{"id":854,"date":"2016-06-27T09:52:24","date_gmt":"2016-06-27T15:52:24","guid":{"rendered":"http:\/\/srcturnkey.com\/teachers\/?page_id=854"},"modified":"2017-07-27T07:42:16","modified_gmt":"2017-07-27T13:42:16","slug":"gmd-1-1","status":"publish","type":"page","link":"https:\/\/srcturnkey.com\/teachers\/math\/geometry\/gmd-1-1\/","title":{"rendered":"G-GMD.1.1"},"content":{"rendered":"

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

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri\u2019s principle, and informal limit arguments.<\/em><\/h3>\n

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\"Assessment
Students are asked to derive and explain a formula for the volume of a cone given a pyramid with the same height and the same cross-sectional area at every height.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491937336611{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Volume of a Cone<\/h5>\n

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

\"Assessment
Students are asked to derive and explain a formula for the volume of a cylinder given a prism with the same height and the same cross-sectional area at every height.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491937374172{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Volume of a Cylinder<\/h5>\n

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

\"Assessment
Students are guided through the process of writing an informal argument for the volume of a pyramid formula using Cavalieri\u2019s Principle.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1491937409877{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Volume of a Pyramid<\/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_column width=”1\/3″]

\"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_1470938670432{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

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

\"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_column width=”1\/3″]

\"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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Story of Pi<\/h5>\n

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

\"Decorative
A science teacher demonstrates stepwise calculations involving multiple variables for designing robots with desired characteristics.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1499957895417{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Robot Mathematics: Gearing Ratio Calculations for Performance<\/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=”Math Literature” 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=”Math Literature” hover_toggle_icon=”fa fa-leanpub” hover_toggle_icon_color=”#ffffff” hover_toggle_icon_position=”button-left”][vc_column width=”1\/3″]

\"Achievement
High school students will know that the circumference of a circle of radius r is 2\u03c0r and therefore the goal of this task is to help them understand this formula from the point of view of similarity.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1501162714006{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Circumference of a Circle<\/h5>\n

[\/vc_column_text]

\"Achievement
The goal of this task is to calculate the volume of a particular pyramid with square base, which is easily reasoned by viewing it as one sixth of a cube.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1501162933142{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Volume of a Special Pyramid<\/h5>\n

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

\"Achievement
This purpose of this task is to develop an understanding of the formula for the area of the circle. The argument presented is essentially due to Archimedes.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1501162759994{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Area of a Circle<\/h5>\n

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

\"Achievement
The goal of this task is to establish formulas for volumes of right prisms and cylinders. Students encounter these formulas in eighth grade (8.G.9) but arguments based on dissections are introduced in high school.<\/i><\/a><\/div><\/div><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1501162893964{margin-top: 0px !important;border-top-width: 0px !important;padding-top: 0px !important;padding-left: 10px !important;background-color: #8dc53e !important;}”]<\/p>\n
Volume Formulas for Cylinders and Prisms<\/h5>\n

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

[vc_row][vc_column][vc_column_text] Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri\u2019s principle, and informal limit arguments. [\/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;”<\/p>\n","protected":false},"author":15,"featured_media":0,"parent":114,"menu_order":17,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/854"}],"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\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/comments?post=854"}],"version-history":[{"count":0,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/854\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/pages\/114"}],"wp:attachment":[{"href":"https:\/\/srcturnkey.com\/teachers\/wp-json\/wp\/v2\/media?parent=854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}