{"id":12682,"date":"2023-12-15T13:57:29","date_gmt":"2023-12-15T08:27:29","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=12682"},"modified":"2023-12-16T09:31:20","modified_gmt":"2023-12-16T04:01:20","slug":"envision-math-common-core-grade-5-answer-key-topic-14","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-5-answer-key-topic-14\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 14 Graph Points on the Coordinate Plane"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key<\/a>\u00a0Topic 14 Graph Points on the Coordinate Plane<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 5th Grade Answers Key Topic 14 Graph Points on the Coordinate Plane<\/h2>\n

\"Envision
\nenVision STEM Project: Earth’s Rotation<\/strong>
\nDo Research<\/strong> Use the Internet or other sources to find out more about Earth’s rotation. Investigate why it appears that the Sun is moving across the sky. Design a model to explain Earth’s day\/night cycle. Compare Earth’s rotation to another planet’s rotation.
\nWrite a Report: Journal<\/strong> Include what you found. Also in your report:
\n\u2022 Write a step-by-step procedure of how to use a ball and a flashlight to represent the day\/night cycle.
\n\u2022 Explain what happens if the ball rotates slowly. What happens if the ball rotates quickly?
\n\u2022 Make up and solve problems for plotting points and using graphs to show relationships.<\/p>\n

Review What You Know<\/strong><\/p>\n

A-Z Vocabulary<\/strong>
\nChoose the best term from the Word List. Write it on the blank.<\/p>\n

\u2022 equation
\n\u2022 factor
\n\u2022 line plot
\n\u2022 numerical expression
\n\u2022 variable<\/p>\n

Question 1.
\nA(n) ____ contains numbers and at least one operation.<\/p>\n

Answer:
\nA(n) numerical expression contains numbers and at least one operation.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA(n) numerical expression contains numbers and at least one operation.
\nfor example:
\n8x + 4y.
\nwhere x and y are variables.
\n8 and 4 are constants.<\/p>\n

Question 2.
\nA letter or symbol that represents an unknown amount is a(n) ____.<\/p>\n

Answer:
\nA letter or symbol that represents an unknown amount is a(n) variable.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA letter or symbol that represents an unknown amount is a(n) variable.
\nfor example:
\n8 + n = 12.
\na variable is a letter or symbol that represents a number(unknown quantity).<\/p>\n

Question 3.
\nA number sentence that uses the = symbol is a(n) ____.<\/p>\n

Answer:
\nA number sentence that uses the = symbol is a(n) equation.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA number sentence that uses the = symbol is a(n) equation.
\nfor example:
\n4 + 5 = 9.
\n8 – 2 = 6.<\/p>\n

\"Graph<\/p>\n

Question 4.
\nA display that shows Xs or dots above a number line is a(n) ___.<\/p>\n

Answer:
\nA display that shows Xs or dots above a number line is a(n) line plot.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA display that shows Xs or dots above a number line is a(n) line plot.
\nfor example:
\nx < 3.<\/p>\n

Evaluate Expressions<\/strong>
\nEvaluate each numerical expression.<\/p>\n

Question 5.
\n3 \u00d7 4 \u00d7 (10 – 7) \u00f7 2<\/p>\n

Answer:
\n3 x 4 x (10 – 7) \/ 2 = 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 3 x 4 x (10 – 7) \/ 2.
\n3 x 4 x (3)\/3.
\n3 x 4 x 1.
\n3 x 4 = 12.
\n3 x 4 x (10 – 7) \/ 2 = 12.<\/p>\n

Question 6.
\n(8 + 2) 6 – 4<\/p>\n

Answer:
\n(8 + 2) 6 – 4 = 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is (8 + 2) 6 – 4.
\n(6) 6 – 4.
\n(6) 2.
\n6 x 2 = 12.
\n(8 + 2) 6 – 4 = 12.<\/p>\n

Question 7.
\n8 + 2 \u00d7 6 – 4<\/p>\n

Answer:
\n8 + 2 x 6 – 4 = 20.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 8 + 2 x 6 – 4.
\n10 x 6 – 4.
\n10 x 2 = 20.
\n8 + 2 x 6 – 4 = 20.<\/p>\n

\"Graph<\/p>\n

Question 8.
\n40 \u00f7 5 + 5 \u00d7 (3 \u2013 1)<\/p>\n

Answer:
\n40 \/ 5 + 5 x (3 – 1) = 18.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 40 \/ 5 + 5 x (3 – 1).
\n40 \/ 5 + 5 x (2).
\n8 + 5 x 2.
\n8 + 10 = 18.
\n40 \/ 5 + 5 x (3 – 1) = 18.<\/p>\n

Question 9.
\n15 \u00f7 3 + 2 \u00d7 10<\/p>\n

Answer:
\n15 \/ 3 + 2 x 10 =<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 15 \/ 3 + 2 x 10.
\n5 + 2 x 10.
\n5 + 20.
\n25.
\n15 \/ 3 + 2 x 10 = 25.<\/p>\n

Question 10.
\n21 \u00d7 (8 – 6) \u00f7 14<\/p>\n

Answer:
\n21 x (8 – 6) \/ 14 = 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 21 x (8 – 6) \/ 14.
\n21 x ( 2) \/ 14.
\n21 x 1\/7.
\n21 \/ 7 = 3.
\n21 x (8 – 6) \/ 14 = 3.<\/p>\n

Write Expressions<\/strong>
\nWrite a numerical expression for each word phrase.<\/p>\n

Question 11.
\nThree less than the product of eight and six<\/p>\n

Answer:
\nThree less than the product of eight and six = 45.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthree less than the product of eight and six.
\nproduct of 6 and 8 is 48.
\n6 x 8 = 48.
\n48 – 3 = 45.<\/p>\n

Question 12.
\nThirteen more than the quotient of twenty divided by four<\/p>\n

Answer:
\nThirteen more than the quotient of twenty divided by four is 18.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthirteen more than the quotient of twenty divided by four is 18.
\n20 \/ 4 = 5.
\n5 + 13 = 18.
\nso thirteen more than the quotient of twenty divided by four is 18.<\/p>\n

Question 13.
\nFour times the difference between seven and two<\/p>\n

Answer:
\nFour times the difference between seven and two is 20.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nFour times the difference between seven and two is 20.
\n7 – 2 = 5.
\n4 x 5 = 20.
\nso four times the difference between seven and two is 20.<\/p>\n

Compare Expressions<\/strong><\/p>\n

Question 14.
\nUse < or > to compare 13 \u00d7 (54 + 28) and 13 \u00d7 54 + 28 without calculating. Explain your reasoning.<\/p>\n

Answer:
\n13 x (54 + 28) < 13 x 54 + 28.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 13 x (54 + 28).
\n13 x 82 = 1066.
\n13 x 54 + 28.
\n702 + 28 = 730.
\nso 13 x (54 + 28) < 13 x 54 + 28.<\/p>\n

Pick a Project<\/strong><\/p>\n

PROJECT 14A<\/strong>
\nWhat does a city planner do?
\nProject: Plan a City
\n\"Envision<\/p>\n

PROJECT 14B<\/strong>
\nWhat are some of the oldest childhood games?
\nProject: Make Your Own Game
\n\"Envision<\/p>\n

PROJECT 14C<\/strong>
\nHow can dogs help rescue people?
\nProject: Write a Story of a Missing Hiker
\n\"Envision<\/p>\n

