Transcript Lesson 5.3 - handsonmath8

Lesson 5.3
Exploring Repeating
Decimals
ALCOS Standards
• PRE-ALGEBRA
• DAILY PACING
GUIDE
• 2ND QUARTER
12-14
8-3
4, 4a, 4b, 5,
5b
III-1, IV2
V-1, V-2
Connected Math
Moving Straight
Ahead –
Investigations 5.1
and 5.2
ARMT Standards 4
&5
A87-A92
Objectives
1. Students will be able to distinguish
between terminating and repeating
decimals.
2. Students will be able to identify rational
and irrational numbers.
3. Students will be able to convert decimals
to fractions.
4. Students will be able to identify patterns
in repeating decimals.
Problem of the Day
A) What are the
decimal
representations of
1/33, 2/33, 3/33,
and 4/33?
B) Find other fractions
with decimal
representations the
same as those of
1/33, 2/33, 3/33,
and 4/33.
Answers to POD
A) 1/33=.030303…
2/33=.060606…
3/33=.090909…
4/33=.121212…
B) 2/66=.030303…
4/66=.060606…
6/66=.090909…
8/66=.121212…
Review-Problem 5.2
•
Write each fraction as a decimal. Tell
whether the decimal is terminating or
repeating. If the decimal is repeating,
tell which digits repeat.
A) 2/3 B) 3/8 C) 5/6 D) 35/10 E) 8/99
*Counting decimal places (power of 10)
Place Value: Hands-on role play activity-Counting the
Rice
http://arcytech.org/java/b10blocks/counting.html
Problem 5.2
Answers:
A) 2/3 =0.666… R
B) 3/8 =0.375 T
C) 5/6 =0.8333… R
D) 35/10 =3.5 T
E) 8/99 =0.080808… R
Repeating Decimals
What is a fraction representation of the
decimal 0.333…?
A) 3/10
B) 1/3
C) 33/100
*Journal: Explain how you got your answer
and why the other two are incorrect.
Repeating Decimals
Correct answer:
B) 0.333… equals 1/3
Discuss journal entry.
Repeating Decimals
How could you
write the
decimal
0.454545… as
a fraction?
Repeating Decimals
In today’s lesson, we will look for patterns
that can help us write repeating
decimals as fractions. Let’s begin
working on the problem (5.3) and followup in pairs (pgs. 57-58).
Students will break off into pairs.
Explore
Problem 5.3
Page 57
A, B, C, D
*Transparency
Explore
*A fraction with a
denominator of 9 has a
decimal representation
with a one-digit repeating
pattern, or repetend, and
the repetend is the
number in the numerator.
*A fraction with a
denominator of 99 has a
decimal representation
with a two-digit repetend:
a 0 followed by the
number in the numerator
if that number is less than
10; the number in the
numerator if that number
is equal to or greater than
10.
Explore
*A fraction with a
denominator of 999 has a
decimal representation
with a three-digit
repetend: two 0’s
followed by the number
in the numerator if that
number is less than 10;
one 0 followed by the
number in the numerator
if that number is equal to
or greater than
10 but less than 1000; the
number in the numerator
if that number is equal to
or greater than 100.
Explore
Problem 5.3 Follow Up
Page 58
1, 2, 3
Follow Up 5.3
Answers:
1. 1/99=0.0101…
2/99=0.0202…
3/99=0.0303…
A fraction with a denominator of 99 is equal
to a repeating decimal. The repeating
pattern has two digits.
Follow Up 5.3
2. 1/999=0.001001…
2/999=0.002002…
3/999=0.003003…
10/999=0.010010…
A fraction with a denominator of 999 is equal
to a repeating decimal. The repeating
pattern has 3 digits.
Follow Up 5.3
3. a) 0.333…=1/3
b) 0.050505…=5/99
c) 0.454545…=45/99
d) 0.045045…=45/999
e) 10.1212…=10 12/99
f) 3.999…=3 9/9, or 4
Repeating Decimals
• Discuss the patterns in the decimals.
*Question: What is the decimal
representation for 19/9?
For 20/9?
*Write 19/9 as a mixed number.
*Write 20/9 as a mixed number.
Repeating Decimals
Question: What
fraction is
equivalent to
4.111111…?
Answer: (write as
a fraction and
mixed number)
Repeating Decimals
Answers:
4.111…=37/9
mixed number: 4 1/9
Rational / Irrational Numbers
Did you know?
Refer to text
page 58.
*http://www.eduplace.co
m/math/mathsteps/7/
a/index.html
Rational/Irrational Numbers
Math Video Clip:
http://www.youtube.com/watch?v=OjjcF0t6CZ0
ACE Problems
Page 59 # 5 - 8
Pages 61-62 # 26 - 30
Homework
ACE Problem #25
Assessment
Teacher Observation
Class Discussion / ACE Problems
Mathematical Reflections Page 63
Additional
Resources/Activities
*Interactive Fractions to Decimals
http://www.learner.org/channel/courses/learningmath/numb
er/session7/part_a/rings.html
*A Well Planned Diet
http://www.glencoe.com/sec/math/msmath/mac04/course2/
webquest/unit3.php/
*Interactive activities: www.aplusmath.com/
*Interactive activities: www.aaamath.com/
*Interactive Baseball Game: http://www.funbrain.com/math/