{"id":786,"date":"2016-06-27T09:37:01","date_gmt":"2016-06-27T15:37:01","guid":{"rendered":"http:\/\/srcturnkey.com\/teachers\/?page_id=786"},"modified":"2017-12-16T18:41:47","modified_gmt":"2017-12-17T00:41:47","slug":"f-1-3","status":"publish","type":"page","link":"https:\/\/srcturnkey.com\/teachers\/math\/8th-grade\/f-1-3\/","title":{"rendered":"F.1.3"},"content":{"rendered":"

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

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s\u00b2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.<\/em><\/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 describe defining properties of linear functions.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491918000689{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Explaining Linear Functions[\/vc_column_text]
\"Assessment
CPALMS: Students are asked to describe a linear function, its graph, and the meaning of its parameters.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491918037368{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]What Am I?[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Assessment
CPALMS: Students are asked to identify a function as either linear or nonlinear and to justify their decision.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491918014236{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Linear or Nonlinear?[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Assessment
CPALMS: Students are asked to provide an example of a nonlinear function and explain why it is nonlinear.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491918027343{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Nonlinear 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
CPALMS: This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496692319220{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Equation Grapher[\/vc_column_text]
\"Virtual
CPALMS: This resource allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496692373423{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Graphing Lines[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Virtual
CPALMS: This tutorial will help students to graph a line using its slope and y-intercept, or to identify the slope and y-intercept from a linear equation written in slope-intercept form.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496692343095{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Graph a Line Using Y-Intercept and Slope[\/vc_column_text]
\"Virtual
CPALMS: This resource provides guided practice for writing and graphing linear functions.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496692393475{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Linear Equations[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Virtual
CPALMS: This manipulative will help students to explore the world of lines. Students can investigate the relationships between linear equations, slope, and graphs of lines. <\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496692354558{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Graphing Lines[\/vc_column_text]
\"Virtual
CPALMS: In this activity, students adjust slider bars which adjust the coefficients and constants of a linear function and examine how their changes affect the graph. It allows them to explore linear equations, slopes, and y-intercepts and their visual representation on a graph. <\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496692407840{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Slope Slider[\/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_1471970065479{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][\/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_1471970083678{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Multi-Select<\/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_1471970092671{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_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=”Videos 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=”Videos 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
Students will build fluency with predicting input\/outputs for nonlinear functions from patterns based on nonlinear tables and graphs. The representations used here provide a structure for analyzing rates of change. This work develops students' understanding that nonlinear functions can be predictable. Video and lesson materials are available.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513457475531{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Using Tables and Graphs to Make Predictions” by LearnZillion<\/h5>\n

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

\"Decorative
In this video (approx. 3:30 min.), Sal uses a real-world context to model assigning variables to the unknown quantities within the problem. He explains how to write the equation in slope intercept form to confirm that it is an example of a function.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513467504115{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]”Linear and Nonlinear Functions: Word Problems” by Khan Academy[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Decorative
This video (approx. 5:15 min) shows examples of linear functions who\u2019s graphs do and do not pass through the origin. Vertical translation is modeled. The y-intercept and it\u2019s x-coordinate of zero is demonstrated. Explanation of y=mx + b termed \u201cslope-intercept form\u201d is given.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513470154767{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
“Slope-Intercept Form” 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: Students explore the differences between linear and non-linear functions and then contrast the two. This reinforces the properties of linear functions. Encourage discussion about noticeable differences and relating them back to the equation and the graph.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1493668225728{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Introduction to Linear Functions[\/vc_column_text][\/vc_column][vc_column width=”1\/3″]
\"Achievement
We're currently looking for great content to go here.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513457098940{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Change Me To Real Text<\/p>\n

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

\"Achievement
We're currently looking for great content to go here.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513457114063{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Change Me To Real Text<\/p>\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=”Real World Application” 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-globe” 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=”Real World Application” hover_toggle_icon=”fa fa-globe” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]

\"Replace
In this video (approx. 6:30 min), 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_1513457301051{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Slope and Deep Sea Sharks<\/p>\n

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

\"Replace
We're currently looking for great content to go here.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513457098940{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Change Me To Real Text<\/p>\n

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

\"Replace
We're currently looking for great content to go here.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1513457114063{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]Change Me To Real Text<\/p>\n

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

[vc_row][vc_column][vc_column_text] Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s\u00b2 giving the area of a square as a function of its side length is not linear because its graph contains<\/p>\n","protected":false},"author":19,"featured_media":0,"parent":108,"menu_order":13,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/786"}],"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=786"}],"version-history":[{"count":0,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/786\/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=786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}