Download Use Square Root

Drafting (15.1301) T – Chart
page 1 of 4
USE ESTIMATED VALUES
Program Task: Determine materials required to meet
project specifications.
=
LOCATE IRRATIONAL NUMBERS ON A NUMBER LINE
PSSA Eligible Content Anchor: M11.A.1.3.1
Description: Locate / Identify irrational numbers at the
approximate location on a number line.
Program Associated Vocabulary
ESTIMATE, TRUNCATE
Math Associated Vocabulary
IRRATIONAL NUMBER, SQUARE ROOT, PI
Program Formulas and Procedures
Formulas and Procedures
Machine designers and machinists don’t always think
of numbers in terms of rational or irrational. They
simply truncate repeating decimals and provide
solutions that are task-appropriate. Whether we are
conscious of their irrational classification or not, we
often attribute concrete values to these numbers.
Anytime we use Pi (π) or the square root of numbers
like 3, we are working with irrational numbers. Since
we derive concrete measurements from irrational
numbers, one could argue that, in effect, we have
located them on a number line (tape measure, ruler,
scale).
Irrational Number: a non-repeating & non-terminating
decimal number, cannot be written as a fraction.
Examples:
2, 5,
General steps
1. Rewrite the number as a decimal to the nearest tenth
or hundredth digit.
2. Use quarter marks (¼, ½, ¾) to approximate the
location on the number line.
Example:
Pi (3.141592…) is about midway between 3 and 3.25.
Example: Identify
Answer:
2 on the number line below:
2 =1.41421356237…. ≈ 1.41
1.41 is between 1.25 and 1.5, but closer to 1.5.
.
-2
2
3
-1
0
1
2
4
In examples 1-3 shown on page 3, a part needs to be
machined to fit into a specific area of an existing
machine. The existing drawings do not have a
dimension for this angled location, and you do not
have access to the machine to take a direct
measurement. You calculate the dimension and arrive
at an irrational number. You must then determine
where this irrational number falls on a tape measure in
relationship to a rational number before proceeding
with the design.
Calculator Method to find Square Root:
Two Lines Display Screen Calculator:
Ex.
7 -
press
enter 7
press Enter or =
2.64575
One line Display Screen:
Ex.
7 -
enter 7
press
press Enter or =
2.64575
C. Plesnarski (Math) S. Plesnarski (Drafting)
M11.A.1.3.1
Rev. 6/29/09
PDE/BCTE Math Council
Drafting (15.1301) T – Chart
page 2 of 4
Teacher's Script - Comparing and Contrasting
Drafters may not need to know the formal definition of an irrational number, but they must be able to locate these
numbers on a tape measure. Irrational numbers appear when taking the square root of a prime number (like 2, 3, or 5)
or when performing calculations with pi. Taking the square root of a prime number yields a non-terminating, nonrepeating decimal and drafters must be able to round these numbers and then locate them on a tape measure.
Common Mistakes Made By Students
Taking the square root of a number:

This is mostly occurs when the student is unfamiliar with a calculator. Some calculators require the student to
press the number then the square root button and others require the square root button before the number. It
may be important to show students to take the square root of 4, using both methods to evaluate which order
gives the correct answer of 2.
Using the appropriate rounding technique for the given situation:

In most cases, it is beneficial to round the number to the nearest hundredth. If the number line is broken into
quarters, thirds, tenths, or twentieths, then rounding the number to the closest hundredth would provide the
information necessary to correctly identify the number’s location.
Being able to partition a number line and identify the location of the decimal number:

Sometimes the number line uses integer values only (…,-2, -1, 0, 1, 2, 3, …). In this case, the student must be
able to mentally divide the space between the integers into quarters or thirds to best approximate the location of
the irrational number.
Lab Teacher's Extended Discussion
While drafters try to avoid irrational numbers, it is not always possible to do so. Think of Pi! Pi is an irrational number
and has been computed to over a million decimal places using a computer. While we don’t think of Pi as an irrational
number, it definitely is, and is used by drafters almost on a daily basis.
Being able to locate an irrational number on a number line will give the drafter and or machinist a much better idea of its
closest relationship to a rational number on a tape measure.
C. Plesnarski (Math) S. Plesnarski (Drafting)
M11.A.1.3.1
Rev. 6/29/09
PDE/BCTE Math Council
Drafting (15.1301) T – Chart
page 3 of 4
Problems
Occupational (Contextual) Math Concepts
Solutions
1) Locate the square root of 7 on a tape measure.
2
3
2
3
2
3
2) Locate the square root of 6 on a tape measure.
3) Locate the square root of 5 on a tape measure.
Problems
4) The location of
number line below?
A
Related, Generic Math Concepts
8 is closest to which point on the
B
-1
Solutions
C
0
1
D
2
E
3
4
5) Why can’t the square root of Pi be a rational number?
6) Using the Pythagorean Theorem, a student finds that
she needs 7 inches of material. Identify the location of
this measurement on the measuring tape below.
2
3
Problems
PSSA Math Look
Solutions
7) Which of the following numbers would be located
between 9 and 10 on the number line?
a. 2π
b. 3π
c. 2√5
d. 5√2
8) The location of
number line below?
A
B
0
1
2
13 is closest to which point on the
C
D
E
3
4
5
9) Which of the following would be closest to the value
of
8?
a. 2 ¾
b. 3 ¼
c. 4
d. 2 ½
C. Plesnarski (Math) S. Plesnarski (Drafting)
M11.A.1.3.1
Rev. 6/29/09
PDE/BCTE Math Council
Drafting (15.1301) T – Chart
page 4 of 4
Problems
Occupational (Contextual) Math Concepts
Solutions
1) Locate the square root of 7 on a tape measure.
The square root of 7 is 2.645, between 2 5/8” and 2 ¾”
2) Locate the square root of 6 on a tape measure.
The square root of 6 is 2.449, between 2 ¼” and 2 ½”
3) Locate the square root of 5 on a tape measure.
The square root of 5 is 2.236”, between 2 1/8” and 2 ¼”
Problems
4) The location of
number line below?
A
3
2
3
2
3
Related, Generic Math Concepts
Solutions
8 is closest to which point on the
B
-1
2
C
0
1
D
2
E
3
8 = 2.828
D.
4
5) What can’t the square root of Pi be a rational number?
Because Pi is an irrational number, and any rational
number squared would produce a rational number.
6) Using the Pythagorean Theorem, a student finds that
Since
she needs 7 inches of material. Identify the location of
this measurement on the measuring tape below.
2
2
PSSA Math Look
7) Which of the following numbers would be located
between 9 and 10 on the number line?
a. 2π
b. 3π
c. 2√5
d. 5√2
A
B
0
1
2
6
x

 6(16)  10 x  96  10 x  9.6  x , 210
16
10 16
3
Problems
8) The location of
number line below?
7 =2.645751…., We round to 2.65 inches.
3
Solutions
b. 3π
13 is closest to which point on the
C
D
E
3
4
5
D.
13 ≈3.61
9) Which of the following would be closest to the value
of
8?
a. 2 ¾
a. 2 ¾
b. 3 ¼
c. 4
8  2.828
d. 2 ½
C. Plesnarski (Math) S. Plesnarski (Drafting)
M11.A.1.3.1
Rev. 6/29/09
PDE/BCTE Math Council