PROJECT 14D<\/strong>
\nHow can artists use grids in their work?
\nProject: Draw a Picture Using a Grid
\n\"Envision<\/p>\n

Lesson 14.1 The Coordinate System<\/h3>\n

Activity<\/strong><\/p>\n

Solve&Share<\/strong>
\nOn the first grid, plot a point where two lines intersect. Name the location of the point. Plot and name another point. Work with a partner. Take turns describing the locations of the points on your first grid. Then plot the points your partner describes on your second grid. Compare your first grid with your partner’s second grid to see if they match. Use the grids below to solve this problem.
\n\"Envision<\/p>\n

You can use grid paper to graph ordered pairs. Show your work!
\n\"Envision<\/p>\n

Look Back! Construct Arguments<\/strong> Why does the order of the two numbers that name a point matter? Explain your thinking<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong>
\nHow Do You Name a Point on a Coordinate Grid?<\/p>\n

A.<\/strong>
\nA map shows the locations of landmarks and has guides for finding them. In a similar way, a coordinate grid is used to graph and name the locations of points in a plane.
\n\"Envision<\/p>\n

You can use ordered pairs to locate points on a coordinate grid.
\n\"Envision<\/p>\n

B.<\/strong>
\nA coordinate grid has a horizontal x-axis and a vertical y-axis. The point at which the x-axis and y-axis intersect is called the origin.
\n\"Envision<\/p>\n

C.<\/strong>
\nA point on the grid is named using an ordered pair of numbers. The first number, the x-coordinate, names the distance from the origin along the x-axis. The second number, the y-coordinate, names the distance from the origin along the y-axis.
\n\"Envision<\/p>\n

Convince Me! Reasoning<\/strong> in the example above, name the ordered pair for Point B if it is 3 units to the right of Point A. Tell how you decided<\/p>\n

Answer:
\nThe points are (3, 3).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point B if it is 3 units to the right of point A.
\nthe point is (1, 3).
\non the x-axis, the point is 1.
\non the y-axis, the point is 3.
\nso the point is (1,3).
\nif it is 3 units to the right of point A.
\nso the points are (3, 3).<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nYou are graphing Point E at (0,5). Do you move to the right zero units, or up zero units? Explain.<\/p>\n

Answer:
\nWe will move up to zero units.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (0, 5).
\nthe point 0 on the x-axis.
\nthe point 5 on the y-axis.
\nwe have to move up zero units.
\nso we will move up to zero units.<\/p>\n

Question 2.
\nA-Z Vocabulary What ordered pair names the origin of any coordinate grid?<\/p>\n

Answer:
\nThe points (0, 0) names the origin of any coordinate grid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pair names the origin of any coordinate grid.
\nthe points are (0, 0), (1, 1), (2, 2), (3, 3) and so on.
\nthe points (0, 0) names the origin of any coordinate grid.<\/p>\n

Question 3.
\nDescribe how to graph Point K at (5, 4).<\/p>\n

Answer:
\nPoint 5 on the x-axis and 4 on the y-axis.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point k at (5, 4) on the co-ordinate axis.
\nwe have to move up zero units.
\npoint 5 is on the x-axis.
\npoint 4 is on the y-axis.
\npoint 5 on the x-axis and 4 on the y-axis.<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 4 and 5, write the ordered pair for each point. Use the grid.<\/p>\n

Question 4.
\nB<\/p>\n

\"Envision<\/p>\n

Answer:
\nThe ordered pairs are (3, 2), (1, 4), and (5, 3).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe points are A, B, C, and D.
\nthe points are (1, 4).
\n1 is on the x-axis.
\n4 is on the y-axis.
\nthe point is (3, 2).
\n3 is on the x-axis.
\n2 is on the y-axis.
\nthe point is (5, 3).
\n5 is on the x-axis.
\n3 is on the y-axis.
\nso the ordered pairs are (3, 2), (1, 4), and (5, 3).<\/p>\n

Question 5.
\nA
\nAnswer:<\/p>\n

In 6 and 7, name the point for each ordered pair on the grid above.<\/p>\n

Question 6.
\n(5, 3)<\/p>\n

Answer:
\nPoint 5 moves up to 3 units.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 5 is on the x-axis.
\npoint 3 is on the y-axis.
\nso the point is (5, 3).
\npoint 5 moves up zero units.<\/p>\n

Question 7.
\n(1, 4)<\/p>\n

Answer:
\nPoint 1 moves up to 4 units.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 1 is on the x-axis.
\npoint 4 is on the y-axis.
\nso the point is (1, 4).
\npoint 1 moves up to 4 units.<\/p>\n

Independent Practice<\/strong><\/p>\n

In 8-13, write the ordered pair for each point. Use the grid.<\/p>\n

\"Envision<\/p>\n

Question 8.
\nT<\/p>\n

Answer:
\nThe ordered pair is (0, 5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 0 is on the origin.
\npoint 5 is on the y-axis.
\nthe ordered pair is (0, 5).
\nso the ordered pair is (0, 5).<\/p>\n

Question 9.
\nX<\/p>\n

Answer:
\nThe ordered pair is (4, 3).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 4 is on the x-axis.
\npoint 3 is on the y-axis.
\nthe ordered pair is (4, 3).
\nso the ordered pair is (4, 3).<\/p>\n

Question 10.
\nY<\/p>\n

Answer:
\nThe ordered pair is (1, 0).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 1 is on the X-axis.
\npoint 0 is on the y-axis.
\nthe ordered pair is (1, 0).
\nso the ordered pair is (1, 0).<\/p>\n

Question 11.
\nW<\/p>\n

Answer:
\nThe ordered pair is (3, 3).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 3 is on the x-axis.
\npoint 3 is on the y-axis.
\nthe ordered pair is (3, 3).
\nso the ordered pair is (3, 3).<\/p>\n

Question 12.
\nZ<\/p>\n

Answer:
\nThe ordered pair is (1, 4).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 1 is on the x-axis.
\npoint 4 is on the y-axis.
\nthe ordered pair is (1, 4).
\nso the ordered pair is (1, 4).<\/p>\n

Question 13.
\nS<\/p>\n

Answer:
\nThe ordered pair is (5, 5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 5 is on the x-axis.
\npoint 5 is on the y-axis.
\nthe ordered pair is (5, 5).
\nso the ordered pair is (5, 5).<\/p>\n

In 14-18, name the point for each ordered pair on the grid above.<\/p>\n

Question 14.
\n(2, 2)<\/p>\n

Answer:
\nThe point is L.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (2,2).
\n2 is on the x-axis.
\n2 is on the y-axis.
\nso the point is 2.<\/p>\n

Question 15.
\n(5, 4)<\/p>\n

Answer:
\nThe point is Q.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (5, 4).
\n5 is on the x-axis.
\n4 is on the y-axis.
\nso the point is Q.<\/p>\n

Question 16.
\n(1, 5)<\/p>\n

Answer:
\nThe point is N.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (1, 5).
\n1 is on the x-axis.
\n5 is on the y-axis.
\nso the point is N.<\/p>\n

Question 17.
\n(0, 3)<\/p>\n

Answer:
\nThe point is M.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (0, 3).
\n0 is on the x-axis.
\n3 is on the y-axis.
\nso the point is M.<\/p>\n

