Question

What stage will have closest to 1,00,00,00,000 circles?

Answer 1

Task: Here we review the concept of exponents in anticipation of exponent rules and scientific notation in future lessons. In the first part, you are introduced to a picture that shows the stages of cell division. Later stages, would require you to think of large- numbered stages of doubling and allow you to reason about how one can use exponential notation to compare the relative size of numbers. Read through the problem, and fill in your answers in the space provided.

The picture below shows you the 4 stages of cell division. You are to find out the number of circles that correspond to each stage. Fill in the table provided below.

Stage Number of circles

1 2

2 4

3 8

4 16

Describe the pattern you see?

Ans. 2+2=4+4=8+8=16

Here is how three students filled in the table. Complete the rows in the table to show what John and Noah would write for Stage 5 and Stage 10 if they continue their patterns.

Stage Number of circles (Kim) Number of circles (John) Number of circles (Noah)

1 2 2 21

2 4 2 x 2 22

3 8 2 x 2 x 2 23

4 16 2 x 2 x 2 x 2 24

5 32 2 x 2 x 2 x 2 x 2 2^5

… … … …

10 1024 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 2^10

a) Now, write an expression to represent the number of circles in stage 20:

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b) How many times as many circles will there be at Stage 21 compared to Stage 20?

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c) Stage 23 will have more circles than Stage 20. Tina believes that Stage 23 will have three times as many circles as Stage 20. Lin believes that Stage 23 will have eight times as many circles as Stage 20. Who is correct?

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d) What stage will have closest to 1,00,00,00,000 circles? Use a calculator if it helps you with your thinking.

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e) Comparing Stages: 246 is how many times as many as 242 ?

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