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Mathematics 10C: Module 2
1
MODULE 2 ASSIGNMENT
Lesson 2 Assignment
Try This
TT 1. Complete Steps 1 to 3 for the number 36.
Step 1: Generate the prime factorization for the number.
Answer:
Step 2: Rearrange the prime factors into two identical groups.
Answer:
Step 3: Evaluate the product of the factors in each group.
Answer:
TT 2. Repeat Steps 1 to 3 for the following numbers:
a. 81
Answer:
b. 144
Answer:
TT 3. Generate the prime factorization for the following numbers:
a. 30
Answer:
b. 56
Assignment
Mathematics 10C: Module 2
2
Assignment
Answer:
TT 4. Can you rearrange the prime factors of these numbers into identical groups as you did for the
numbers in TT 1 and TT 2? Explain.
Answer:
Once you have completed TT 1 to TT 4, save the Lesson 2 Assignment to your course folder. You will
return to the Lesson 2 Assignment later in this lesson.
Share
Answer the following questions based on your Try This investigation:
1. What is the difference between the numbers examined in TT 1 and TT 2 and the numbers in TT 3
and TT 4?
Answer:
2. In Step 3, how is the product of the factors in each identical group related to the original number?
Answer:
3. a. How can you use prime factorization as a method to determine that a number is a perfect
square?
Answer:
b. How can you use prime factorization as a method to determine the square root of a number?
Answer:
Once you have completed the Share activity, save the Lesson 2 Assignment to your course folder. You
will return to the Lesson 2 Assignment later in this lesson.
Math Lab: Manipulatives
Mathematics 10C: Module 2
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Assignment
Materials
 150 counters or pennies
 150 unit blocks or sugar cubes
 printed copy of data sheet – Perfect Squares and Perfect Cubes Data Sheet
Procedure
The following steps assume you are using pennies and sugar cubes, but you could also use counters
and unit blocks respectively.
Step 1: Arrange the pennies into squares with different side lengths. Record the total number of
pennies used for each square in the first table on the data sheet.
Step 2: Arrange the sugar cubes into cubes with different side lengths. Record the total number of
sugar cubes used for each cube in the second table on the data sheet.
Lab Analysis
Answer the following questions:
1. Which numbers less than 150 are perfect squares?
Answer:
2. Which numbers less than 150 are perfect cubes?
Answer:
3. How could you use a sheet of graph paper, instead of counters or pennies, to do Step 1 in the
procedure?
Answer:
4. What other methods could you use to determine whether a number is a perfect square or a perfect
cube?
Answer:
Mathematics 10C: Module 2
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Assignment
Share
How can prime factorization be used to determine cube roots?
Answer:
Try This
Practise applying the concepts of square roots and cube roots to these problems in your textbook.
Read the questions carefully as they may require you to do more than one step.
Note: The questions that you answer will depend on which textbook you are using to complete
Mathematics 10C.
Math 10 (McGraw-Hill Ryerson)
TT 5. Complete “Check Your Understanding” questions 11 and 16 on pages 159 and 160.
Answer:
TT 6. Complete “Check Your Understanding” questions 5.e), 6.e), 7.f), 8.c), and 14 on pages 158 to
160.
Answer:
OR
Foundations and Pre-calculus Mathematics 10 (Pearson)
TT 5. Complete “Exercises” questions 6.b) and 14 on pages 146 and 147.
Answer:
TT 6. Complete “Exercises” questions 4.b), 5.c), 6.d), 9, and 11 on pages 146 and 147.
Answer:
Mathematics 10C: Module 2
5
Assignment
Once you have completed TT 5 and TT 6, save the Lesson 2 Assignment to your course folder. You will
return to the Lesson 2 Assignment later in this lesson.
Reflect and Connect
Reflect on this lesson by answering the questions that follow.
The number 1 is both a perfect square and a perfect cube. Its square root is 1 and its cube root is
also 1.
RC 1. There are other numbers that are both perfect squares and perfect cubes. Can you find at least
three of these numbers? List them.
Answer:
RC 2. Can you discover a pattern that can help you find more numbers that are both perfect squares
and perfect cubes?
Answer:
Once you have completed these questions, save the Lesson 2 Assignment to your course folder. You
will also submit the Lesson 2 Assignment to your teacher for marks.