{"id":76807,"date":"2022-06-12T21:32:20","date_gmt":"2022-06-12T16:02:20","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=76807"},"modified":"2022-05-10T14:14:17","modified_gmt":"2022-05-10T08:44:17","slug":"eureka-math-grade-7-module-3-lesson-3","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-3-lesson-3\/","title":{"rendered":"Eureka Math Grade 7 Module 3 Lesson 3 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 3 Lesson 3 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 3 Lesson 3 Example Answer Key<\/h3>\n

Example 1.
\nRepresent 3+2 using a tape diagram.
\nAnswer:
\n\"Engage<\/p>\n

\u2192 Now, let\u2019s represent another expression, x+2. Make sure the units are the same size when you are drawing the known 2 units.<\/p>\n

Represent x+2 using a tape diagram.
\n\"Engage<\/p>\n

\u2192 Note the size of the units that represent 2 in the expression x+2. Using the size of these units, can you predict what value x represents?
\n\u2192 Approximately six units<\/p>\n

Draw a rectangular array for 3(3+2).
\n\"Engage<\/p>\n

Then, have students draw a similar array for 3(x+2).<\/p>\n

Draw an array for 3(x+2).
\nAnswer:
\n\"Engage<\/p>\n

\u2192 Determine the area of the shaded region.
\n\u2192 6
\n\u2192 Determine the area of the unshaded region.
\n\u2192 3x
\nRecord the areas of each region:
\n\"Engage<\/p>\n

Example 2.
\nDraw a tape diagram to represent each expression.
\na. (x+y)+(x+y)+(x+y)
\nAnswer:
\n\"Engage<\/p>\n

b. (x+x+x)+(y+y+y)
\nAnswer:
\n\"Engage<\/p>\n

c. 3x+3y
\nAnswer:
\n\"Engage<\/p>\n

d. 3(x+y)
\nAnswer:
\n\"Engage<\/p>\n

Ask students to explain to their neighbors why all of these expressions are equivalent.
\nDiscuss how to rearrange the units representing x and y into each of the configurations on the previous page.
\n\u2192 What can we conclude about all of these expressions?
\n\u2192 They are all equivalent.
\n\u2192 How does 3(x+y)=3x+3y?
\n\u2192 Three groups of (x+y) is the same as multiplying 3 with the x and the y.
\n\u2192 How do you know the three representations of the expressions are equivalent?
\n\u2192 The arithmetic, algebraic, and graphic representations are equivalent. Problem (c) is the standard form of problems (b) and (d). Problem (a) is the equivalent of problems (b) and (c) before the distributive property is applied. Problem (b) is the expanded form before collecting like terms.
\n\u2192 Under which conditions would each representation be most useful?
\n\u2192 Either 3(x+y) or 3x+3y because it is clear to see that there are 3 groups of (x+y), which is the product of the sum of x and y, or that the second expression is the sum of 3x and 3y.
\n\u2192 Which model best represents the distributive property?
\n\"Engage
\nSummarize the distributive property.<\/p>\n

Example 3.
\nFind an equivalent expression by modeling with a rectangular array and applying the distributive property to the expression 5(8x+3).
\n\"Engage
\nAnswer:
\n\"Engage
\nSubstitute given numerical value to demonstrate equivalency. Let x=2
\n5(8x+3)=5 (8(2)+3)=5(16+3)=5(19)=95
\n40x+15=40(2)+15=80+15=95
\nBoth equal 95, so the expressions are equal.<\/p>\n

Example 4.
\nRewrite the expression (6x+15)\u00f73 in standard form using the distributive property.
\nAnswer:
\n(6x+15)\u00d7\\(\\frac{1}{3}\\)
\n(6x) \\(\\frac{1}{3}\\)+(15) \\(\\frac{1}{3}\\)
\n2x+5<\/p>\n

\u2192 How can we rewrite the expression so that the distributive property can be used?
\n\u2192 We can change from dividing by 3 to multiplying by \\(\\frac{1}{3}\\).<\/p>\n

