Download real numbers - Education 5105 portfolio

Author
Brent Burke, Blair Cooke, Chris MacDonald
Title
The Number System
Grade Level
Grade 9
Subject Area
Math
This lesson will focus on the identification of the subset of real numbers
Overview of
unit/lessons/activities through interactive lessons and activities. Prior knowledge of number sense
(assumptions of prior with emphasis on fractions and decimals.
knowledge/learning)
Correlations to ICT
and curriculum
outcomes
GCO
A3 demonstrate an understanding of the meaning and uses of irrational
numbers
A4 demonstrate an understanding of the interrelationships of subsets of
real numbers
A5 compare and order real numbers
ICT
BOC 9.1
9.3
9.5
9.7
SEHI 9.6
PTS
9.2
9.3
9.6
Projected timeline for 60 min if front end loading is done to include repeating and terminate
decimals, ratios and fractions as comparison.
preparation and for
carrying out activities
Equipment
Requirements:
(computers,
software, etc)
Bundle of computers with internet connections. Calculators or online
calculators.
Teaching materials
provided (Blacklines,
worksheets,
templates, teacher
materials)
Definition sheet, BLM 1.1 Real Number Chart, BLM 1.1 Real Number
Activity (Venn Diagram), BLM 1.1 Card Template, BLM 1.1 Rational
Number Line, Real Number Chart checklist, Activity three samples,
Activity four sheet and Samples. You will also require a number on
envelopes of various sizes. The lessons all follow.
Resources available
for teacher/student
use (websites,
references, etc)
http://argyll.epsb.ca/jreed/math9/strand1/1101.htm For Definition sheet and
flash video on the number system. Text book Mathematics 9 Focus on
Understanding.
Detailed instructions
for each activity or
lesson (teacher
notes, activity
information, learning
strategies, teacher
role, student roles)
As given in lesson and Group activity directions. It starts with an
introductory into the number system and moves into a discussion of each
group activity.
Student products
expected
A better understanding of the number system and the common symbols
used.
Samples (include
teacher notes,
assessment
information, student
work if available)
Logistics
(organization,
grouping,
management issues,
access to
technology)
After a collective introduction the class is divided into 4 groups. Each
activity will take up to 10 minutes. All students must be provided with a
complete copy of the instructions and data collection sheets during the
introduction.
Assessment
information (e.g.,
rubrics for products
and/or process)
All charts and collection sheets from group / activity four can be collected
and assessed. A student completed assessment of the group and individual
work is linked below.
Group work assessment rubric below.
Possible extensions
Adaptations for
students requiring
additional support
Number Systems
Number Systems
The real number system is made up of rational and irrational numbers.
RATIONAL NUMBERS (Q)
INTEGERS (Z)
{...-2, -1, 0, 1, 2, ...}
WHOLE NUMBERS
(W)
{0, 1, 2, 3,...}
NATURAL
NUMBERS
(N)
{1, 2, 3,...}
Number
System
Symbol
Origin of
Symbol
IRRATIONAL
NUMBERS
__
(Q)
Description
1, 2, 3, ...
natural
N
Natural
Improper factions, powers and square roots may be natural numbers
if their standard form is a natural number For example:
6/2 = 3 52 = 25
16 = 4
0, 1, 2, 3, ...
whole
W
Whole
Improper factions, powers and square roots may be whole numbers
if their standard form is a whole number For example:
9/3 = 3.33... 62 = 36
integers
I
49 = 7
...-3, -2, -1, 0, 1, 2, 3, ...
Improper factions, powers and square roots may be integers if their
standard form is an integer number For example:
-12/3 = -6
82 = 64
81 = 9
Any number that can be written as a fraction where the numerator
and denominator are integers. The resulting decimal will be either
repeating or terminating.
rational
Q
Quotient
Improper factions, powers and square roots may be rational numbers
if their standard form is a rational number For example:
-13/9 = -1.444...
8-2 = 0.015625
(16)/3 = ±1.333...
Note: the denominator of the fraction cannot be zero.
Any number that cannot be written as a fraction where the
numerator and denominator are integers.
_
Q
Note: Since irrational numbers cannot be expressed as a fraction
they form decimals that are neither repeating nor terminating.
Not Quotient Powers, square roots, and some constants may be irrational numbers
if their standard form is an irrational number For example:
irrational

2
3
5
7
8
Irrational numbers fill the gaps in the rational number line.
real
R
Real
Includes the rational and the irrational numbers.
