Homework Helper Lesson 2 Hands On: Prime Factorization

Name
Number and Operations in Base Ten
Preparation for 5.NBT.2
Lesson 2
Homework Helper
Hands On: Prime
Factorization
Patterns
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A design with equilateral triangles is shown. The triangle
is divided into four equal-sized, smaller triangles as shown.
Then each of the four triangles is divided into four equal-sized,
smaller triangles. If the pattern continues, how many triangles
will there be in Figure 3?
Figure 1
In Figure 1, there are 4 resulting triangles. In Figure 2,
there are 16 triangles.
How many triangles will be in Figure 3?
The table shows the Figure numbers, the number of triangles
formed, and the prime factorization of the number of triangles.
Figure
Number
Number of
Triangles Formed
Prime Factorization
1
4
2×2
2
16
2×2×2×2
3
64
2×2×2×2×2×2
Figure 2
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By following the pattern, there are 64 triangles formed in Figure 3.
Practice
1. Complete the table for Figures 4 and 5 if the above pattern continues.
Figure
Number
Number of
Triangles Formed
Prime Factorization
4
5
Lesson 2 My Homework91
Problem Solving
2. A population of rabbits triples every month.
The population starts with two rabbits. How
many rabbits are there after three months?
3. Three friends each create 4 bags of starter
bread dough. After ten days, each of those
four bags is then divided into four more
bags of dough. How many days pass before
192 bags of dough are created?
5.
8
Look for a Pattern Annie opened a savings
account and deposited $10. If the balance in her account doubles
each month, what is the account balance after 4 months?
6. Elyse folded a piece of paper in half 3 times. She then punched
3 holes in the paper. How many holes are in the paper when
she unfolds it?
92Chapter 2 Multiply Whole Numbers
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4. Sam sent an E-mail to 3 friends on Monday. Each of the friends
then sent an E-mail to 3 friends on Tuesday. On Wednesday, each
of those friends then sent an E-mail to 3 friends. Write the prime
factorization of the number of E-mails that were sent on Wednesday.