Example 5.
\nExpand the expression 4(x+y+z).
\nAnswer:
\n\"Engage<\/p>\n

Example 6.
\nA square fountain area with side length s ft. is bordered by a single row of square tiles as shown. Express the total number of tiles needed in terms of s three different ways.
\n\"Engage
\nAnswer:
\n\u2192 What if s=4? How many tiles would you need to border the fountain?
\n\u2192 I would need 20 tiles to border the fountain\u2014four for each side and one for each corner.
\n\"Engage
\n\u2192 What if s=2? How many tiles would you need to border the fountain?
\n\u2192 I would need 12 tiles to border the fountain\u2014two for each side and one for each corner.
\n\u2192 What pattern or generalization do you notice?
\n\u2192 Answers may vary. Sample response: There is one tile for each corner and four times the number of tiles to fit one side length.
\nAfter using numerical values, allow students two minutes to create as many expressions as they can think of to find the total number of tiles in the border in terms of s. Reconvene by asking students to share their expressions with the class from their seat.
\n\u2192 Which expressions would you use and why?
\n\u2192 Although all the expressions are equivalent, 4(s+1), or 4s+4, is useful because it is the most simplified, concise form. It is in standard form with all like terms collected.
\n\"Engage<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 3 Opening Exercise Answer Key<\/h3>\n

Solve the problem using a tape diagram. A sum of money was shared between George and Benjamin in a ratio of 3\u22364.
\nIf the sum of money was $56.00, how much did George get?
\nAnswer:
\nHave students label one unit as x in the diagram.
\n\"Eureka
\n\u2192 What does the rectangle labeled x represent?
\n\u2192 $8.00<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 3 Exercise Answer Key<\/h3>\n

Exercise 1
\nDetermine the area of each region using the distributive property.
\n\"Eureka
\nAnswer:
\n176, 55<\/p>\n

Draw in the units in the diagram for students.
\n\"Eureka<\/p>\n

\u2192 Is it easier to just imagine the 176 and 55 square units?
\n\u2192 Yes<\/p>\n

Exercise 2.
\nFor parts (a) and (b), draw an array for each expression and apply the distributive property to expand each expression. Substitute the given numerical values to demonstrate equivalency.
\na. 2(x+1), x=5
\nAnswer:
\n\"Eureka<\/p>\n

b. 10(2c+5), c=1
\nAnswer:
\n\"Eureka<\/p>\n

For parts (c) and (d), apply the distributive property. Substitute the given numerical values to demonstrate equivalency.<\/p>\n

c. 3(4f-1), f=2
\nAnswer:
\n12f-3, 21<\/p>\n

d. 9(-3r-11), r=10
\nAnswer:
\n-27r-99, -369<\/p>\n

Exercise 3.
\nRewrite the expressions in standard form.
\na. (2b+12)\u00f72
\nAnswer:
\n\\(\\frac{1}{2}\\) (2b+12)
\n\\(\\frac{1}{2}\\) (2b)+\\(\\frac{1}{2}\\)(12)
\nb+6<\/p>\n

b. (20r-8)\u00f74
\n\\(\\frac{1}{4}\\) (20r-8)
\n\\(\\frac{1}{4}\\) (20r)-\\(\\frac{1}{4}\\)(8)
\n5r-2<\/p>\n

c. (49g-7)\u00f77
\n\\(\\frac{1}{7}\\) (49g-7)
\n\\(\\frac{1}{7}\\) (49g)-\\(\\frac{1}{7}\\)(7)
\n7g-1<\/p>\n

Exercise 4.
\nExpand the expression from a product to a sum by removing grouping symbols using an area model and the repeated use of the distributive property: 3(x+2y+5z).
\nAnswer:
\nRepeated use of the distributive property: Visually:
\n3(x+2y+5z)
\n3\u2219x+3\u22192y+3\u22195z
\n3x+3\u22192\u2219y+3\u22195\u2219z
\n3x+6y+15z
\n\"Eureka<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 3 Problem Set Answer Key<\/h3>\n

