-
Notifications
You must be signed in to change notification settings - Fork 0
/
e0c84508-d9d5-4830-b9cc-380f369e8fc5.html
174 lines (174 loc) · 7.67 KB
/
e0c84508-d9d5-4830-b9cc-380f369e8fc5.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
<h4>Lesson Narrative</h4>
<p>In this lesson, students examine the meaning of negative exponents in context. In these cases, time \(t\) is the
independent variable, and \(t=0\) corresponds to a particular moment when a quantity is first measured. In these
situations, a value of \(t\) that is less than 0 corresponds to a time before the initial measurement, while a value
of \(t\) that is greater than 0 refers to a time after the measurement. Students write equations given a table, and
then they use those equations to answer questions, which requires working with negative values representing time. In
one case, students also produce a graph. As with many other activities in this unit, the mathematical work is grounded
and interpreted in a context.</p>
<p>Students learn to convert fluently between decimal form and scientific notation. They will solve problems in context
involving numbers in decimal form and scientific notation. They will combine what they have learned using negative
exponents to find the solution to a real-world problem in scientific notation.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<ul>
<li> Interpret a negative exponent in equations that represent exponential growth and decay. </li>
<li> Derive equations that represent exponential growth and decay in real-world problems. </li>
<li> Select a proper window while graphing an equation they derived from a real-world problem involving exponential
decay. </li>
<li> Fluently convert between decimal form and scientific notation. </li>
<li> Apply measurements in scientific notation and decimal form to solve a problem in a real-world situation. </li>
</ul>
<h4>Learning Targets (Student Facing)</h4>
<ul>
<li> Describe the meaning of a negative exponent in equations that represent exponential growth and decay. </li>
<li> Write equations that represent exponential growth and decay to solve problems. </li>
<li> Graph an equation that represents exponential decay to solve a problem. </li>
<li> Convert numbers between decimal form and scientific notation. </li>
<li> Use scientific notation to solve problems arising from real-world situations. </li>
</ul>
<table class="os-raise-textheavytable">
<caption> Texas Essential Knowledge and Skills (TEKS)</caption>
<thead>
<tr>
<th scope="col">TEKS</th>
<th scope="col">Explanation of Coverage</th>
</tr>
</thead>
<tbody>
<tr>
<td>
A1(A) apply mathematics to problems arising in everyday life, society, and the workplace
</td>
<td>
Math process coverage: Lesson provides content that supports this TEKS.
</td>
</tr>
<tr>
<td>
A1(E) create and use representations to organize, record, and communicate mathematical ideas
</td>
<td>
Math process coverage: Lesson provides content that supports this TEKS.
</td>
</tr>
<tr>
<td>
A1(F) analyze mathematical relationships to connect and communicate mathematical ideas
</td>
<td>
Math process coverage: Lesson provides content that supports this TEKS.
</td>
</tr>
<tr>
<td>
A9(C) <u>write exponential functions in the form </u>
\(f(x)=ab^x\) <u>(where \(b\) is a rational number) to describe problems arising from</u> mathematical and
<u>real-world situations, including growth and decay</u>
</td>
<td>
Partial coverage: Lesson provides content that covers part of this TEKS. The parts that are covered have been
underlined.
</td>
</tr>
</tbody>
</table>
<br>
<h4>Lesson Activities</h4>
<ul>
<li> 5.6.1: Checking Exponent Rules </li>
<li> 5.6.2: Interpreting Negative Exponents in Exponential Growth </li>
<ul>
<li> 5.6.2: Self Check</li>
<li>5.6.2: Additional Resources</li>
</ul>
<li> 5.6.3: Interpreting Negative Exponents in Exponential Decay </li>
<ul>
<li> 5.6.3: Self Check</li>
<li>5.6.3: Additional Resources</li>
</ul>
<li>5.6.4: Using Scientific Notation </li>
<ul>
<li> 5.6.4: Self Check</li>
<li>5.6.4: Additional Resources</li>
</ul>
<li>5.6.5: Applying Scientific Notation
<ul>
<li>5.6.5: Self Check</li>
<li>5.6.5: Additional Resources</li>
</ul>
</li>
<li>5.6.6: Interpreting Negative Exponents and Scientific Notation </li>
</ul>
<p>Students will also complete a series of problems in the 5.6.7: Practice.</p>
<h4>Required Materials</h4>
<ul>
<li> Graphing technology </li>
</ul>
<h4>Required Preparation</h4>
<ul>
<li>None </li>
</ul>
<h4>Lesson Vocabulary</h4>
<p>During this lesson, it is important to:</p>
<ul>
<li> Familiarize students with the vocabulary words they will see throughout the lesson. </li>
<li> Encourage students to look for these words and notice their use and meanings. </li>
<li> Encourage students to use key vocabulary words in “math talk” and their written and oral
explanations. </li>
<li> Utilize a word wall. Sample cards are located here: <a
href="https://k12.openstax.org/contents/raise/resources/8ed3aa68763498713b44d3c2e537ffe61b4755f0"
target="_blank">Mathematics Vocabulary Word Wall Cards</a> </li>
</ul>
<p>Vocabulary words that are emphasized in this lesson include:</p>
<table class="os-raise-textheavytable">
<thead>
<tr>
<th scope="col">Previous Vocabulary</th>
<th scope="col">New Vocabulary</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<ul>
<li>equation </li>
</ul>
</td>
<td>
<ul>
<li> scientific notation</li>
</ul>
</td>
</tr>
</tbody>
</table>
<br>
<p>To support newcomers or students identified at the beginning level of language proficiency, share the following Quizlet links to help students gain an understanding of the academic vocabulary. Use the Spanish versions to anchor student understanding before bridging to the English versions. </p>
<ul>
<li><a href="https://quizlet.com/881785671/raise-unit-5-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 5 Spanish Vocabulary</a></li>
<li><a href="https://quizlet.com/881507407/raise-unit-5-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 5 Vocabulary</a></li>
</ul>
<br>
<h4>Support for English Language Learners</h4>
<p>Throughout this lesson, activities are incorporated that align to the following ELPS. The suggested activities are
only a sampling of the types of support and scaffolding that can extend the learning for English language learners.
Continue to find additional opportunities as you build your own set of ELL learning routines.</p>
<ul>
<li>ELPS 2(F) listen to and derive meaning from a variety of media such as audiotape, video, DVD, and CD-ROM to build and
reinforce concept and language attainment </li>
<li>ELPS 2(G) understand the general meaning, main points, and important details of spoken language ranging from
situations in which topics, language, and contexts are familiar to unfamiliar </li>
<li>ELPS 2(H) understand implicit ideas and information in increasingly complex spoken language commensurate with
grade-level learning expectations</li>
</ul>
<br>
<h4>Support for Building Character</h4>
<p>Throughout this unit, find ways to encourage and support students to work on cultivating their <strong>grit</strong>.
</p>
<p>Here are some tips to try during this lesson:</p>
<ul>
<li> <a href="https://characterlab.org/tips-of-the-week/me-to-me/" target="_blank">Me to Me</a> </li>
<li> <a href="https://characterlab.org/tips-of-the-week/success-story-tips/" target="_blank">Success Story</a> </li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/grit/" target="_blank">Grit
Playbook</a> from Character Lab.</p>