Question 18.
\n(4, 0)<\/p>\n

Answer:
\nThe point is P.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (4, 0).
\n4 is on the x-axis.
\n0 is on the y-axis.
\nso the point is p.<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 19.
\nHigher Order Thinking<\/strong> Describe to a friend how to find and name the ordered pair for Point R on the grid.
\n\"Envision<\/p>\n

Answer:
\nThe point is (4, 5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is R.
\n4 is on the x-axis.
\n5 is on the y-axis.
\nso the point is (4, 5).<\/p>\n

In 20-24, complete the table. List the point and ordered pair for each vertex of the pentagon at the right.<\/p>\n

\"Envision<\/p>\n

\"Envision<\/p>\n

Answer:
\nThe points are B, C, D, E, and F.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe point E is on the ordered pair (1, 1).
\nthe point D is on the ordered pair (1, 2).
\npoint C is on the ordered pair (1, 3).
\npoint B is on the ordered pair (2, 4).
\npoint F is on the ordered pair (3, 1).<\/p>\n

Question 25.
\nReasoning<\/strong> Why is the order important when naming or graphing the coordinates of a point?<\/p>\n

Answer:
\nThe order is important when naming or graphing the coordinates of a point.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe order is important because A is on the (3, 3).
\nB is on the (2, 4).
\nC is on the (1, 3).
\nD is on the (1, 2).
\nE is on the (1, 1).
\nF is on the (3, 1).
\nG is on the (5, 1).<\/p>\n

Question 26.
\nHow are the x-axis and the y-axis related on a coordinate grid?<\/p>\n

Answer:
\nThe x-axis and the y-axis are related.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe order is important because A is on the (3, 3).
\nB is on the (2, 4).
\nC is on the (1, 3).
\nD is on the (1, 2).
\nE is on the (1, 1).
\nF is on the (3, 1).
\nG is on the (5, 1).<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 27.
\nWhich of the following points is located at (4, 2)?
\n\"Envision
\nA. Point A
\nB. Point M
\nC. Point B
\nD. Point P<\/p>\n

Answer:
\nOption M is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (4, 2).
\n4 is located on the x-axis.
\n2 is located on the y-axis.
\nso option M is correct.<\/p>\n

Lesson 14.2 Graph Data Using Ordered Pairs<\/h3>\n

Activity<\/strong><\/p>\n

Sole & Share<\/strong>
\nGraph and label the point for each ordered pair below on the grid. Then connect the points with line segments to form a shape. What shape did you draw?<\/p>\n

Use Appropriate Tools<\/strong> You can graph points on a coordinate grid. Show your work!
\n\"Envision<\/p>\n

Answer:
\nThe shape formed is square.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pairs are (2, 1), (5, 1), (5, 4), and (2, 4).
\nthe point (2, 1) is on the A.
\nthe point (5, 1) is on the B.
\nthe point (5, 4) is on the C.
\nthe point (2, 4) is on the D.
\nso the shape formed is square.
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Look Back!<\/strong> What tool could you use to help connect points A, B, C, and D? Explain.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Do You Graph a Point on a Coordinate Grid?<\/p>\n

A.<\/strong>
\nThe table below shows the growth of a plant over a period of several days. Graph ordered pairs to show the plant’s growth.
\n\"Envision
\nLet x be the number of days and let y be the height of the plant in centimeters.
\n\"Envision
\nThe ordered pairs are (1, 4), (3, 8), (5, 10), (7, 11), and (9, 14).<\/p>\n

B.<\/strong>
\nStep 1<\/strong>
\nGraph the first point (1, 4).
\nStart at (0, 0). Move 1 unit to the right along the x-axis. Then move 4 units up.
\n\"Envision<\/p>\n

C.<\/strong>
\nStep 2<\/strong>
\nPlot the rest of the ordered pairs from the table. Use a ruler to connect the points.
\n\"Envision<\/p>\n

Convince Me! Reasoning<\/strong> Based on the data, about how tall was the plant on day 4? Day 8?<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nNatalie is graphing Point T at (1,8). Should she move to the right 8 units or up 8 units? Explain.<\/p>\n

Answer:
\nShe moves 8 units up.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point T at (1, 8).
\npoint 1 is on the x-axis.
\npoint 8 is on the y-axis.
\nso she moves 8 units up.<\/p>\n

Question 2.
\nDescribe how to graph the point (c, d).<\/p>\n

Answer:<\/p>\n

Do You Know How?<\/strong><\/p>\n

In 3-6, graph each point on the grid and label it with the appropriate letter.<\/p>\n

\"Envision<\/p>\n

Question 3.
\nE (1, 3)<\/p>\n

Answer:
\nThe point is E.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 1 is on the x-axis.
\npoint 3 is on the y-axis.
\nthe ordered pair is (1, 3).
\nso the point is E.<\/p>\n

Question 4.
\nF (4, 4)<\/p>\n

Answer:
\nThe point is F.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 4 is on the x-axis.
\npoint 4 is on the y-axis.
\nthe ordered pair is (4, 4).
\nso the point is F.<\/p>\n

Question 5.
\nG (5, 2)<\/p>\n

Answer:
\nThe point is G.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 5 is on the x-axis.
\npoint 2 is on the y-axis.
\nthe ordered pair is (5, 2).
\nso the point is G.<\/p>\n

Question 6.
\nH (0, 2)<\/p>\n

Answer:
\nThe point is H.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 0 is on the x-axis.
\npoint 2 is on the y-axis.
\nthe ordered pair is (0, 2).
\nso the point is H.
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Independent Practice<\/strong><\/p>\n

In 7-18, graph and label each point on the grid at the right.<\/p>\n

\"Envision<\/p>\n

Question 7.
\nJ (2, 6)<\/p>\n

Answer:
\nThe point is J.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 2 is on the x-axis.
\npoint 6 is on the y-axis.
\nthe ordered pair is (2, 6).
\nso the point is J.<\/p>\n

Question 8.
\nK (6, 2)<\/p>\n

Answer:
\nThe point is K.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 6 is on the x-axis.
\npoint 2 is on the y-axis.
\nthe ordered pair is (6, 2).
\nso the point is K.<\/p>\n

Question 9.
\nL (4, 5)<\/p>\n

Answer:
\nThe point is L.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 4 is on the x-axis.
\npoint 5 is on the y-axis.
\nthe ordered pair is (4, 5).
\nso the point is L.<\/p>\n

Question 10.
\nM (0, 8)<\/p>\n

Answer:
\nThe point is M.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 0 is on the x-axis.
\npoint 8 is on the y-axis.
\nthe ordered pair is (0, 8).
\nso the point is M.<\/p>\n

Question 11.
\nN (3, 9)<\/p>\n

Answer:
\nThe point is N.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 3 is on the x-axis.
\npoint 9 is on the y-axis.
\nthe ordered pair is (3, 9).
\nso the point is N.<\/p>\n

Question 12.
\nV (6, 6)<\/p>\n

Answer:
\nThe point is V.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 6 is on the x-axis.
\npoint 6 is on the y-axis.
\nthe ordered pair is (6, 6).
\nso the point is V.<\/p>\n

Question 13.
\nP (1, 4)<\/p>\n

Answer:
\nThe point is P.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 1 is on the x-axis.
\npoint 4 is on the y-axis.
\nthe ordered pair is (1, 4).
\nso the point is P.<\/p>\n

