{"id":779,"date":"2016-06-27T09:35:52","date_gmt":"2016-06-27T15:35:52","guid":{"rendered":"http:\/\/srcturnkey.com\/teachers\/?page_id=779"},"modified":"2019-05-23T10:17:27","modified_gmt":"2019-05-23T16:17:27","slug":"f-1-1","status":"publish","type":"page","link":"https:\/\/srcturnkey.com\/teachers\/math\/8th-grade\/f-1-1\/","title":{"rendered":"F.1.1"},"content":{"rendered":"

[vc_row][vc_column][vc_column_text]<\/p>\n

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.<\/h3>\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
CPALMS: Students are asked to determine if each of three equations represents a function.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491917037771{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Identifying Algebraic Functions[\/vc_column_text]
\"Assessment
CPALMS: Students are asked to define the term function including important properties.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491917128740{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]What Is a Function?[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Assessment
CPALMS: Students are asked to determine whether or not each of two graphs represent functions.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491917049263{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Recognizing Functions[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Assessment
CPALMS: Students are asked to determine whether or not tables of ordered pairs represent functions.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491917114616{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Tabulating Functions[\/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
This animation helps students to understand the function concept through the machine metaphor. The domain elements are dragged into the machine, which then goes through some process and outputs the range element corresponding to the input.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513451247610{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Function Machine by National Library of Virtual Manipulatives (Java Required)[\/vc_column_text]
\"Virtual
This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. It can be used to can be used to practice students' pattern finding skills, introduce basic notions from algebra, and motivate the idea of a function of one variable.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513449951231{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Introduction to Functions – “Function Machine” by Shodor Interactivate[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Virtual
CPALMS: This lesson is designed to introduce students to the vertical line test for functions as well as practice plotting points and drawing simple functions.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513449815502{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Functions and Vertical Line Test by Shodor Interactivate[\/vc_column_text]
\"Virtual
Students enter inputs into a function machine. Then, by examining the outputs, they must determine what function the machine is performing. It allows students to explore functions and what inputs are most useful for determining the function rule.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513451574901{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Number Cruncher by Shodor Interactivate[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Virtual
This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. The function is always a simple line of the following form: y = m * x + b where m, the slope, and b, the y-intercept, can be any integer between -10 and 10.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513451418870{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Linear Function Machine by Shodor Interactivate[\/vc_column_text]
\"Virtual
This manipulative is great for students to practice recognizing the function rule. Student or computer can choose the input. Different activity levels for play and self-checking.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513666583630{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Function Machine by Math Playground (Java Required)[\/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=”Assessment Questions” 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-question” 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=”Assessment Questions” hover_toggle_icon=”fa fa-question” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]
\"Assessments
Click on this text to download this document.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1471969303331{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Multiple Choice<\/strong><\/h5>\n

[\/vc_column_text]

\"Assessments
Click on this text to download this document.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1471969333764{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Table Item 4<\/strong><\/h5>\n

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

\"Assessments
Click on this text to download this document.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1471969313329{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Open Response<\/strong><\/h5>\n

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

\"Assessments
Click on this text to download this document.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1471969324241{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Table Item 3<\/strong><\/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=”Video of Expert Instruction” 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-video-camera” 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=”Video of Expert Instruction” hover_toggle_icon=”fa fa-video-camera” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]

\"Decorative
A table is given with information regarding height. Sal models and explains how to plot the ordered pairs and discusses what to consider in order to decide if there is a functional relationship between each person and his or her height. Video is approx. 4:35 min.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513460866618{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Recognizing Functions from a Table” by Khan Academy<\/strong><\/h5>\n

[\/vc_column_text]

\"Decorative
In this video, vocabulary (independent and dependent variables, input and output values, function, domain, range) are important. What does\/doesn\u2019t make a function is modeled as well as explained. Demonstrations of linear and nonlinear functions are shown. The vertical line test is demonstrated.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513471862476{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Vertical Line Test” by WhyU<\/strong><\/h5>\n

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

\"Decorative
This video is approx. 4:00 min and explains examples and non-examples of a function, given points on the coordinate plane.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513460123973{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Identifying a Function from a Graph by Khan Academy<\/strong><\/h5>\n

[\/vc_column_text]

\"Decorative
This video (approx. 7:30 min) explains how a \u201cbinary relation\u201d is a way of associating or relating elements of one set to elements of another set and how this information can be conveyed using ordered pairs. Domain and Range are initially explained with visuals that are not numbers.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513471391101{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Binary Relations” by WhyU<\/strong><\/h5>\n

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

\"Decorative
This short video (approx. 1:15 min.) uses a table of ordered pairs in order to explain how to decide if each represents a function or not.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513460226133{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Checking if a Table Represents a Function” by Khan Academy<\/strong><\/h5>\n

[\/vc_column_text]

\"Decorative
This video (approx. 6:25 min) connects to prior WhyU Algebra series videos and extends understanding of binary relations to a function and its characteristics. The concepts of domain and codomain are initially explained with examples that are more \u201cfriendly\u201d than numbers.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513471490802{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Functions” by WhyU<\/strong><\/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-leanpub” 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-leanpub” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]

\"Achievement
Illustrative Mathematics: This task could introduce functions. It illustrates examples as well as non examples of functions. Since the data is a collection of input-output pairs, no verbal description is given, so students can process what the ``rule form`` of the proposed functions would look like.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493665711295{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Foxes and Rabbits[\/vc_column_text]
\"Achievement
Illustrative Mathematics: The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493665747936{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Pennies to Heaven[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Achievement
Illustrative Mathematics: The purpose of this task is to connect the function described by a verbal rule with corresponding values in a table. It also encourages students to think more broadly about functions as relating objects other than numbers.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493665723293{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Function Rules[\/vc_column_text]
\"Achievement
Illustrative Mathematics:The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493665757716{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]The Customers[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Achievement
Illustrative Mathematics: The goal of this task is to give motivation to understanding the definition of a function by carefully analyzing different relationships. In some, one quantity can be determined in terms of the other, while in others this isn't possible. At least 2 valid approaches are open.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493665734450{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Introducing Functions[\/vc_column_text]
\"Achievement
Illustrative Mathematics: This task presents an opportunity to explore a more general and non-algebraic view of functions. This will help with students with conceptual understanding of the rule of a function when the context offers a real-world ``input`` and exactly one ``output``.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493665777705{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]US Garbage, Version 1[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"

[vc_row][vc_column][vc_column_text] Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [\/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”<\/p>\n","protected":false},"author":19,"featured_media":0,"parent":108,"menu_order":11,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/779"}],"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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/comments?post=779"}],"version-history":[{"count":0,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/779\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/108"}],"wp:attachment":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/media?parent=779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}