Question 1.
\na. Write two equivalent expressions that represent the rectangular array below.
\n\"Eureka
\nAnswer:
\n3(2a+5) or 6a+15<\/p>\n

b. Verify informally that the two expressions are equivalent using substitution.
\nAnswer:
\nLet a=4.
\n3(2a+5)
\n3(2(4)+5)
\n3(8+5)
\n3(13)
\n39
\n6a+15
\n6(4)+15
\n24+15
\n39<\/p>\n

Question 2.
\nYou and your friend made up a basketball shooting game. Every shot made from the free throw line is worth 3 points, and every shot made from the half-court mark is worth 6 points. Write an equation that represents the total number of points, P, if f represents the number of shots made from the free throw line, and h represents the number of shots made from half-court. Explain the equation in words.
\nAnswer:
\nP=3f+6h or P=3(f+2h)
\nThe total number of points can be determined by multiplying each free throw shot by 3 and then adding that to the product of each half-court shot multiplied by 6.
\nThe total number of points can also be determined by adding the number of free throw shots to twice the number of half-court shots and then multiplying the sum by three.<\/p>\n

Question 3.
\nUse a rectangular array to write the products in standard form.
\na. 2(x+10)
\nAnswer:
\n\"Eureka
\n2x+20<\/p>\n

b. 3(4b+12c+11)
\nAnswer:
\n\"Eureka
\n12b+36c+33<\/p>\n

Question 4.
\nUse the distributive property to write the products in standard form.
\na. 3(2x-1)
\nAnswer:
\n6x-3<\/p>\n

b. 10(b+4c)
\nAnswer:
\n10b+40c<\/p>\n

c. 9(g-5h)
\nAnswer:
\n9g-45h<\/p>\n

d. 7(4n-5m-2)
\nAnswer:
\n28n-35m-14<\/p>\n

e. a(b+c+1)
\nAnswer:
\nab+ac+a<\/p>\n

f. (8j-3l+9)6
\nAnswer:
\n48j-18l+54<\/p>\n

g. (40s+100t)\u00f710
\nAnswer:
\n4s+10t<\/p>\n

h. (48p+24)\u00f76
\nAnswer:
\n8p+4<\/p>\n

i. (2b+12)\u00f72
\nAnswer:
\nb+6<\/p>\n

j. (20r-8)\u00f74
\nAnswer:
\n5r-2<\/p>\n

k. (49g-7)\u00f77
\nAnswer:
\n7g-1<\/p>\n

l. (14g+22h)\u00f7\\(\\frac{1}{2}\\)
\nAnswer:
\n28g+44h<\/p>\n

Question 5.
\nWrite the expression in standard form by expanding and collecting like terms.
\na. 4(8m-7n)+6(3n-4m)
\nAnswer:
\n8m-10n<\/p>\n

b. 9(r-s)+5(2r-2s)
\nAnswer:
\n19r-19s<\/p>\n

c. 12(1-3g)+8(g+f)
\nAnswer:
\n-28g+8f+12<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 3 Exit Ticket Answer Key<\/h3>\n

A square fountain area with side length s ft. is bordered by two rows of square tiles along its perimeter as shown. Express the total number of grey tiles (the second border of tiles) needed in terms of s three different ways.
\nAnswer:
\n\"Engage<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 3 Lesson 3 Answer Key Eureka Math Grade 7 Module 3 Lesson 3 Example Answer Key Example 1. Represent 3+2 using a tape diagram. Answer: \u2192 Now, let\u2019s represent another expression, x+2. Make sure the units are the same size when you are drawing the known 2 units. … 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\/76807"}],"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=76807"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/76807\/revisions"}],"predecessor-version":[{"id":137754,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/76807\/revisions\/137754"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=76807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=76807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=76807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}