Question 14.
\nQ (5, 0)<\/p>\n

Answer:
\nThe point is Q.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 5 is on the x-axis.
\npoint 0 is on the y-axis.
\nthe ordered pair is (5, 0).
\nso the point is Q.<\/p>\n

Question 15.
\nR (7, 3)<\/p>\n

Answer:
\nThe point is R.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 7 is on the x-axis.
\npoint 3 is on the y-axis.
\nthe ordered pair is (7, 3).
\nso the point is R.<\/p>\n

Question 16.
\nS (7, 8)<\/p>\n

Answer:
\nThe point is S.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 7 is on the x-axis.
\npoint 8 is on the y-axis.
\nthe ordered pair is (7, 8).
\nso the point is S.<\/p>\n

Question 17.
\nT (8, 1)<\/p>\n

Answer:
\nThe point is T.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 8 is on the x-axis.
\npoint 1 is on the y-axis.
\nthe ordered pair is (8, 1).
\nso the point is T.<\/p>\n

Question 18.
\nU (3, 3)<\/p>\n

Answer:
\nThe point is E.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint 1 is on the x-axis.
\npoint 3 is on the y-axis.
\nthe ordered pair is (1, 3).
\nso the point is E.
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 19.
\nReasoning<\/strong> How is graphing (0, 2) different from graphing (2,0)?<\/p>\n

Answer:
\n(0, 2) is on the y-axis, and (2, 0) is on the x-axis.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pairs are (0, 2) and (2, 0).
\n(0, 2) is 2 units up from the origin.
\n(2, 0) is 2 units right from the origin.<\/p>\n

Question 20.
\nNumber Sense<\/strong> Shane took a test that had a total of 21 items. He got about of the items correct. About how many items did he get correct?<\/p>\n

Answer:<\/p>\n

Question 21.
\nHigher Order Thinking<\/strong> Point C is located at (10, 3) and Point D is located at (4,3). What is the horizontal distance between the two points? Explain.<\/p>\n

Answer:
\nThe distance between the points is (6, 0).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint C is located at (10, 3).
\npoint D is located at (4, 3).
\n10 – 4 = 6.
\n3 – 3 = 0.
\nso the distance between the points is (6, 0).<\/p>\n

Question 22.
\nLaurel buys 3 balls of yarn. Each ball of yarn costs $4.75. She also buys 2 pairs of knitting needles. Each pair costs $5.75. She pays for her purchase with two 20-dollar bills. What is her change?<\/p>\n

Answer:
\nThe change is $14.25.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLaurel buys 3 balls of yarn.
\nEach ball of yarn costs $4.75.
\nShe also buys 2 pairs of knitting needles.
\nEach pair costs $5.75.
\n3 x $4.75 = $14.25.
\n$5.75 x 2 = $11.5.
\n$14.25 + $11.5 = $25.75.
\n20 x 2 = 40 dollar bills.
\n40 – 25.75 = $14.25.<\/p>\n

Question 23.
\nGraph the points below on the grid at the right.
\nA (2, 4) B (1, 2) C (2, 0) D (3, 0) E (4, 2) F (3, 4)
\n\"Envision<\/p>\n

Answer:
\nThe points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4).
\npoint 2 is on the x-axis.
\npoint 4 is on the y-axis.
\npoint 1 is on the x-axis.
\npoint 2 is on the y-axis.
\npoint 2 is on the x-axis.
\npoint 0 is on the y-axis.
\npoint 3 is on the x-axis.
\npoint 4 is on the x-axis.
\npoint 2 is on the y-axis.
\npoint 3 is on the x-axis.
\npoint 4 is on the y-axis.
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Question 24.
\nAlejandro wants to connect the points to form a shape. What would be the most appropriate tool for him to use? Use the tool to connect the points.<\/p>\n

Answer:
\nThe shape formed is the hexagon.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAlejandro wants to connect the points to form a shape.
\npoints are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4).
\npoint 2 is on the x-axis.
\npoint 4 is on the y-axis.
\npoint 1 is on the x-axis.
\npoint 2 is on the y-axis.
\npoint 2 is on the x-axis.
\npoint 0 is on the y-axis.
\npoint 3 is on the x-axis.
\npoint 4 is on the x-axis.
\npoint 2 is on the y-axis.
\npoint 3 is on the x-axis.
\npoint 4 is on the y-axis.
\nso the shape formed is the hexagon.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 25.
\nTalia draws a map of her neighborhood on a coordinate grid. Her map shows the school at S (1,6), her house at H (4,3), and the library at L (7,2). Graph and label each location on the grid at the right.
\n\"Envision<\/p>\n

Answer:
\nPoints are (1, 6), (4, 3), and (7, 2).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTalia draws a map of her neighborhood on a coordinate grid.
\nHer map shows the school at S (1,6), her house at H (4,3), and the library at L (7,2).
\npoint 1 is on the x-axis.
\npoint 6 is on the y-axis.
\npoint 4 is on the x-axis.
\npoint 3 is on the y-axis.
\npoint 7 is on the x-axis.
\npoint 2 is on the y-axis.
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Lesson 14.3 Solve Problems Using Ordered Pairs<\/h3>\n

Activity<\/strong><\/p>\n

Solve&Share<\/strong>
\nThe table below uses number patterns to describe changes in the width and length of a rectangle. Let x be the width and y be the length. Then plot each of the four ordered pairs in the table on the coordinate grid. What do you think the length is if the width is 5?
\n\"Envision<\/p>\n

You can make a graph to help solve the problem. Show your work!
\n\"Envision<\/p>\n

Look Back! Look for Relationships<\/strong> What pattern do the points form on your graph?<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Use Ordered Pairs to Solve Problems?<\/p>\n

A.<\/strong>
\nBoth Ann and Bill earn the amount shown each week. Ann starts with no money, but Bill starts with $5. How much will Bill have when Ann has $30? Represent this situation using a table and a graph.<\/p>\n

You know that when Ann has $0, Bill has $5.
\n\"Envision<\/p>\n

B.<\/strong>
\nMake a table showing how much money Ann and Bill have after each week.
\n\"Envision
\nLet x = Ann’s earnings and y = Bill’s earnings.<\/p>\n

C.<\/strong>
\nPlot the ordered pairs from the table. Draw a line to show the pattern. Extend your line to the point where the x-coordinate is 30. The corresponding y-coordinate is 35.
\n\"Envision
\nSo, Bill has $35 when Ann has $30.<\/p>\n

Convince Me! Look for Relationships<\/strong> What is the relationship between Bill’s earnings and Ann’s earnings?<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nIn the example on page 574, find another point on the line. What does this point represent?<\/p>\n

Answer:<\/p>\n

Question 2.
\nAlgebra In the example on page 574, write an equation to show the relationship between Ann’s earnings and Bill’s earnings. Remember to let x = Ann’s earnings and y = Bill’s earnings.<\/p>\n

Answer:
\nLet x = Ann’s earnings.
\ny = Bill’s earnings.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nx + 5.
\nAnn has $30 and $35.
\n$30 + 5 = $35.<\/p>\n

Do You Know How?<\/strong><\/p>\n

Write the missing coordinates and tell what the point represents.<\/p>\n

Question 3.
\n\"Envision<\/p>\n

Answer:
\nThe missing coordinates are (5, 200).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe points are (20, 800), (15, 600), (10, 400).
\n20 – 5 = 15.
\n15 – 5 = 10.
\n10 – 5 = 5.
\n800- 200 = 600.
\n600 – 200 = 400.
\n400 – 200 = 200.
\nso the missing coordinates are (5, 200).<\/p>\n

