{"id":865,"date":"2016-06-27T10:09:17","date_gmt":"2016-06-27T16:09:17","guid":{"rendered":"http:\/\/srcturnkey.com\/teachers\/?page_id=865"},"modified":"2017-07-07T11:33:48","modified_gmt":"2017-07-07T17:33:48","slug":"a-rei-4-11","status":"publish","type":"page","link":"https:\/\/srcturnkey.com\/teachers\/math\/algebra-1\/a-rei-4-11\/","title":{"rendered":"A-REI.4.11"},"content":{"rendered":"

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Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x)= g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and\/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.<\/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 find the solution(s) of the equation f(x) = g(x) given the graphs of f and g and explain their reasoning.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1487774408661{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Graphs and Solutions – 2<\/h5>\n

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\"Assessment
Students are asked to explain why the x-coordinate of the intersection of two functions, f and g, is a solution of the equation f(x) = g(x).<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1487774553931{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Graphs and Solutions -1<\/h5>\n

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\"Assessment
Students are asked to find solutions of the equation f(x) = g(x) for two given functions, f and g, by constructing a table of values.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1487774801096{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<\/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
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_1496409461862{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Equation Grapher<\/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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\"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

[\/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 question.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1470924367066{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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\"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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\"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

[\/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″][vc_video link=”https:\/\/player.vimeo.com\/video\/166250310″ css=”.vc_custom_1462991847514{margin-bottom: 0px !important;border-bottom-width: 0px !important;padding-bottom: 0px !important;}”][vc_column_text css=”.vc_custom_1461772043672{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n

Use Real Link and Title<\/strong><\/h5>\n

[\/vc_column_text][\/vc_column][vc_column width=”1\/3″][vc_video link=”https:\/\/player.vimeo.com\/video\/166250310″ css=”.vc_custom_1462991847514{margin-bottom: 0px !important;border-bottom-width: 0px !important;padding-bottom: 0px !important;}”][vc_column_text css=”.vc_custom_1461772043672{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n

Use Real Link and Title<\/strong><\/h5>\n

[\/vc_column_text][\/vc_column][vc_column width=”1\/3″][vc_video link=”https:\/\/player.vimeo.com\/video\/166250310″ css=”.vc_custom_1462991847514{margin-bottom: 0px !important;border-bottom-width: 0px !important;padding-bottom: 0px !important;}”][vc_column_text css=”.vc_custom_1461772043672{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n

Use Real Link and Title<\/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-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
In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496409523152{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Population and Food Supply<\/h5>\n

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\"Achievement
Students add the monthly payments together with the initial down payment and compare it to the single annual payment. <\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499442812803{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Is It Cheaper To Pay Monthly or Annually?<\/h5>\n

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\"Achievement
This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1496409560953{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Two Squares are Equal<\/h5>\n

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\"Achievement
Students will have to decompose 450 and account for the nine rolls.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499445173167{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
How Can You Win Every Prize At Chuck E. Cheese\u2019s?<\/strong><\/h5>\n

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\"Achievement
This context makes for an interesting application of calculating interest.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499436111216{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
How Much Did Peterson Lose By Not Cashing His Check?<\/strong><\/h5>\n

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\"Achievement
Students should be able to reach the conclusion that the toilets\u2019 water usage would be about the same when the dual flush toilet is used slightly less than 50% of the time for \u201csolids\u201d and slightly more than 50% of the time for \u201cliquids\u201d.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499448728168{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Which Toilet Uses Less Water?<\/strong><\/h5>\n

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

[vc_row][vc_column][vc_column_text] Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x)= g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and\/or g(x)<\/p>\n","protected":false},"author":17,"featured_media":0,"parent":109,"menu_order":13,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/865"}],"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=865"}],"version-history":[{"count":0,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/865\/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=865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}