PowerTeaching 3rd Edition Level 8 Unit 2 Cycle 1 Lesson 1
© 2014 Success for All Foundation Homework Problems 1
Homework Problems
Name
Team Name Team Complete?
Team Did Not Agree On
Questions…
#’s
Quick Look
Write the vocabulary introduced in this cycle:
Today we defined and explored irrational numbers. An irrational number is a number that cannot be
written in fractional form. We know a number is irrational if it is a decimal number that is infinitely long and
has no repeating pattern. We also learned the difference between rational and irrational numbers.
For example:
Number Type and Explanation
2
Irrational; 2 is not a perfect square.
9
Rational; 9 is a perfect square,
9
= 3.
0.0101010101… Rational; repeating decimal, it has a pattern
0.01001000100001… Irrational; non-repeating, non-terminating decimal
We learned that the square root of a number is a number that, when multiplied by itself, equals the
original number. Square roots include both positive and negative numbers. For example: the square root
of 25 is ±5 because (5)
2
= 25 and (
–
5)
2
= 25. However, if we write it as
25
, then we are only talking
about the positive root, 5.
1) Provide two examples that show that the statement is false. Explain your thinking.
Zoe said that an irrational number can be expressed as a terminating decimal.
PowerTeaching Math 3rd Edition Level 8 Unit 2 Cycle 1 Lesson 1
2 © 2014 Success for All Foundation Homework Problems
Directions for questions 2–6: Classify the numbers as rational or irrational.
2) π
3)
110
4)
81
5) 14
6)
–
3
2
Directions for questions 7 and 8: Find the square roots for each number.
7) 100
8) 49
Mixed Practice
9) Evaluate the expression.
2 – 9 • 1 – 3 • 9
10) Solve for x.
6x – 5 = 59
11) You have a number cube labeled 1–6. What is the probability of rolling an even number?
12) What is the measure of the radius of the circle whose circumference is 21.98 inches? Use 3.14 for π.
Word Problem
13) Tell what an irrational number is in your own words. Give an example of an irrational number and a
rational number.
PowerTeaching 3rd Edition Level 8 Unit 2 Cycle 1 Lesson 1
© 2014 Success for All Foundation Homework Problems 3
For the Guide on the Side
Today your student defined irrational numbers. An irrational number is a number that cannot be written
in fractional form. Any infinite nonrepeating decimal is an irrational number.
Your student also discussed square roots, by learning to identify perfect squares and non-perfect
squares, and to tell when a non-perfect square is irrational. Your student learned that the square root of a
perfect square is a rational number. Furthermore, the square root of a number that is not a perfect square
is an irrational number.
Your student should be able to answer the following questions about irrational numbers:
1) What is an irrational number?
2) What’s the difference between a rational number and an irrational number?
3) How did you know this was an irrational number?
4) How can a number have two square roots?
5) What is a perfect square?
6) How does the square root of a number relate to its classification?
Here are some ideas to work on irrational numbers:
1) Video: Understand and apply the definition of irrational numbers:
http://learnzillion.com/lessons/220-understand-and-apply-the-definition-of-irrational-numbers
2) Video: What’s an Irrational Number?:
http://virtualnerd.com/pre-algebra/real-numbers-right-
triangles/real-and-irrational/define-real-numbers/irrational-number-definition
3) Video: Understanding Square Roots:
https://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-
radicals/v/understanding-square-roots
4) Think of two integers on a number line. What rational numbers can you think of that fall between
the two integers? What irrational numbers fall between them?
PowerTeaching Math 3rd Edition Level 8 Unit 2 Cycle 1 Lesson 1
4 © 2014 Success for All Foundation Homework Problems
Homework Answers
1) Possible answers: Example 1: π Example 2: 2
Possible explanation: I know the statement is false because an irrational number cannot be
expressed as in fractional form. A terminating decimal is a number that can be written over a power of
10, in fractional form. I examined the statement Zoe made to determine if her argument made sense.
I used what I know about the definitions of irrational numbers and terminating decimals to prove her
statement as false. I know that any example of a terminating decimal cannot be an irrational number
and an irrational number (since its decimal does not repeat or terminate) cannot be expressed as a
terminating decimal.
2) irrational
3) irrational
4) rational
5) irrational
6) rational
7) 10 and
–
10
8) 7 and
–
7
Mixed Practice
9)
–
34
10) 10
3
2
11) 0.5 or
2
1
12) r = 3.5 in.
Word Problem
13) Possible answer: An irrational number is a number that cannot be written in fractional form. It includes
the square roots of non-perfect squares, as well as decimals that keep going without any pattern.
Accept appropriate examples.
