{"id":899,"date":"2016-06-27T10:22:32","date_gmt":"2016-06-27T16:22:32","guid":{"rendered":"http:\/\/srcturnkey.com\/teachers\/?page_id=899"},"modified":"2017-07-20T07:45:11","modified_gmt":"2017-07-20T13:45:11","slug":"f-le-1-1","status":"publish","type":"page","link":"https:\/\/srcturnkey.com\/teachers\/math\/algebra-1\/f-le-1-1\/","title":{"rendered":"F-LE.1.1.a"},"content":{"rendered":"

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Distinguish between situations that can be modeled with linear functions and with exponential functions.<\/h3>\n

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

[\/vc_column_text][vc_single_image image=”2664″ img_size=”full”][\/vc_column][\/vc_row][vc_row toggle_enable=”true” toggle_stretch=”true” toggle_font_preset=”default” toggle_font_color=”#333333″ toggle_font_size=”24″ toggle_font_line_height=”2″ toggle_font_transform=”capitalize” toggle_font_align=”left” toggle_title=”Formative Assessments” toggle_background_color=”#8dc53e” toggle_border_css=”border-color:#333333;border-style:solid;” toggle_margin_divider=”true” toggle_margin_css=”margin-bottom:5px;” toggle_icon=”fa fa-file-text” toggle_icon_position=”button-left” toggle_icon_border_css=”border-width:0px;” toggle_icon_padding_css=”padding:5px;” toggle_icon_margin_css=”margin:5px;” hover_toggle_font_color=”#ffffff” hover_toggle_font_size=”24″ hover_toggle_font_align=”left” hover_toggle_title=”Formative Assessments” hover_toggle_icon=”fa fa-file-text” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]

\"Assessment
Students are asked to prove that an exponential function grows by equal factors over equal intervals.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1487966246199{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Prove Exponential<\/h5>\n

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\"Assessment
http:\/\/www.cpalms.org\/Public\/PreviewResourceAssessment\/Preview\/69183<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1487966366935{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Prove Linear<\/h5>\n

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\"Assessment
Students are given four verbal descriptions of functions and asked to identify each as either linear or exponential and to justify their choices.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1487966467628{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Linear or Exponential?<\/h5>\n

[\/vc_column_text][\/vc_column][\/vc_row][vc_row toggle_enable=”true” toggle_stretch=”true” toggle_font_preset=”default” toggle_font_color=”#333333″ toggle_font_size=”24″ toggle_font_line_height=”2″ toggle_font_transform=”capitalize” toggle_font_align=”left” toggle_title=”Virtual\/Hands-on Manipulatives” toggle_background_color=”#8dc53e” toggle_border_divider=”true” toggle_border_css=”border-top:0px;border-right:0px;border-bottom:0px;border-left:0px;border-color:#333333;border-style:solid;” toggle_padding_divider=”true” toggle_margin_divider=”true” toggle_margin_css=”margin-top:0px;margin-right:0px;margin-bottom:5px;margin-left:0px;” toggle_icon=”mi mi-pan_tool” toggle_icon_color=”#333333″ toggle_icon_position=”button-left” toggle_icon_border_divider=”true” toggle_icon_border_css=”border-top:0px;border-right:0px;border-bottom:0px;border-left:0px;” toggle_icon_padding_divider=”true” toggle_icon_padding_css=”padding-top:5px;padding-right:5px;padding-bottom:5px;padding-left:5px;” toggle_icon_margin_divider=”true” toggle_icon_margin_css=”margin-top:5px;margin-right:5px;margin-bottom:5px;margin-left:5px;” hover_toggle_font_color=”#ffffff” hover_toggle_font_size=”24″ hover_toggle_font_align=”left” hover_toggle_title=”Virtual\/Hands-on Manipulatives” hover_toggle_border_divider=”true” hover_toggle_border_css=”border-top:0px;border-right:0px;border-bottom:0px;border-left:0px;” hover_toggle_icon=”mi mi-pan_tool” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left” hover_toggle_icon_border_divider=”true” hover_toggle_icon_border_css=”border-top:0px;border-right:0px;border-bottom:0px;border-left:0px;”][vc_column width=”1\/3″]

\"Virtual
Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496425828021{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Data Flyer<\/h5>\n

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\"Virtual
In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496425861192{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Function Flyer<\/h5>\n

