{"id":79646,"date":"2022-06-10T09:07:30","date_gmt":"2022-06-10T03:37:30","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=79646"},"modified":"2022-05-10T14:14:39","modified_gmt":"2022-05-10T08:44:39","slug":"eureka-math-grade-7-module-3-end-of-module-assessment","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-3-end-of-module-assessment\/","title":{"rendered":"Eureka Math Grade 7 Module 3 End of Module Assessment Answer Key"},"content":{"rendered":"<h2>Engage NY Eureka Math 7th Grade Module 3 End of Module Assessment Answer Key<\/h2>\n<h3>Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key<\/h3>\n<p>Question 1.<br \/>\nGloria says the two expressions \\(\\frac{1}{4}\\) (12x+24)-9x and -6(x+1) are equivalent. Is she correct? Explain how you know.<br \/>\nAnswer:<br \/>\nNo, Gloria is not correct.<br \/>\nThe standard form of \\(\\frac{1}{4}\\) (12x+24)-9x is -6x + 6 and the standard form of -6(x + 1) is -6x &#8211; 6. -6x + 6 is not equivalent to -6x &#8211; 6<br \/>\n\\(\\frac{1}{4}\\) (12x+24)-9x<br \/>\n\\(\\frac{1}{4}\\)(12x) + \\(\\frac{1}{4}\\)(24) &#8211; 9x<br \/>\n3x + 6 &#8211; 9x<br \/>\n3x &#8211; 9x + 6<br \/>\n-6x + 6<br \/>\n-6(x + 1)<br \/>\n(-6)(x) + (-6)(1)<br \/>\n-6x &#8211; 6<\/p>\n<p>Question 2.<br \/>\nA grocery store has advertised a sale on ice cream. Each carton of any flavor of ice cream costs $3.79.<br \/>\na. If Millie buys one carton of strawberry ice cream and one carton of chocolate ice cream, write an algebraic expression that represents the total cost of buying the ice cream.<br \/>\nAnswer:<br \/>\n3.79(s + c)<\/p>\n<p>b. Write an equivalent expression for your answer in part (a).<br \/>\nAnswer:<br \/>\n3.79s + 3.79c<\/p>\n<p>c. Explain how the expressions are equivalent.<br \/>\nAnswer:<br \/>\nPart b is the same expression as part a with the distributive property applied and in standard form.<\/p>\n<p>Question 3.<br \/>\nA new park was designed to contain two circular gardens. Garden A has a diameter of 50 m, and garden B has a diameter of 70 m.<br \/>\na. If the gardener wants to outline the gardens in edging, how many meters will be needed to outline the smaller garden? (Write in terms of \u03c0.)<br \/>\nAnswer:<br \/>\nC = 2\u03c0r r = \\(\\frac{1}{2} \\cdot 50\\) = 25<br \/>\nC = 2\u03c0(25)<br \/>\nC = 50\u03c0m<br \/>\nThe smaller garden will need 50\u03c0m of ending<\/p>\n<p>b. How much more edging will be needed for the larger garden than the smaller one? (Write in terms of \u03c0.)<br \/>\nAnswer:<br \/>\nC = 2\u03c0r r = \\(\\frac{1}{2} \\cdot 70\\) = 35<br \/>\nC = 2\u03c0(35)<br \/>\nC = 70\u03c0m<br \/>\nLarger garden &#8211; smaller garden<br \/>\n70\u03c0m &#8211; 50\u03c0m<br \/>\nThe larger garden will need 50\u03c0m of ending<\/p>\n<p>c. The gardener wishes to put down weed block fabric on the two gardens before the plants are planted in the ground. How much fabric will be needed to cover the area of both gardens? (Write in terms of \u03c0.)<br \/>\nAnswer:<br \/>\nA<sub>larger<\/sub> + A<sub>smaller<\/sub><br \/>\n\u03c0r<sup>2<\/sup> + \u03c0r<sup>2<\/sup><br \/>\n\u03c0(35)<sup>2<\/sup> + \u03c0(25)<sup>2<\/sup><br \/>\n1225\u03c0 + 625\u03c0<br \/>\n1850\u03c0m<sup>2<\/sup> of fabric will be needed to cover the area of both gardens.<\/p>\n<p>Question 4.<br \/>\nA play court on the school playground is shaped like a square joined by a semicircle. The perimeter around the entire play court is 182.8 ft., and 62.8 ft. of the total perimeter comes from the semicircle.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79653\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-1.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 1\" width=\"235\" height=\"168\" \/><\/p>\n<p>a. What is the radius of the semicircle? Use 3.14 for \u03c0.<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\)C = 62.8<br \/>\n\\(\\frac{1}{2}\\)(2\u03c0r) = 62.8<br \/>\n\u03c0r = 62.8<br \/>\n62.8\u00f7 3.14 = 20<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79666\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-500.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 500\" width=\"105\" height=\"61\" \/><br \/>\nr = 20<br \/>\nThe radius of the semi-circle is 20ft.<\/p>\n<p>b. The school wants to cover the play court with sports court flooring. Using 3.14 for \u03c0, how many square feet of flooring does the school need to purchase to cover the play court?<br \/>\nAnswer:<br \/>\nAre square + Area semicircle<br \/>\ns.s + \\(\\frac{1}{2}\\)(\u03c0r<sup>2<\/sup>)<br \/>\n40.40 + \\(\\frac{1}{2}\\)(3.14 (20)<sup>2<\/sup>)<br \/>\nThe school needs to purchase enough flooring to cover 2,228 ft<sup>2<\/sup><br \/>\n1600 + \\(\\frac{1}{2}\\)(3.14(400))<br \/>\n1600 + 628<br \/>\n2228<\/p>\n<p>Question 5.<br \/>\nMarcus drew two adjacent angles.<\/p>\n<p>a. If \u2220ABC has a measure one-third of \u2220CBD, then what is the degree measurement of \u2220CBD?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79655\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-27.