1.1 Real Numbers
Discover the Math: Real Numbers Chart
BLM 1.1
REAL NUMBERS
____________________________
• Can be expressed as the ratio
of two integers
• Decimal numbers that are terminating
or have a repeating pattern of digits
Examples:
____________________________
Whole numbers and their opposites
Examples:
____________________________
Positive integers and zero
Examples:
____________________________
Positive integers
Examples:
Not Rational Numbers
• Cannot be expressed as the ratio of
the ratio of two integers
• Decimal numbers that are nonterminating and do not have a repeating
pattern of digits
Examples:
GROUP ONE
Video Activity
Have the children follow the link http://argyll.epsb.ca/jreed/math9/strand1/1101.htm and scroll down to the
classifying numbers activity. On the top blue tab, click on relationships and then play to start. The video is
short so it can be played 2-3 times.
Envelope Activity
Make an envelope for each number system sub set. The envelopes will have to be made by folding paper to
start and then use actual store purchased envelopes. The smallest envelop will be used for natural numbers
with each envelop getting progressively larger for whole numbers, integers, rational and irrational (can be
the same size), and real numbers. Each envelope should be able to fit into its sub-set envelop.
Spread the envelops out on the desk and ask the students to place the sub sets in the proper order. Once they
are in order the students place the subset envelop inside the group envelop. The activity continues until all
envelops are inside the real number envelop. The size of the envelops will aid the students with the sorting
and stuffing, so students must be prompted to take note of how the sub sets fit together.
Charting activity
1.1 REAL NUMBERS
BLM 1.1
Materials
• Card templates with six cards on a page and real numbers centered on each card
(15–20 pages. Use BLM 1.1 Blank Cards and BLM 1.1 Card Definitions.)
• BLM 1.1 Venn Diagram
Divide the class into groups of 6. Each group will have 5 cards. Each card will contain a number from each subset of the
real numbers. Each student in the group will also have a card that has one of the definitions on it, and that student will be
responsible for finding that number as well as placing it on the diagram. The group will also have a large Venn diagram
(BLM 1.1 Venn Diagram) and 5 blank cards.
1. In groups, have students discuss where the following labels should be placed on the Venn diagram: rational numbers,
irrational numbers, integers, whole numbers, or natural numbers. After agreement, have students label the Venn
diagram. Each person in the group should copy the diagram and give reasons why they placed the labels where they
did.
REAL NUMBERS
Rational Numbers
Irrational Numbers
Integers
Natural Numbers
Whole Numbers
2. Have students discuss where each number card should be placed on the Venn diagram. Students can tape the cards to
their appropriate places. Each person in the group should copy the new information onto their Venn diagram. Students
should give reasons why they placed the numbers where they did.
Make up another set of cue cards with samples of different types of numbers and have the students categorize their
cue cards.
1.1 Real Numbers
Blank Cards Template
BLM 1.1
GROUP 3 - RATIONAL NUMBER LINES
Give each student a copy of the rational number line sheet below. With the sheet give them a
list of rational numbers and have them place each on their number line. It would be useful to
give a few irrational numbers as well so the students will see that they can not be placed on the
number line.
Example #1
9. 7.56
1. 22/ 7
10. -∏
2. 1.131 131…
11. 6
3. 21/4
12. -1/2
4. -4
13. 4.25
5. –√6
14. √16
6. -5.37
15. -1.333…
7. ∏/2
16. 3/4
8. 0
Rational Number Lines
GROUP 4 - ACTIVITY FOUR
1. Place the numbers in the appropriate category.
Put a check mark by each category which can apply.
N
W
I
Q
Q
6
2
1
3
3.149 62011957
-4
-0.75
10
0. 36
2.
Ordering numbers
Given a group of real numbers, students must organize them from
greatest to least.
{-7, 2/3, ∏, 0 .4, 3.14, -6.5, 1/5, 0.45, -3.1, 22/7, -6.53}
Teamwork Rubric
Name__________________________
Date_________________
The scores below are for your teamwork or participation in the group.
0=No participation.
1=I kind of worked with my group.
2=Yes, I worked together with my group.
3=Yes, I worked a lot with my group.
4=Yes, I worked with my group all of the time.
Circle your score.
1. I worked well with my
group.
2. I shared ideas with my
group.
3. I listened to my partners in
the group.
4. I helped to create the play.
5. I did my best in my group.
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
0
1
1
2
2
3
3
4
4
Please score your group's teamwork. How well did your group work
together?
0=Most people did not participate.
1=Only a few people worked on the play.
2=Some people created the play.
3=Most of my group worked on the play together.
4=My group worked well together all of the time.
Circle your score.
1. My group worked well together.
2. My group shared ideas with each
other.
3. My group listened to each other
in the group.
4. We all helped to create the play.
5. We all did our best in the group.
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
0
1
1
2
2
3
3
4
4