Independent Practice<\/strong><\/p>\n

In 4 and 5, find the missing coordinates and tell what the point represents.<\/p>\n

Question 4.
\n\"Envision<\/p>\n

Answer:
\nThe missing coordinates are (900, 800).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pairs are (1500, 1200), (1200, 1000), (600, 600), and (300, 400).
\non x-axis subtract 300.
\n1500 – 300 = 1200.
\n1200 – 300 = 900.
\n900 – 300 = 600.
\n600 – 300 = 300.
\non y-axis subtract 200.
\n1200 – 200 = 1000.
\n1000 – 200 = 800.
\n800 – 200 = 600.
\n600 – 200 = 400.
\nso the missing coordinates are (900, 800).<\/p>\n

Question 5.
\n\"Envision<\/p>\n

Answer:
\nThe missing coordinates are (200, 150).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pairs are (600, 550), (500, 450), (400, 350), (300, 250), and (100, 50).
\nsubtract 100 on x-axis.
\nsubtract 100 on y-axis.
\n600 – 100 = 500.
\n500 – 100 = 400.
\n400 – 100 = 300.
\n300 – 100 = 200.
\n200 – 100 = 100.
\nso the missing coordinates are (200, 150).<\/p>\n

Question 6.
\nFor Exercise 5, find two other points on the line. Then graph and label them. Describe the relationship between deer sightings and elk sightings.<\/p>\n

Answer:<\/p>\n

Problem Solving<\/strong><\/p>\n

In 7 and 8, use the table at the right.<\/p>\n

Question 7.
\nGraph the points in the table on the grid at the right. Then draw a line through the points.
\n\"Envision<\/p>\n

Answer:
\nTime(h) is on the x-axis.
\npages read is on the y-axis.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nin 1 hour number of pages read is 20.
\nin 2 hours number of pages read is 40.
\nin 3 hours number of pages read is 60.
\nin 4 hours number of pages read is 80.
\nin 5 hours number of pages read is 100.<\/p>\n

Question 8.
\nLook for Relationships<\/strong> If the pattern continues, how many pages will have been read after 6 hours? Extend your graph to solve.
\n\"Envision<\/p>\n

Answer:
\nThe number of pages that will have been read after 6 hours = 120.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nin 1 hour number of pages read is 20.
\nin 2 hours number of pages read is 40.
\nin 3 hours number of pages read is 60.
\nin 4 hours number of pages read is 80.
\nin 5 hours number of pages read is 100.
\nin 6 hours number of pages read is 120.<\/p>\n

Question 9.
\nHigher Order Thinking<\/strong> Suppose you have a graph of speed that shows a lion can run four times as fast as a squirrel. Name an ordered pair that shows this relationship. What does this ordered pair represent?<\/p>\n

Answer:
\nThe ordered pair represents (1, 4).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe lion can run four times as fast as a squirrel.
\nx + 4y.
\nx represents the speed of a squirrel.
\ny represents the speed of a lion.
\nso a lion can run four times as fast as a squirrel.<\/p>\n

Question 10.
\nNumber Sense<\/strong> Candace drives a total of 48 miles each day to get to work and back home. She works 5 days a week. Her car gets 21 miles per gallon of gas. About how many gallons of gas does she need to drive to work and back home each week?!<\/p>\n

Answer:
\nThe number of gallons of gas does she need to drive to work = 48 gallons.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nCandace drives a total of 48 miles each day to get to work and back home.
\nShe works 5 days a week.
\nHer car gets 21 miles per gallon of gas.
\n48 x 5 = 240.
\n240 \/ 5 = 48.
\nso the number of gallons of gas does she need to drive to work.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 11.
\nWhat does the point (15, 4) represent on the graph at the right?
\n\"Envision
\nA. The ant crawled 15 meters in 19 seconds.
\nB. The ant crawled 15 meters in 4 seconds.
\nC. The ant crawled 4 meters in 19 seconds.
\nD. The ant crawled 4 meters in 15 seconds.<\/p>\n

Answer:
\nOption B is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint (15, 4) is in the coordinate plane.
\n15 is on the x-axis.
\n4 is on the y-axis.
\nthe ant crawled 15 meters in 4 seconds.
\nso option B is correct.<\/p>\n

Question 12.
\nWhat does the point (20, 5) represent on the graph?
\nA. In 20 seconds, the ant crawled 5 centimeters.
\nB. In 20 seconds, the ant crawled 5 meters.
\nC. In 5 seconds, the ant crawled 20 meters.
\nD. In 5 seconds, the ant crawled 15 meters.<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (20, 5).
\n20 is on the x-axis.
\n5 is on the y-axis.
\nin 5 seconds the ant crawled 20 meters.
\nso option C is correct.<\/p>\n

Lesson 14.4 Reasoning<\/h3>\n

Activity<\/strong><\/p>\n

Problem Solving<\/strong><\/p>\n

Solve & Share<\/strong>
\nSix clowns apply for a circus job. The specific job requires the clown to have a clown shoe size less than 15 inches and to be shorter than 5 ft 8 in. tall.
\nHow many clowns meet the size requirements for the job? Complete the graph below to help you decide.<\/p>\n

\"Envision<\/p>\n

Thinking Habits<\/strong>
\nBe a good thinker! These questions can help you.
\n\u2022 What do the numbers and symbols in the problem mean?
\n\u2022 How are the numbers or quantities related?
\n\u2022 How can I represent a word problem using pictures, numbers, or equations?
\n\"Envision<\/p>\n

Look Back! Reasoning<\/strong> How can you use reasoning about the completed graph to find the number of clowns that meet the requirements? Explain.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Use Reasoning to Solve Mathematical Problems?<\/p>\n

A.<\/strong>
\nIn 1705, a ship sank in the ocean at the point shown. Every year the ocean currents moved the ship 1 mile east and 2 miles north. Where was the ship located after 4 years? Where was the ship located after 10 years? Tell how you decided.
\n\"Envision<\/p>\n

What do I need to do to solve the problem?
\nI need to find the ship’s location after 4 years and after 10 years.<\/p>\n

B.<\/strong>
\nHow can I use reasoning to solve this problem?
\nI can
\n\u2022 use what I know about graphing points.
\n\u2022 graph ordered pairs.
\n\u2022 look for relationships in the coordinates.
\n\u2022 decide if my answer makes sense.<\/p>\n

Here’s my thinking..
\n\"Envision<\/p>\n

C.<\/strong>
\nI will use the graph to show the location each year for 4 years. Each point is 1 mile east and 2 miles north from the previous point.
\nAfter 4 years the ship was at (8, 14).
\nI see a pattern. The x-coordinate increases by 1, and the y-coordinate increases by 2:
\n(4, 6), (5, 8), (6, 10), (7, 12), (8, 14)
\n\"Envision
\nI can continue the pattern for another 6 years:
\n(9,16), (10, 18), (11, 20), (12, 22), (13, 24), (14, 26)
\nAfter 10 years, the ship was at (14, 26).<\/p>\n

Convince Me! Make Sense and Persevere<\/strong> How could you decide if your answers make sense?<\/p>\n

