1 U n t er r ich t splan Plotting Points In Four Quad rants Altersgruppe: Grade 6 Virginia - Mathematics Standards of Learning (2009): 6.11a, 6.11b Virginia - Mathematics Standards of Learning (2016): 6.8.a, 6.8.b Fairfax County Public Schools Program of Studies: 6.11.a.4, 6.11.b.1 Online-Ressourcen: K e e p Yo ur Di st anc e Opening Teacher present s Students pract ice Math Pract ice Closing 1 2 1 0 1 0 1 1 2 M at h Obj ect ives E xpe ri e nc e plotting points in four quadrants. P rac t i c e plotting points in cartesian coordinate system. Learn about the four quadrants. Ope ni ng 12 Draw the cartesian coordinate system on the board.
2 Ask: This is the cartesian coordinate system. Why is it called cartesian? Because the person who invented it, in the 17th century, called cartesius (the Latin name of the mathematician and philosopher René Descartes). Say: This coordinate system is composed of two coordinate axis - a horizontal axis and vertical axis. The point where they meet, which is also the 0 point of the two axis, is called the origin. During your explanation, point on the axis, to identify the numbers and the origin. Say: Notice that the coordinate system is divided into four quadrants. Point to the quadrants and mark each one of them. Say: In the first quadrant the x axis numbers and the y axis numbers are both positive, in the second quadrant the x axis numbers are negative and the y axis numbers are positive, in the third quadrant the x axis numbers and the y axis numbers are both negative and in the fourth quadrant the x axis numbers are positive and the y axis
3 numbers are negative. Say: Each point can be marked by its position within the coordinates. We mark the point using brackets (parenthesis) and inside them two places that are divided (separated) with a comma. The first place, left to the comma, is for the x axis number and the second, right to the comma, is for the y axis number. Write on the board a few examples of points (such as (2,1)) and demonstrate their position on the coordinate system that's on the board (you can also invite students to plot a given point on the coordinate system). Ask: In what quadrant is the point (3,4)? In the first quadrant. Ask: In what quadrant is the point (1,-5)? In the fourth quadrant. Continue asking questions about the position of points until you feel the students understand. T e ac he r prese nt s M at h game : K e e p Yo ur Di st anc e - Co o rdi nat e P l ane : F o ur Quadrant s 10 Present Matific s episode Ke e p Y o ur Dis t a nc e - C o o rdinat e Pla ne : Fo ur Quadra nt s to the class, using the projector, in the Preset mode. This episode offers a first hand experience with the coordinate plane, as a means for labeling positions. Place points at designated positions on the plane. The coordinates may also assume negative values. Example :
4 Say: On the screen there is a coordinate plane and two points, A and B, that are already placed on the plane. The point A (3,-3) is on the intersection of the value 3 on the horizontal axis, with the value -3 on the vertical axis. The point B(2,5) is on the intersection of the value 2 on the horizontal axis with the value 5 on the vertical axis. Ask: Read the instructions on the bottom of the screen. Where should we place point C (-5,4)? We place point C on the intersection of the value -5 on the horizontal axis with the value 4 on the vertical axis. Place point C. In the Preset mode there are 5 questions. When you feel the students understand you can continue.
5 St ude nt s prac t i c e M at h game : K e e p Yo ur Di st anc e - Co o rdi nat e P l ane : F o ur Quadrant s 10 Have students play Ke e p Y o ur Dis t a nc e - C o o rdinat e Pla ne : Fo ur Quadra nt s on their personal devices. Circulate among them answering questions. M at h P rac t i c e : Co o rdi nat e pl ane Wo rkshe e t 11 Print for students the Coordinate plane worksheet at the end of this section. Ask the students to work independently. Say: You have a coordinate plane, without numbers. Follow the instructions: 1. Mark the numbers on the right places, for every axis. 2. Place the following points on the plane: (-5,2) (-2,2) (-2,-2) (-5,-2) (1,2) (1,-2) (3,2) (1,0)
6 (3,-2) 3. Draw a line between the points, in the order listed. Where there is a gap, don't connect between the points. 4. What did you get? Circulate among them answering questions. Say: We got - "ok". Print a ble H a ndo ut : C o o rdinat e pla ne w o rks he e t
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8 Cl o si ng 2 Ask: In the second quadrant, are the numbers on the axis positive or negative? In the second quadrant the x axis numbers are negative and the y axis numbers are positive. Ask: In the third quadrant, are the numbers on the axis positive or negative? In the third quadrant the x axis and the y axis numbers are both negative. Ask: In the fourth quadrant, are the numbers on the axis positive or negative? In the fourth quadrant, the x axis numbers are positive and the y axis numbers are negative. Ask: In the first quadrant, are the numbers on the axis positive or negative? In the first quadrant the x axis and the y axis numbers are both positive.