T632 Mathematics Success Grade 6 [OBJECTIVE] The students will draw polygons in the coordinate plane given the coordinates for the vertices and use the coordinates to find the length of the sides in mathematical and real-world problems. [PREREQUISITE SKILLS] Plotting points, absolute value [MATERIALS] Student pages S329 S342 [ESSENTIAL QUESTIONS] 1. When plotting points on the coordinate plane, what type of line is created when the x-coordinates are the same? Explain your answer. 2. Describe what type of line is created when the y-coordinates are the same for two points on the coordinate plane. Explain your answer. 3. Explain how to find the length of the side of a rectangle that is plotted within one quadrant. Explain how to find the length of the side of a rectangle that has the two vertices in two different quadrants. [WORDS FOR WORD WALL] quadrants, coordinate plane, absolute value, x-coordinate, y-coordinate, area, perimeter [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) *For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson. [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Verbal Description, Pictorial Representation, Concrete Representation, Graphic Organizer [WARM-UP] (IP, WG,) S329 (Answers on T640.) Have students turn to S329 in their books to begin the Warm-Up. Students will be plotting ordered pairs containing rational numbers. Have students complete the activity and then review the answers as a whole group. {Verbal Description} [HOMEWORK] Take time to go over the homework from the previous night. [LESSON] [1 2 days (1 day = 80 minutes) - (M, GP, WG, CP, IP)]
Mathematics Success Grade 6 T633 SOLVE Problem Coordinate Plane Review Step 1: Direct students to the coordinate plane on S331. (WG, CP, IP) S330 (Answers on T641.) Have students turn to S330 in their books. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to draw polygons in the coordinate plane given the coordinates for the vertices and use the coordinates to find the length of the sides. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer, Verbal Description} Coordinate Plane Review (M, GP, CP, WG, IP) S330 (Answers on T641.) M, WG, CP, WG: Have students turn to S330 in their books. Use the following activity to review the coordinate plane and plotting points. Make sure students know their designation as Partner A or Partner B. {Pictorial Representation, Graphic Organizer, Verbal Description} Have student pairs complete Questions 1 5 and then discuss the answers as a whole group. This is a review of the coordinate plane. Partner A, identify the direction of the x-axis on the coordinate plane. (horizontal axis) Partner B, identify the direction of the y-axis on the coordinate plane. (vertical axis) Partner A, what is another name for the coordinate point (0, 0)? (the origin) Partner B, the number values on the x-axis and the y-axis are called the (scale). Review the placement of the points on the coordinate plane for the next activity. Plotting Missing Points (M, GP, CP, WG) S331, S332, S333 (Answers on T642, T643, T644.) M, WG, CP, WG: Have students turn to S331 in their books. Use the following activity to work with students on plotting missing points. Make sure students know their designation as Partner A or Partner B. {Pictorial Representation, Graphic Organizer, Verbal Description}
T634 Mathematics Success Grade 6 Step 1: Have students look at Question 1. Have students plot and label the coordinate points for Question 1. Have students connect the four points. Partner A, what shape is formed by the coordinates? (rectangle) Step 2: Have students look at Point A and Point B and identify the x-coordinate. Partner B, what do you notice about the x-coordinates of the two points? (The x-coordinates are the same.) Have students locate Point A and Point B on the coordinate plane. Partner A, what do you notice about the points and their location on the coordinate plane? (They are on the same vertical line.) Have student locate Point D and Point C on the coordinate plane. Partner B, what do you notice about the points and their location on the coordinate plane? (They are on the same vertical line.) Have student pairs discuss the conclusion section below Question 6. Partner A, when two points lie on the same vertical line, the (x-coordinates) are the same. Partner B, when two points have the same x-coordinate, they will lie on the same (vertical) line. Step 3: Have students look at Point A and Point D and identify the y-coordinate. Partner A, what do you notice about the y-coordinates of the two points? (The y-coordinates are the same.) Have students locate Point A and Point D on the coordinate plane. Partner B, what do you notice about the points and their location on the coordinate plane? (They are on the same horizontal line.) Have student locate Point B and Point C on the coordinate plane. Partner A, what do you notice about the points and their location on the coordinate plane? (They are on the same horizontal line.) Have student pairs discuss the conclusion section below Question 10. Partner B, when two points lie on the same horizontal line, the (y-coordinates) are the same. Partner A, when two points have the same y-coordinate, they will lie on the same (horizontal) line.