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 27\" width=\"135\" height=\"88\" \/><br \/>\nLet m be the measure of \u2220CBD in degrees<br \/>\n\u2220ABC + \u2220CBD = 180<br \/>\n\\(\\frac{1}{3}\\)m + m = 180<br \/>\n1\\(\\frac{1}{3}\\)m = 180<br \/>\n(\\(\\frac{3}{4}\\)m)\\(\\frac{4}{3}\\)m = 180(\\(\\frac{3}{4}\\)m)<br \/>\nm = 135<\/p>\n<p>b. If the measure of \u2220CBD is 9(8x+11) degrees, then what is the value of x?<br \/>\nAnswer:<br \/>\n135 = 9(8x+11)<br \/>\n135 = 72x + 99<br \/>\n135 &#8211; 99 = 72x + 99 &#8211; 99<br \/>\n36 = 72x<br \/>\n36.\\(\\frac{1}{72}\\) = 72x.\\(\\frac{1}{72}\\)m<br \/>\nx = \\(\\frac{1}{72}\\)m<\/p>\n<p>135 = 9(8x+11)<br \/>\n135 \u00d7 \\(\\frac{1}{9}\\) = 9(8x + 11) \u00d7 \\(\\frac{1}{9}\\)<br \/>\n15 &#8211; 11 = 8x + 11 &#8211; 11<br \/>\n4 = 8x<br \/>\n4.\\(\\frac{1}{8}\\) = 8x.\\(\\frac{1}{8}\\)<br \/>\n\\(\\frac{1}{2}\\) = X<\/p>\n<p>Question 6.<br \/>\nThe dimensions of an above-ground, rectangular pool are 25 feet long, 18 feet wide, and 6 feet deep.<br \/>\na. How much water is needed to fill the pool?<br \/>\nAnswer:<br \/>\nV = l.w.h<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79656\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-50.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 50\" width=\"94\" height=\"99\" \/><br \/>\nV = 25ft. \u22198ft\u22196ft<br \/>\nV = 2,700ft<sup>3<\/sup><\/p>\n<p>b. If there are 7.48 gallons in 1 cubic foot, how many gallons are needed to fill the pool?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79657\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-51.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 51\" width=\"106\" height=\"126\" \/><br \/>\nTo fill pool, 20,196 gallons are needed<\/p>\n<p>c. Assume there was a hole in the pool, and 3,366 gallons of water leaked from the pool. How many feet did the water level drop?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79658\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-52.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 52\" width=\"281\" height=\"121\" \/><br \/>\nThe water level dropped one foot.<\/p>\n<p>d. After the leak was repaired, it was necessary to lay a thin layer of concrete to protect the sides of the pool. Calculate the area to be covered to complete the job.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-53.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 53\" width=\"152\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-53.png 152w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-53-150x86.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nbase : 25.18<br \/>\nlateral faces: 2(6\u221918) and 2(6\u221925)<br \/>\n(25\u221918) + 2(6\u221918) + 2(6\u221925)<br \/>\n450 + 216 + 300<br \/>\n966<br \/>\nThe surface area that needs to be covered is 966ft<sup>2<\/sup><\/p>\n<p>Question 7.<br \/>\nGary is learning about mosaics in art class. His teacher passes out small square tiles and encourages the students to cut up the tiles in various angles. Gary\u2019s first cut tile looks like this:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-79660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-End-of-Module-Assessment-Task-Answer-Key-60.png\" alt=\"Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key 60\" width=\"219\" height=\"208\" \/><br \/>\nAnswer:<br \/>\na. Write an equation relating \u2220TIL with \u2220LIE.<br \/>\nAnswer:<br \/>\n3m + (m &#8211; 10) = 90<\/p>\n<p>b. Solve for m.<br \/>\nAnswer:<br \/>\n3m + (m &#8211; 10) = 90<br \/>\n3m + m &#8211; 10 = 90<br \/>\n4m &#8211; 10 = 90<br \/>\n4m &#8211; 10 + 10 = 90 + 10<br \/>\n4m = 100<br \/>\n4m\u2219\\(\\frac{1}{4}\\) = 100\u2219\\(\\frac{1}{4}\\)<br \/>\nm = 25<\/p>\n<p>c. What is the measure of \u2220TIL?<br \/>\nAnswer:<br \/>\n3m<br \/>\n3(25) = 75<br \/>\nThe measure of \u2220TIL is 75\u00b0<\/p>\n<p>d. What is the measure of \u2220LIE?<br \/>\nAnswer:<br \/>\nm &#8211; 10<br \/>\n25 &#8211; 10<br \/>\nThe measure of \u2220LIE is 15\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Engage NY Eureka Math 7th Grade Module 3 End of Module Assessment Answer Key Eureka Math Grade 7 Module 3 End of Module Assessment Task Answer Key Question 1. Gloria says the two expressions (12x+24)-9x and -6(x+1) are equivalent. Is she correct? Explain how you know. Answer: No, Gloria is not correct. The standard form &#8230; <a title=\"Eureka Math Grade 7 Module 3 End of Module Assessment Answer Key\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-3-end-of-module-assessment\/\" aria-label=\"More on Eureka Math Grade 7 Module 3 End of Module Assessment Answer Key\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79646"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=79646"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79646\/revisions"}],"predecessor-version":[{"id":137636,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79646\/revisions\/137636"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=79646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=79646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=79646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}