Guided Practice<\/strong><\/p>\n

Tanya marked a grid in her garden. She planted a rose bush at (3, 1). She moved 2 feet east and 1 foot north and planted the second rose bush. She continued planting rose bushes so that each bush is 2 feet east and 1 foot north of the previous bush.<\/p>\n

\"Envision<\/p>\n

Question 1.
\nHow can a coordinate grid help you reason about the problem?<\/p>\n

Answer:
\nThe point is (3, 1), (5, 2), and (7, 3).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (3, 1).
\nShe moved 2 feet east and 1 foot north and planted the second rose bush.
\n3 + 2 = 5.
\n5 + 2 = 7.
\n1 + 1 = 2.
\n2 + 1 = 3.
\nso the points are (3, 1), (5, 2), and (7, 3).
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Question 2.
\nDraw and label the locations of the first four bushes on the grid. Do Tanya’s 0 2 bushes lie on a straight line? How do you know?<\/p>\n

Answer:
\nThe bushes lie in a straight line.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (3, 1).
\nShe moved 2 feet east and 1 foot north and planted the second rose bush.
\n3 + 2 = 5.
\n5 + 2 = 7.
\n1 + 1 = 2.
\n2 + 1 = 3.
\nso the points are (3, 1), (5, 2), and (7, 3).<\/p>\n

Question 3.
\nWhat are the locations of the fifth and ninth rose bushes?<\/p>\n

Answer:
\nThe locations of the fifth and ninth rose bushes are in a straight line.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (3, 1).
\nShe moved 2 feet east and 1 foot north and planted the second rose bush.
\n3 + 2 = 5.
\n5 + 2 = 7.
\n7 + 2 = 9.
\n1 + 1 = 2.
\n2 + 1 = 3.
\n3 + 1 = 4.
\nso the points are (3, 1), (5, 2), and (7, 3), (9, 4).<\/p>\n

Independent Practice<\/strong><\/p>\n

Reasoning<\/strong>
\nA marching band uses a grid to determine the members’ positions. Juan starts at (2, 2). Every 15 seconds, he moves 4 yards east and 3 yards north.<\/p>\n

\"Envision<\/p>\n

Question 4.
\nHow can you model this problem?<\/p>\n

Answer:
\nAfter 15 seconds Juan moves (6, 5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA marching band uses a grid to determine the members’ positions.
\nJuan starts at (2, 2).
\nEvery 15 seconds, he moves 4 yards east and 3 yards north.
\n2 + 4 = 6.
\n2 + 3 = 5.
\nso after 15 seconds Juan moves (6, 5).<\/p>\n

Question 5.
\nDraw and label the locations of Juan’s first four positions. Do the points form a pattern? How can you tell?<\/p>\n

Answer:
\nJuan’s first four positions are (6, 5), (10, 8), (14, 11), and (18, 14).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA marching band uses a grid to determine the members’ positions.
\nJuan starts at (2, 2).
\nEvery 15 seconds, he moves 4 yards east and 3 yards north.
\n2 + 4 = 6, 6 + 4 = 10, 10 + 4 = 14, and 14 + 4 = 18.
\n2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and 11 + 3 = 14.
\nso Juan’s first four positions are (6, 5), (10, 8), (14, 11), and (18, 14).<\/p>\n

Question 6.
\nWhat will Juan’s location be after 60 seconds? 90 seconds? How does the coordinate grid help you reason about the locations?<\/p>\n

Answer:
\nJuan,s location be after 60 and 90 seconds are (14, 11), and (18, 14).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA marching band uses a grid to determine the members’ positions.
\nJuan starts at (2, 2).
\nEvery 15 seconds, he moves 4 yards east and 3 yards north.
\n2 + 4 = 6, 6 + 4 = 10, 10 + 4 = 14, and 14 + 4 = 18.
\n2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and 11 + 3 = 14.
\nso Juan,s location be after 60 and 90 seconds are (14, 11), and (18, 14).<\/p>\n

Problem Solving<\/strong><\/p>\n

Performance Task<\/strong><\/p>\n

Rozo Robot<\/strong>
\nA toy company is testing Rozo Robot. Rozo is 18 inches tall and weighs 2 pounds. The employees of the company marked a grid on the floor and set Rozo at (2,5). They programmed Rozo to walk 3 yards east and 4 yards north each minute. What will Rozo’s location be after 7 minutes?<\/p>\n

\"Envision<\/p>\n

Question 7.
\nMake Sense and Persevere<\/strong> Do you need all of the information given in the problem to solve the problem? Describe any information that is not needed.<\/p>\n

Answer:<\/p>\n

Question 8.
\nModel with Math<\/strong> Label the graph and plot Rozo’s starting position. Then plot and label Rozo’s position at the end of each of the first 4 minutes.
\nAnswer:<\/p>\n

Question 9.
\nUse Appropriate Tools<\/strong> What tool would you choose for drawing a line segment between points on a coordinate grid? Explain your thinking.
\nAnswer:<\/p>\n

You can use the coordinate grid to reason about relationships between the points
\n\"Envision<\/p>\n

Question 10.
\nLook for Relationships<\/strong> Describe the relationships between the coordinates of the points that represent Rozo’s locations.
\nAnswer:<\/p>\n

Question 11.
\nReasoning<\/strong> What will Rozo’s location be after 7 minutes? Explain how you determined your answer.
\nAnswer:<\/p>\n

Topic 14 Fluency Practice<\/h3>\n

Activity<\/strong><\/p>\n

Point & Tally<\/strong><\/p>\n

Find a partner. Get paper and a pencil. Each partner chooses light blue or dark blue.
\nAt the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers.
\nThe partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.
\n\"Envision<\/p>\n

\"Envision<\/p>\n

Topic 14 Vocabulary Review<\/strong><\/p>\n

Glossary<\/strong><\/p>\n

Understand Vocabulary<\/strong><\/p>\n

Choose the best term from the Word List. Write it on the blank.<\/p>\n

Word List<\/strong>
\n\u2022 coordinate grid
\n\u2022 ordered pair
\n\u2022 origin
\n\u2022 x-axis
\n\u2022 x-coordinate
\n\u2022 y-axis
\n\u2022 y-coordinate<\/p>\n

Question 1.
\nThe point where the axes of a coordinate grid intersect is the _____<\/p>\n

Answer:
\nThe point where the axes of a coordinate grid intersect is the origin.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point where the axes of a coordinate grid intersect is the origin.
\nfor example:
\n(x, y) = (3, 2).<\/p>\n

Question 2.
\nA(n) ____ names an exact location on a coordinate grid.<\/p>\n

Answer:
\nA(n) coordinate grid names an exact location on a coordinate grid.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA(n) coordinate grid names an exact location on a coordinate grid.
\nfor example:
\n(2, 3) is on the coordinate plane.
\n2 is on the x-axis.
\n3 is on the y-axis.<\/p>\n

Question 3.
\nThe first number of an ordered pair describes the distance from the origin along the ____<\/p>\n

Answer:
\nThe first number of an ordered pair describes the distance from the origin along with the ordered pair.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe first number of an ordered pair describes the distance from the origin along with the ordered pair.
\nfor example:
\n(4, 5) 4 units on the x-axis.
\n5 units on the y-axis.<\/p>\n

Question 4.
\nThe second number of an ordered pair is the ______<\/p>\n

Answer:
\nThe second number of an ordered pair is the y-coordinate.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe second number of an ordered pair is the y-coordinate.
\nfor example:
\nIn an ordered pair, the first number is always the x-coordinate.
\nthe second number is the y-coordinate.<\/p>\n

