Number Lab Slides
Lab Report 6.2A
NUMBER LAB
SPECIMEN SORTING
Classifying Rational Numbers using Venn Diagrams
The Nested Hierarchy
Natural Numbers
The "counting" numbers: \(1, 2, 3, \dots\)
Whole Numbers
Natural numbers plus zero: \(0, 1, 2, 3, \dots\)
Integers
Whole numbers and their opposites: \(\dots, -2, -1, 0, 1, 2, \dots\)
Rational Numbers
Any number that can be written as \(\frac{a}{b}\) (fractions, decimals).
Natural
Whole
Integers
Rational
Specimen Inspection
Before placing a specimen in the diagram, always simplify it first!
\(\frac{10}{2}\) \(5\) (Natural/Whole)
\(-3.0\) \(-3\) (Integer)
\(- | -8 |\) \(-8\) (Integer)
The "Most Specific" Rule
A number lives in the innermost circle it belongs to.
Example: \(0\) is Rational, and an Integer, but its most specific home is the Whole Numbers.
Quick Lab Check
Where does each specimen belong? (Find the most specific set)
\(-12.5\)
Rational
\(15\)
Natural
\(-9\)
Integer
\(\frac{1}{4}\)
Rational
\(0\)
Whole
\(- | 4 |\)
Integer
Specimen Sorting Worksheet
SPECIMEN SORTING LAB
LAB REPORT: TEKS 6.2A
Researcher:
Date:
Part 1: Pre-Lab Preparation
Before classifying, simplify each specimen to its basic form.
1. \( \frac{18}{3} = \)
2. \( - | -5 | = \)
3. \( 4.0 = \)
4. \( - ( -7 ) = \)
Part 2: The Sorting Chamber
SPECIMENS TO SORT
\( -3 \)
\( 1.5 \)
\( \frac{2}{3} \)
\( 0 \)
\( -7.2 \)
\( 11 \)
\( \frac{20}{5} \)
\( -8 \)
Rational Numbers
Integers
Whole Numbers
Natural
Part 3: Lab Analysis
5. Circle the word that correctly completes the statement:
Every integer is
ALWAYS SOMETIMES NEVER
a natural number.
Explain your reasoning:
6. Which set of numbers contains only integers?
\( \{ -3, 0.5, 4 \} \)
\( \{ -2, 0, 15 \} \)
\( \{ \frac{1}{2}, -4, 9 \} \)
\( \{ -8, -1.2, 0 \} \)
7. Determine if each statement is True or False:
The number \( -10 \) is a rational number.
TRUE FALSE
Zero is a natural number.
TRUE FALSE
Every whole number is also an integer.
TRUE FALSE
Specimen Sorting Key
ANSWER KEY
Specimen Sorting Lab
Status: VERIFIED
Part 1: Pre-Lab Preparation
1. \( \frac{18}{3} = \)
\( 6 \)
2. \( - | -5 | = \)
\( -5 \)
3. \( 4.0 = \)
\( 4 \)
4. \( - ( -7 ) = \)
\( 7 \)
Part 2: The Sorting Chamber
Rational Numbers
\( 1.5 \) \( \frac{2}{3} \) \( -7.2 \)
Integers
\( -3 \) \( -8 \)
Whole Numbers
\( 0 \)
Natural
\( 11 \) \( \frac{20}{5} \)
Part 3: Lab Analysis
5. Circle the word that correctly completes the statement:
Every integer is
ALWAYS SOMETIMES NEVER
a natural number.
Reasoning: Positive integers like 5 are natural numbers, but negative integers like -5 are not natural numbers.
6. Which set of numbers contains only integers?
\( \{ -3, 0.5, 4 \} \)
\( \{ -2, 0, 15 \} \)
\( \{ \frac{1}{2}, -4, 9 \} \)
\( \{ -8, -1.2, 0 \} \)
7. Determine if each statement is True or False:
The number \( -10 \) is a rational number.
TRUE FALSE
Zero is a natural number.
TRUE FALSE
Every whole number is also an integer.
TRUE FALSE
