

Evaluate.

What happens to our base when the exponent is negative?

If Evaluate.

Evaluate.

Evaluate. Remember that this means a half count of multiplication to 9.

Evaluate. Remember that this means a fourth count of multiplication to 9.

Evaluate. Remember that this means a 3/4 count of multiplication to 9.

You will remember that the base of an exponential expression is the big number we are multiplying by. What happens when the base is a fraction?

Evaluate.

Find the missing part of the following exponential equation

Explain in a sentence how you came up with your answer to the problem before this. If you just guessed, why did the answer you guess work?

What is the best food you have eaten since you have been at home?

Watch the following video. It is a clip of a Vi Hart video, and the link is also in today's lesson plans.Stop after watching the first minute, and answer the following question.How is multiplication similar to counting by addition? Write 1-2 full sentences and give an example.

Since division is the inverse operation of multiplication, it is related when you count by adding. State one item you have noticed or wondered in the first minute and forty five seconds of this video.

Explain how counting in exponentiation is different than counting by multiplication or addition(around 2 minutes in). Please write 1-2 sentences.

Use the number line to show what four to the power of four looks like.

Evaluate

Evaluate

What happens when our exponent is zero?

Evaluate.

What happens to our base when the exponent is negative?

If Evaluate.

Evaluate.

Evaluate. Remember that this means a half count of multiplication to 9.

Evaluate. Remember that this means a fourth count of multiplication to 9.

Evaluate. Remember that this means a 3/4 count of multiplication to 9.

You will remember that the base of an exponential expression is the big number we are multiplying by. What happens when the base is a fraction?

Evaluate.

Find the missing part of the following exponential equation

Explain in a sentence how you came up with your answer to the problem before this. If you just guessed, why did the answer you guess work?

What is the best food you have eaten since you have been at home?

Watch the following video. It is a clip of a Vi Hart video, and the link is also in today's lesson plans.
Stop after watching the first minute, and answer the following question.
How is multiplication similar to counting by addition? Write 1-2 full sentences and give an example.

If

Evaluate.

Watch the following video. It is a clip of a Vi Hart video, and the link is also in today's lesson plans.
Stop after watching the first minute, and answer the following question.
How is multiplication similar to counting by addition? Write 1-2 full sentences and give an example.

If

Evaluate.