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\"Virtual
This virtual manipulative allows the user to explore scenarios of a loan repayment by manipulating the amount of the loan, interest rate, payment amount, frequency of payments, and length of the loan in years.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496425897920{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Loan Calculator<\/h5>\n

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\"Assessments
Click on this text to download this question.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1470927959685{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
FSA Sample Question<\/h5>\n

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We're currently looking for great content to go here!<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1461771776012{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Change Me\u00a0To Real Text<\/strong><\/h5>\n

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\"Content
We're currently looking for great content to go here!<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1461771776012{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Change Me\u00a0To Real Text<\/strong><\/h5>\n

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\"Decorative
Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499952663214{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Slope and Deep Sea Sharks<\/h5>\n

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\"Decorative
What will be the percent tint with both sunglasses?<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1500557172243{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Double Sunglasses<\/h5>\n

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\"Decorative
Will Ryan describes how linear regression models contribute towards his research on sea anemones.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499952696269{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Linear Regression for Analysis of Sea Anemone Data<\/h5>\n

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\"Decorative
How much money does Fry have in his bank account right now?<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1500558307509{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Fry’s Bank<\/h5>\n

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\"Decorative
How much food do you need to cross the Pacific in a kayak? Get a calculator and a bag of almonds before you watch this.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499952724782{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
KROS Pacific Ocean Kayak Journey: Calories, Exercise, and Metabolism Rates<\/h5>\n

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\"Decorative
A seafaring teacher filters all the good information you need to understand water purification rates for distance traveling.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499952752229{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
KROS Pacific Ocean Kayak Journey: Water Usage Rates<\/h5>\n

[\/vc_column_text][\/vc_column][\/vc_row][vc_row toggle_enable=”true” toggle_stretch=”true” toggle_font_preset=”default” toggle_font_color=”#333333″ toggle_font_size=”24″ toggle_font_line_height=”1.8″ toggle_font_transform=”capitalize” toggle_font_align=”left” toggle_title=”Hook\/Performance Tasks” toggle_background_color=”#8dc53e” toggle_border_css=”border-color:#333333;border-style:solid;” toggle_padding_divider=”true” toggle_margin_divider=”true” toggle_margin_css=”margin-bottom:5px;” toggle_icon=”fa fa-wrench” toggle_icon_color=”#333333″ toggle_icon_position=”button-left” toggle_icon_padding_css=”padding:5px;” toggle_icon_margin_css=”margin:5px;” hover_toggle_font_color=”#ffffff” hover_toggle_font_size=”24″ hover_toggle_font_align=”left” hover_toggle_title=”Hook\/Performance Tasks” hover_toggle_icon=”fa fa-wrench” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]

\"Achievement
An important property of linear functions is that they grow by equal differences over equal intervals. In F.LE Equal Differences over Equal Intervals 1, students prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496425134528{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Equal Differences over Equal Intervals 1<\/h5>\n

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\"Achievement
There are three challenges for this problem depending on the whether this is approached as a simple percent increase problem or a compound interest problem<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499447102877{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
How Did Motel 6 Go From $6 To $66?<\/strong><\/h5>\n

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\"Achievement
This task assumes that students are familiar with the ?x and ?y notations. Students most likely developed this familiarity in their work with slope.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496425162519{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Equal Differences over Equal Intervals 2<\/h5>\n

[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]

\"Achievement
This problem assumes that students are familiar with the notation x0 and \u0394x. However, the language ``successive quotient`` may be new.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496425192377{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Equal Factors over Equal Intervals<\/h5>\n

[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"

[vc_row][vc_column][vc_column_text] Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. [\/vc_column_text][vc_single_image image=”2664″ img_size=”full”][\/vc_column][\/vc_row][vc_row toggle_enable=”true” toggle_stretch=”true” toggle_font_preset=”default” toggle_font_color=”#333333″ toggle_font_size=”24″ toggle_font_line_height=”2″ toggle_font_transform=”capitalize” toggle_font_align=”left” toggle_title=”Formative Assessments” toggle_background_color=”#8dc53e” toggle_border_css=”border-color:#333333;border-style:solid;” toggle_margin_divider=”true” toggle_margin_css=”margin-bottom:5px;”<\/p>\n","protected":false},"author":17,"featured_media":0,"parent":109,"menu_order":39,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/899"}],"collection":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/comments?post=899"}],"version-history":[{"count":0,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/899\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/109"}],"wp:attachment":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/media?parent=899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}