Download Real Numbers Get Real

Real Numbers
Get Real
ACTIVITY
1.2
SUGGESTED LEARNING STRATEGIES: Activating Prior
Knowledge, Predict and Confirm, Quickwrite, Think/Pair/Share,
Self/Peer Revision, Interactive Word Wall
My Notes
Your teacher is going to give you a card with six numbers on it.
1. Write the numbers from your card below.
CONNECT TO LANGUAGE
2. Do the numbers you received look like they will be good
numbers? Why or why not?
Criterion (plural: criteria) is a standard on which a decision is based.
The numbers on the cards belong to sets of numbers you have
studied: natural numbers, whole numbers, integers, rational
numbers, and irrational numbers.
3. List some examples and non-examples below for the set of natural numbers.
© 2010 College Board. All rights reserved.
Examples of natural numbers
Non-examples of natural
numbers
4. After reviewing your examples and non-examples above, write
your own definition for natural numbers.
5. List examples and non-examples of whole numbers below and
use your list to write what a whole number is.
Unit 1 • Patterns and Equations
13
ACTIVITY 1.2
Real Numbers
continued
Get Real
My Notes
SUGGESTED LEARNING STRATEGIES: Quickwrite,
Activating Prior Knowledge, Create Representations,
Look for a Pattern, Interactive Word Wall
6. What is the relationship between natural numbers and whole
numbers?
7. Which Venn diagram below shows the relationship between
the sets of natural and whole numbers? Fill in your choice with
the names of these sets of numbers and explain why you chose
the diagram you did.
MATH TERMS
A Venn diagram is a graphic
organizer used to represent
relations between sets and
operations with sets.
9. What do you notice about the relationship between whole
numbers and integers?
14
SpringBoard® Mathematics with Meaning™ Algebra 1
© 2010 College Board. All rights reserved.
8. List examples and non-examples of the set of integers.
Consider these lists to write your own definition of an integer.
Real Numbers
ACTIVITY 1.2
continued
Get Real
SUGGESTED LEARNING STRATEGIES: Graphic Organizer,
Look for a Pattern, Activating Prior Knowledge
My Notes
You have probably noticed that trying to fit the names of the
number sets into a Venn diagram can be difficult. To save time
and space, mathematicians have given the sets of numbers
abbreviations. These abbreviations are:
WRITING MATH
It is obvious why N and W represent natural and whole numbers,
respectively. The abbreviation Z
for integers is not quite as obvious. Z represents the integers
because the term “Zahlen”
means “number” in German.
Natural numbers: N
Whole numbers: W
Integers: Z
© 2010 College Board. All rights reserved.
10. Redraw the Venn diagram you chose in Item 7 below. Add the set
of integers to this Venn diagram to show how these number sets
are related. Use the abbreviations to represent each set of numbers.
Later, you will perform an activity with the numbers on the card
your teacher gave you. Numbers from different sets will have
different point values. But first you will perform a practice round of
the activity using the numbers listed below. Notice that they are all
natural numbers, whole numbers, and/or integers.
17
0
−4
33
−11
−24
11. Place the numbers from the list in the appropriate space in
the second column and compute your score.
Scoring Criterion
1 point for each natural number
__
4
My numbers that
fit the criterion
Score
17, 33
1
__
2
3 points for each odd integer
1 point for each whole number less than 20
__
2
4 points for each integer greater than -5
2 points for each whole number less than 1
Unit 1 • Patterns and Equations
15
ACTIVITY 1.2
Real Numbers
continued
Get Real
SUGGESTED LEARNING STRATEGIES: Look for a Pattern,
Predict and Confirm, Quickwrite, Activating Prior
Knowledge, Interactive Word Wall
My Notes
12. Choose six numbers that will give you a higher score than the
score you got on the previous page.
Your numbers:
Scoring Criterion
My numbers that
fit the criterion
Score
1 point for each natural number
__
4
3 points for each odd integer
1 point for each whole number less than 20
__
2
4 points for each integer greater than -5
2 points for each whole number less than 1
MATH TERMS
A set A is a subset of a set
B if every element of A is an
element of B. Every set is a
subset of itself.
14. How did understanding the number sets and subsets help you
to make good choices when picking your numbers?
The abbreviation for the set of rational numbers is Q, which stands
for quotient.
15. List examples and non-examples of the set of rational
numbers.
16. Why is the term ratio a good word to use when describing
rational numbers?
16
SpringBoard® Mathematics with Meaning™ Algebra 1
© 2010 College Board. All rights reserved.
13. By how much did your score increase?
Real Numbers
ACTIVITY 1.2
continued
Get Real
SUGGESTED LEARNING STRATEGIES: Quickwrite, Think/
Pair/Share, Self/Peer Revision, Graphic Organizer, Look for a
Pattern, Activating Prior Knowledge, Interactive Word Wall
My Notes
17. Considering this abbreviation and your examples and nonexamples, write your own definition for a rational number.
18. In the space below, redraw your Venn diagram from Item 10.
a. Add to the diagram to show how rational numbers are
related to natural numbers, whole numbers, and integers.
© 2010 College Board. All rights reserved.
b. Why did you choose to place the rational numbers in the
diagram where you did?
19. Another set of numbers you have studied is the set of
irrational numbers, which are numbers that cannot be written as the ratio of two integers. Irrational numbers include π,
the square root of any nonnegative number that is not a perfect
square, and decimals that do not repeat or terminate.
a. Give an example of a square root that is irrational and a
decimal that is irrational.
b. Why do you think these numbers are considered to be
irrational?
c. Add the irrational numbers to your Venn diagram in Item
18. Use Ir as an abbreviation for irrational numbers.
Unit 1 • Patterns and Equations
17
ACTIVITY 1.2
Real Numbers
continued
Get Real
SUGGESTED LEARNING STRATEGIES: Graphic Organizer,
Look for a Pattern,
My Notes
All of the numbers discussed in this activity are examples of real
numbers, which are all rational numbers and all irrational numbers
combined.
20. Add the set of real numbers to your Venn diagram in Item 18.
WRITING MATH
The set of real numbers is
abbreviated by the letter R.
21. Use the numbers on the card your teacher gave you. Complete
the table with the numbers from your card and compute your
score.
Criterion
My numbers that
fit the criterion
Score
2 points for each rational number that is not
an integer
4 points for each real number
6 points for each even whole number
3 points for each negative rational numbers
CHECK YOUR UNDERSTANDING
Write your answers on notebook paper.
Write one example for each criterion. If not
possible, write “not possible.”
1. A rational number that is not a whole
number.
6. A real number that is not a rational
number.
7. A rational number that is not an integer.
2. An integer that is not a natural number.
8. An integer that is a real number.
3. A natural number that is not a whole
number.
9. MATHEMATICAL Describe situations that
R E F L E C T I O N you encounter daily for
at least four of the sets of numbers in this
activity.
4. An irrational number.
18
5. A whole number that is not a natural
number.
SpringBoard® Mathematics with Meaning™ Algebra 1
© 2010 College Board. All rights reserved.
4 points for each positive irrational number