Question 5.
\nA ____ is formed by two number lines that intersect at a right angle.<\/p>\n

Answer:
\nA coordinate plane is formed by two number lines that intersect at a right angle.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA coordinate plane is formed by two number lines that intersect at a right angle.
\nfor example:
\nx-axis = horizontal number line.
\ny-axis = vertical number line.
\norigin = where the number lines intersect.
\nthe coordinates of the origin are (0, 0).<\/p>\n

Draw a line from each lettered point in Column A to the ordered pair it represents.<\/p>\n

\"Envision<\/p>\n

\"Envision<\/p>\n

\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Use Vocabulary in Writing<\/strong><\/p>\n

Question 12.
\nWhy is the order of the coordinates important in an ordered pair? Use terms from the Word List in your explanation.<\/p>\n

Answer:
\nThe order of the coordinates is important because it forms a shape, a straight line.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoints are A(5, 2), B(1, 7), C(2, 3), D(0, 7), E(7, 1), and F(0, 6).
\nthe points formed a shape.
\nso the order of the coordinates is important in an ordered pair.<\/p>\n

Topic 14 Reteaching<\/h3>\n

Set A<\/strong>
\npages 565-568<\/p>\n

What ordered pair names Point A?
\nStart at the origin. The x-coordinate is the horizontal distance along the x-axis. The y-coordinate is the vertical distance along the y-axis.
\n\"Envision
\nPoint A is at (7, 3).<\/p>\n

Remember<\/strong> to first find the x-coordinate. Then find the y-coordinate. Write the coordinates in (x, y) order.<\/p>\n

Use the grid to answer the questions.<\/p>\n

Question 1.
\nWhich point is located at (9, 5)?<\/p>\n

Answer:
\nPoint is located at (9, 5) is R.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\npoint is (9, 5).
\n9 is on the x-axis.
\n5 is on the y-axis.
\nso the point is located at (9, 5) is R.<\/p>\n

Question 2.
\nWhich point is located at (2, 3)?<\/p>\n

Answer:
\nPoint is located at (2, 3) is K.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (2, 3).
\n2 is on the x-axis.
\n3 is on the y-axis.
\nso the point is located at (2, 3) is K.<\/p>\n

Question 3.
\nWhat ordered pair names Point T ?<\/p>\n

Answer:
\nPoint is located at (3, 4) is T.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (3, 4).
\n3 is on the x-axis.
\n4 is on the y-axis.
\nso the point is located at (3, 4) is T.<\/p>\n

Question 4.
\nWhat is the ordered pair for the origin?<\/p>\n

Answer:
\nPoint is located at (0, 7).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (0,7).
\n0 is on the x-axis.
\n7 is on the y-axis.
\nso the point is located at (0, 7) is the origin.<\/p>\n

Set B<\/strong>
\npages 569-572, 573-576
\nIn the table, the x-coordinate is in the left column and the y-coordinate is in the right column. Use the table to plot the ordered pairs. Then draw a line to connect the points.
\n\"Envision<\/p>\n

Remember<\/strong> that you can use a tool, such as a ruler, to draw a line to connect the points on the graph.<\/p>\n

Question 1.
\nUse the table below to plot the ordered pairs. Then complete the graph by connecting the points.
\n\"Envision<\/p>\n

Answer:
\nThe points are (2, 1), (4, 2), (6, 3), and (8, 4).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe points on the x-axis are 2, 4, 6, and 8.
\nthe points on the y-axis are 1, 2, 3, and 4.
\nso the ordered pairs are (2, 1), (4, 2), (6, 3), and (8, 4).
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Question 2.
\nWrite two ordered pairs with x-coordinates greater than 10 that are on the line.<\/p>\n

Answer:
\nThe two ordered pairs are (10, 5), and (12, 6).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe points on the x-axis are 2, 4, 6, and 8.
\nthe points on the y-axis are 1, 2, 3, and 4.
\n2 + 2 = 4.
\n4 + 2 = 6.
\n6 + 2 = 8.
\n1 + 1 = 2.
\n2 + 1 = 3.
\n3 + 1 = 4.
\n4 + 1 = 5.
\nso the two ordered pairs are (10, 5), and (12, 6).<\/p>\n

Set C<\/strong>
\npages 577-580
\nThink about these questions to help you use reasoning to solve problems.<\/p>\n

Thinking Habits<\/strong>
\n\u2022 What do the numbers and symbols in the problem mean?
\n\u2022 How are the numbers or quantities related?
\n\u2022 How can I represent a word problem using pictures, numbers, or equations?<\/p>\n

Remember<\/strong> that you can use a graph or a table to reason about and solve word problems.
\nA company uses the graph to show how many packages each truck driver delivers. How many packages will one truck driver deliver in a 7-hour day?
\n\"Envision<\/p>\n

Question 1.
\nWhat information can help you solve the problem?<\/p>\n

Answer:
\nThe number of packages each truck driver delivers in hours.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of packages each truck driver delivers in hours.
\nin 1 hour the number of packages is 15.
\nin 2 hours the number of packages is 30.
\nin 3 hours the number of packages is 45.
\nin 4 hours the number of packages is 60.<\/p>\n

Question 2.
\nHow can you find the number of packages a driver delivers in 3 hours?<\/p>\n

Answer:
\nThe number of packages a driver delivers in 3 hours is 45.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of packages each truck driver delivers in hours.
\nin 1 hour the number of packages is 15.
\nin 2 hours the number of packages is 30.
\nin 3 hours the number of packages is 45.
\nin 4 hours the number of packages is 60.
\nso the number of packages a driver delivers in 3 hours is 45.<\/p>\n

Question 3.
\nHow many packages will one truck driver deliver in a 7-hour day?<\/p>\n

Answer:
\nThe number of packages will one truck deliver in a 7-hour day is 105.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of packages each truck driver delivers in hours.
\nin 1 hour the number of packages is 15.
\nin 2 hours the number of packages is 30.
\nin 3 hours the number of packages is 45.
\nin 4 hours the number of packages is 60.
\nin 5 hours the number of packages is 75.
\nin 6 hours the number of packages is 90.
\nin 7 hours the number of packages is 105.<\/p>\n

Question 4.
\nHow can you find how many hours it will take for one truck driver to deliver 120 packages?<\/p>\n

Answer:
\nThe number of hours is 8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of packages each truck driver delivers in hours.
\nin 1 hour the number of packages is 15.
\nin 2 hours the number of packages is 30.
\nin 3 hours the number of packages is 45.
\nin 4 hours the number of packages is 60.
\nin 5 hours the number of packages is 75.
\nin 6 hours the number of packages is 90.
\nin 7 hours the number of packages is 105.<\/p>\n

Topic 14 Assessment Practice<\/h3>\n

Use the coordinate grid below to answer 1-4.<\/p>\n

\"Envision<\/p>\n

Question 1.
\nWhich is the ordered pair for Point Y?
\nA. (4, 5)
\nB. (4, 9)
\nC. (7, 9)
\nD. (9, 4)<\/p>\n

Answer:
\nOption B is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (4, 9).
\n4 is on the x-axis.
\n9 is on the y-axis.
\nso option B is correct.<\/p>\n

