Transcript Rational Numbers

Mini Lesson on Integers and
Elevation
• Several question you will see involving integers
will be about elevation.
• Ex: Sarah is scuba diving 20 ft below the surface
of the ocean. Her friend Tom is 1,038 ft above
sea level on Buffalo Mountain. What is the
difference in their elevation.
• To solve this problem you would subtract the two
elevation. (Difference always means to subtract)
You should subtract the smallest from the
largest. 1038 – (-20) = 1058 ft.
Students should have a copy
of this on their desk.
Real #
Rational #
Integers
Irrational #
Whole #
Natural #
To read this organizer: Whatever is inside
the circle is makes up the group: for
example: Inside the integer circle is the
whole # and the natural #. They both make
up the integers. On the next slide you will
copy the definitions down.
Copy onto your
sheet
Real #
Rational #
A rational number is a number that can be written as a
simple fraction, or a decimal that terminates or repeats
Integers
whole # Plus negative whole #
Whole #
Natural # Plus 0
Natural #
The whole
numbers from 1
upwards: 1, 2, 3,
and so on ...
Irrational #
Any
number
that
cannot be
written in
fraction
form: √2
Copy the first 3
bullets in your
notes
Rational Numbers
A rational number is any number that can be written as a
fraction, terminating decimal, repeating decimal, or whole
number
FYI… terminating decimals and repeating decimals can be
written as a fraction.
The true definition is any number that can be written as a
fraction is rational.
What does it mean to be rational? (if someone is rational, then
you can understand their behavior, if a number is rational,
then you can understand what it is.) Irrational #s cannot be
understood. They go on forever, but because they do not
repeat, you have to solve math to find the next number.
Real Numbers
• All numbers we will work with in 7th grade
are part of the real numbers. Every
number on your graphic organizer is inside
the real number circle.
Assessment Prompt
• Can a number fit into more than one
category?
• Can irrational numbers be in another
category besides real numbers?
• What are the 4 types of numbers that are
rational?
Assessment Prompt
• Can a number fit into more than one category?
Yes. -1, is an integer, rational #, and real #.
• Can irrational numbers be in another category
besides real numbers? NO
• What are the 4 types of numbers that are
rational? Fractions, terminating decimals,
repeating decimals, and integers.
Practice
Tell if the number is rational or irrational:
¼
-3.987987…
3.14156…
√9
√2
0
0.1254687…
3 5/7
√6
√36
Tic-Tac-Think:Rational Numbers
Choose one task from each column to answer completely.
Name the following
number as many ways
using your diagram:
852
Name the following
number as many ways
using your diagram:
0
Name the following
number as many ways
using your diagram:
-3 ½
Which of the two is
rational
2.3569874123… or
16.666666
Which of the two is
rational
√2 or -2.22
Which of the two is
rational
6.16161616 or 22/7
List 5 numbers that are integers:
List 5 numbers that are natural
numbers
List 5 numbers that whole numbers
Solve together as whole class.
Tic-Tac-Think:Rational Numbers
Choose one task from each column to answer completely.
Name the following
number as many ways
using your diagram:
852
Natural, Whole, integer,
rational, real
Name the following
number as many ways
using your diagram:
0
Whole, integer, rational,
real
Name the following
number as many ways
using your diagram:
-3 ½
Rational, real:
Which of the two is
rational
2.3569874123… or
16.666666
Which of the two is
rational
√2 or -2.22
Which of the two is
rational
6.16161616 or 22/7
Both
List 5 numbers that are integers:
List 5 numbers that are natural
numbers
List 5 numbers that whole numbers
Solve together as whole class.
Homework:
• On the worksheet you get there is a chart
at the bottom.
• You are going to put a check in each box
that the # belongs in.
• Look at the letters at the top of each
column. N=natural, W=whole, Z=integer,
Q=rational, I=irrational, R= real. You may
want to write this down so you don’t forget.