Mathematics Success Grade 6 T635 Step 4: Have students turn to page S332 and plot the point for K, L and M. These three points are vertices of a rectangle. The question is, how can we determine the coordinates of the fourth vertex? Have students look at Point K and Point L. They form one vertical side of the rectangle. Partner B, what do we know about the x-coordinates of those two points? (The x-coordinates are the same.) Point M and Point N form the other vertical side of the rectangle. Partner A, what must be true about the x-coordinates of those two points? (The x-coordinates must be the same.) Partner B, what is the x-coordinate of Point M? (5) Partner A, what will the x-coordinate of Point N be? (5) Partner B, explain the answer. (Point M and Point N are both on the same vertical line.) Step5: Have students look at Point L and Point M. They form one horizontal side of the rectangle. Partner A, what do we know about the y-coordinates of those two points? (The y-coordinates are the same.) Point K and Point N form the other horizontal side of the rectangle. Partner B, what must be true about the y-coordinates of those two points? (The y-coordinates must be the same.) Partner B, what is the y-coordinate of Point K? (-3) Partner A, what will the y-coordinate of Point N be? (-3) Partner B, explain the answer. (Point K and Point N are both on the same horizontal line.) Partner A, what are the coordinates of Point N? (5, -3) Have students plot Point N to complete the rectangle. IP, CP, WG: Have pairs complete Questions 1 8 in the chart on page S333. They will use the coordinate plane to plot points and answer questions for one figure in Quadrant I and a second figure that has points in each of the Quadrants. {Verbal Description, Pictorial Representation, Graphic Organizer}
T636 Mathematics Success Grade 6 Using Length to Find Missing Coordinates When the Figure in One Quadrant (M, GP, CP, WG, IP) S334, S335 (Answers on T645, T646.) M, WG, CP, WG: Have students turn to S334 in their books. Use the following activity to explore finding missing coordinates using length when the figure is in one quadrant. Make sure students know their designation as Partner A or Partner B. {Pictorial Representation, Graphic Organizer, Verbal Description} Using Length to Find Missing Coordinates When the Figure Is in One Quadrant Step 1: Direct students to the coordinate plane on S335. We can also use the length of the known sides of the rectangle to determine the missing vertex of a figure on the coordinate plane. Partner A, what information do we know about the coordinate of the three given vertices? [Point A: (1, 1) Point B: (1, 5) Point C: (4, 5)] Have partners discuss Questions 2 and 3. Partner B, how can we determine the length of the horizontal side of the rectangle? (We can count the units between Point B and Point C.) Partner A, how many units can we count between Point B and Point C? (3 units) Step 2: Tell students there is another way to measure the distance instead of counting the units. *Teacher Note: It may be helpful here to show two points on a horizontal number line and have students discuss strategies for determining the distance between the two numbers. The students should see that they can find the difference between the two values. Partner B, how can we measure the distance without counting units? (We can determine the difference between the x-coordinates.) Partner A, why are we finding the difference between the x-coordinates? (Because they have the same y-coordinate.) Partner B, what is the length of the horizontal side BC? (3 units) Partner A, explain how you found your answer. (4 is the x-value for Point C and 1 is the x-value for Point B. We subtract the two values for a difference of 3.) Step 3: What is the length of side AD? (3 units) Partner B, what is the x-coordinate of Point D? (4)
Mathematics Success Grade 6 T637 Partner A, explain your answer. (AD must be the same length as BC.) Step 4: Have students turn to page S335. Students will work with a partner to answer Questions 1 8. If they need help with the process, they can go back to the questions on S334. After students complete Questions 1 8 review the answers as a whole group. Conclusion: When the coordinates of a figure are all in one quadrant, you can use (subtraction) to find the length of the sides. () Using Length to Find Missing Coordinates When the Coordinates Are in Different Quadrants (M, GP, CP, WG, IP) S336, S337 (Answers on T647, T648.) M, WG, CP, WG: Have students turn to S336 in their books. Use the following activity to explore finding missing coordinates using length when the coordinates of the figure are in different quadrants. Make sure students know their designation as Partner A or Partner B. {Pictorial Representation, Graphic Organizer, Verbal Description} Using Length to Find Missing Coordinates When the Coordinates Are in Different Quadrants Step 1: Direct students to the coordinate plane on S336. Partner A, what information do we know about the coordinates of the three given vertices? [Point K: ( - 2, - 3) Point L: ( - 2, 2) Point M: (5, 2)] Have partners discuss Questions 2 and 3. Partner B, how can we determine the length of the horizontal side of the rectangle? (We can count the units between Point L and Point M.) Partner A, how many units can we count between Point L and Point M? (7 units) Step 2: Tell students there is another way to measure the distance instead of counting the units. Partner B, how did we determine the distance between the two points on the same horizontal line when they were in the same Quadrant? (We used subtraction.) Partner A, will the same strategy work when the points are in different quadrants? (No) Partner B, explain your answer. (Length cannot be a negative value.) Have students draw an arrow from Point L to zero and from Point M to zero. Partner A, how many units from Point L to zero? (2 units) Partner B, how many units from Point M to zero? (5 units)
T638 Mathematics Success Grade 6 What is the total distance from Point L to Point M or the length of LM? (7 units) Explain your answer. (We can represent the distance to the left of the origin as - 2 which is 2. Distance cannot be a negative value. We add the two values together for a length or distance of 7 units. - 2 + 5 = 2 + 5 = 7) Step 3: Have students turn to page S337. They will answer Questions 10 17 with a partner following the same procedure as on page S336. If they have questions they can refer back to page S336. After students have completed the questions, review the answer as a whole group. Remind students that distance cannot be a negative value. Conclusion: When the coordinates of a figure are in different quadrants, you can use (addition with the absolute value of each distance from zero) to find the length of the sides. What are the coordinates of Point N? (5, - 3) Area and Perimeter of Figures on the Coordinate Plane S338, S339 (Answers on T649, T650.) Area and Perimeter of Figures on the Coordinate Plane (M, GP, CP, WG, IP) M, WG, CP, WG: Have students turn to S338 in their books. Use the following activity to explore area and perimeter of figures in the coordinate plane. Make sure students know their designation as Partner A or Partner B. {Pictorial Representation, Graphic Organizer, Verbal Description} Step 1: Direct students to the coordinate plane on S338. Partner A, what is the horizontal length of the Rectangle KLMN? (7 units) Partner B, explain your answer. (We counted the distance between Point K and Point N or Point L and Point M or we used addition of the absolute value from 0. - 2 + 5 = 2 + 5 = 7) Partner A, what is the vertical length of the Rectangle KLMN? (5 units) Partner B, explain your answer. (We counted the distance between Point K and Point L or Points N and Point M or used addition of the absolute value from 0. - 3 + 2 = 3 + 2 = 5 ) Partner A, what is the perimeter of the rectangle: (24 units) Partner B, explain your answer. (We added the length of the four sides together.) Partner A, what is the area of the rectangle? (35 units squared) Partner B, explain the answer. (We used the formula for the area of a rectangle and multiplied the length times the width. 7 5 = 35 units squared.)