Question 2.
\nWhich point is located at (5, 2) on the coordinate grid?
\nA. M
\nB. N
\nC. Q
\nD. P<\/p>\n

Answer:
\nOption B is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (5, 2).
\n5 is on the x-axis.
\n2 is on the y-axis.
\nso option B is correct.<\/p>\n

Question 3.
\nWhat is the ordered pair for Point Z?<\/p>\n

Answer:
\nThe ordered pair for point Z is (9, 1).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (9, 1).
\n9 is on the x-axis.
\n1 is on the y-axis.
\nso the ordered pair for point Z is (9, 1).<\/p>\n

Question 4.
\nWhat is the ordered pair for Point P?<\/p>\n

Answer:
\nThe ordered pair for point P is (4, 5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (4, 5).
\n4 is on the x-axis.
\n5 is on the y-axis.
\nso the ordered pair for point P is (4, 5).<\/p>\n

Question 5.
\nEach year, Ginny recorded the height of a tree growing in her front yard. The graph below shows her data.
\n\"Envision
\nWhat does the point (1, ?) represent?<\/p>\n

Answer:
\nThe point (1, 5) represents the height in feet.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nGinny recorded the height of a tree growing in her front yard.
\nthe points on the x-axis are 0, 1, 2, 3, and 4.
\nthe points on the y-axis are 4, 5, 6, 7, and 8.
\nadd the 1 on the x and y-axis.
\nso the point (1, 5) represents the height in feet.<\/p>\n

Question 6.
\nExplain how to graph the point (6, 4) on a coordinate plane.<\/p>\n

Answer:
\nPoint 6 is on the x-axis and 4 is on the y-axis.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe point is (6, 4).
\npoint 6 is on the x-axis and 4 is on the y-axis.<\/p>\n

Question 7.
\nVarsha draws a map of her neighborhood on a coordinate plane. Her map shows the park at P (3, 1), her house at H (5, 6), and the soccer field at S (2,4). Graph and label each location below.
\n\"Envision<\/p>\n

Answer:
\nThe point is P(3, 1) is the park.
\nthe point H(5, 6) is her house.
\nthe point S(2, 4) is the soccer field.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nVarsha draws a map of her neighborhood on a coordinate plane.
\nHer map shows the park at P (3, 1), her house at H (5, 6), and the soccer field at S (2,4).
\nthe point is p(3, 1) is the park.
\nthe point H(5, 6) is her house.
\nthe point S(2, 4) is the soccer field.
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Question 8.
\nYesterday Billy earned $30 trimming hedges for Mrs. Gant. Today he will earn $10 an hour for weeding her garden. If he weeds her garden for 8 hours, how much in all will he earn working for Mrs. Gant?
\n\"Envision
\nA. $40
\nB. $ 80
\nC. $ 110
\nD. $ 120<\/p>\n

Answer:
\nOption B is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBilly earned $30 trimming hedges for Mrs. Gant.
\nToday he will earn $10 an hour for weeding her garden.
\nIf he weeds her garden for 8 hours,
\n8 x $10 = $80.
\nso option B is correct.<\/p>\n

Question 9.
\nHow is graphing (0, 12) different from graphing (12, 0)?<\/p>\n

Answer:
\n(0, 12) is different from (12, 0).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pairs are (0, 12) and (12, 0).
\n(0, 12) is on the y-coordinate.
\n(12, 0) is on the x-coordinate.
\nso (0, 12) is different from (12, 0).<\/p>\n

Question 10.
\nWhat ordered pair represents the point where the x-axis and y-axis intersect? What is the name of this point?<\/p>\n

Answer:
\nThe ordered pair (0, 0) represents the point where the x-axis and y-axis intersect.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe ordered pair (0, 0) represents the origin.
\nthe x-axis and y-axis intersect are called the origin.
\nso the ordered pair (0, 0) represents the point where the x-axis and y-axis intersect.<\/p>\n

Question 11.
\nThree vertices of a rectangle are located at (1, 4), (1, 2), and (5, 2).
\nA. Graph and label each of the three vertices below.
\n\"Envision
\nB. What are the coordinates of the fourth vertex of the rectangle?<\/p>\n

Answer:
\nThe coordinates of the fourth vertex of the rectangle are (5, 4).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthree vertices of a rectangle are located at (1, 4), (1, 2), and (5, 2).
\nthe other side is (5, 4).
\nfor the rectangle, opposite sides are equal in length.
\nso the coordinates of the fourth vertex of the rectangle are (5, 4).
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n

Topic 14 Performance Task<\/h3>\n

Digging for Dinosaur Bones<\/strong>
\nOmar’s mother is a paleontologist. She digs up and studies dinosaur bones. Omar is helping at the dig site.<\/p>\n

Question 1.
\nThe Dinosaur Bone Dig 1 grid shows the location of the tent and the triceratops skull Omar’s mother found.
\nPart A<\/strong>
\nWhat ordered pair names the location of the triceratops skull? Explain how you know.
\n\"Envision
\nPart B<\/strong>
\nomar found a leg bone at (4, 12). Graph this point on the coordinate grid and label it L. Explain how you located the point using the terms origin, x-coordinate, x-axis, y-coordinate, and y-axis.
\nPart C<\/strong>
\nNext, Omar dug 3 meters east and 1 meter south from the leg bone. Graph a point where Omar dug and label it A. What ordered pair names the point?<\/p>\n

Answer:
\nPart A: (6, 2).
\nPart B: (4, 12).
\nPart C: (7, 13).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOmar found a leg bone at (4, 12).
\nOmar dug 3 meters east and 1 meter south from the leg bone.
\n4 + 3 = 7.
\n12 + 1 = 13.
\nso part C is (7, 13).<\/p>\n

Question 2.
\nOmar’s mother started at the triceratops skull. She kept moving east 1 meter and north 2 meters to dig for more dinosaur bones. Complete the table and the graph to find how far north she was when she was 11 meters east of the tent.<\/p>\n

Answer:
\nWhen she was 11 meters east of the tent, the far = 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOmar’s mother started at the triceratops skull.
\nShe kept moving east 1 meter and north 2 meters to dig for more dinosaur bones.
\n(4, 12) is the ordered pair given?
\n4 + 1 = 5.
\n12 + 2 = 14.
\n(5, 14) is the ordered pair.
\n11 – 5 = 6.
\nso when was 11 meters east of the tent, the far is 6 meters.
\nPart A<\/strong>
\nComplete the table of ordered pairs.
\n\"Envision<\/p>\n

Part B<\/strong>
\nGraph the points from the table in Part A on the coordinate grid in the Dinosaur Bone Dig 2 grid. Draw a line through the points. Extend the line past 11 meters east.
\nPart C<\/strong>
\nHow far north was Omar’s mother when she was 11 meters east of the tent? Explain how to use the graph to solve and why your answer makes sense.<\/p>\n

Answer:
\nThe ordered pairs are (6, 2), (7, 3), ( 8, 4), and (9, 5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEast of the tent in meters is given.
\nthey are 6, 7, 8, and 9 meters are given.
\nthe first ordered pair is (6, 2) is given.
\nso the ordered pairs are (7, 3), (8, 4), and (9, 5).
\nwhen she was 11 meters east of the tent is (11, 7).
\n\"Envision-Math-Common-Core-5th-Grade-Answers-Key-Topic-14-Graph<\/p>\n","protected":false},"excerpt":{"rendered":"

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