1 MATHEMATICS Y6 Geometry 675 Use co-ordinates and etend to quadrants Paper, pencil, ruler Equipment MathSphere
2 675 Use co-ordinates and etend to quadrants. Page Concepts Children should be familiar with the following words and should be able to use, read and write them: position, direction, ascend, descend, journey, route, map, plan, grid, row, column, origin, -ais, y-ais, quadrant, co-ordinates, compass, point, north, south, east, west, north-east, north-west, south-east, south-west, horizontal, vertical, diagonal, intersecting, intersection, parallelogram, perpendicular, plane. The use of the co-ordinate system is now etended to all four quadrants. The quadrants have the names 'First quadrant, Second Quadrant' etc, starting in the top right corner and moving anti-clockwise. Second Quadrant First Quadrant Third Quadrant Fourth Quadrant Children should be able to plot and interpret points in all four quadrants, using negative numbers as appropriate. They should remember at all times that the first number in the co-ordinate pair is the horizontal distance from the origin and the second number is the vertical distance. Using the aes as mirror lines, shapes will be reflected from one quadrant to another and the new co-ordinates interpreted. The concepts of parallel and perpendicular are now etended to the different types of quadrilaterals (parallelograms etc). Children should know that lines that cross are called 'intersecting' and they should be able to count and predict the number of intersections for a given (simple) set of lines. N.B. When drawing polygons, the shape should be finished by returning to the first point.
3 675 Use co-ordinates and etend to quadrants. Page The horizontal ais is often called the -ais and the vertical ais is the y-ais. -ais and y-ais. That sounds simple enough. Here is a set of aes with positive numbers on the y-ais, but positive and negative numbers on the -ais. A J B A is the point (5,) E is the point (,5) H is the point (,5) K is the point (,) y 6 H 5 G Write in the co-ordinates of the points: L K I B(, ) C(, ) D(, ) F(, ) G(, ) I(, ) J(, ) L(, ) F E C D
4 675 Use co-ordinates and etend to quadrants. Page Here is a grid with positive and negative numbers on the -ais and just positive numbers on the y-ais. Plot the shape with the following co-ordinates: (,) (5,) (,) (,) (,) (,) (,5) (,) (6,) (,5) Reflect this shape in the y-ais. y 6 Write down the co-ordinates of the new shape (the 'image') New Shape co-ordinates: Be careful with those negatives! (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) Can you now draw your own aes and reflect a shape you have designed? Do not forget to write down the co-ordinates.
5 675 Use co-ordinates and etend to quadrants. Page 5 Noughts and Crosses on a Grid y Here is a game you can play. You will need two people. It is like noughts and crosses, but you need to get four noughts or crosses in a row instead of three. When a person takes a turn, he/she must say the co-ordinates of the point where they are going to put their nought or cross before they do so. If they do not put it in the correct place, it is cancelled and the other person has a go! First person with four in a row (vertically, horizontally or diagonally) is the winner. To save printing too many of these sheets, you could use counters. 5 Counters. Why didn't I think of that? 'Cause you're divvy, Divvy!
6 675 Use co-ordinates and etend to quadrants. Page 6 Okay, you guys. Ready for the heavy stuff? We are now going to put negative numbers in the y-ais too! Hold onto your seats! y Try drawing this shape: Such great artists at MathSphere! (,5) (,) (,) (5,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) ( 5,) ( 5, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (,) * Now draw a rectangle at (,) (,) (,) (,) Finally draw two circles cm radius at centres (, ) and (, )
7 675 Use co-ordinates and etend to quadrants. Page 7 Make two drawings of your own. Write down the co-ordinates of each. y 5 Co-ordinates: y 5 Co-ordinates: 5 5 5
8 675 Use co-ordinates and etend to quadrants. Page 8 5 y Draw this polygon on the grid: (,) (5,) (5,) (,) (,) (,) What is it called? Mark the parallel sides with arrows. Reflect the shape in the y-ais. Write down the co-ordinates of the reflection. (, ) (, ) (, ) (, ) (, ) (, ) Now reflect the first shape in the -ais. Write down the co-ordinates of this reflection. (, ) (, ) (, ) (, ) (, ) (, ) What do you notice about the co-ordinates?
9 675 Use co-ordinates and etend to quadrants. Page 9 5 y Draw this shape on the grid: (,) (,) (,) (,) (,) (,) Mark the parallel sides with arrows. Reflect the shape in the y-ais. Write down the co-ordinates of the reflection. (, ) (, ) (, ) (, ) (, ) (, ) Now reflect the first shape in the -ais. Write down the co-ordinates of this reflection. (, ) (, ) (, ) (, ) (, ) (, ) What do you notice about the co-ordinates? Can you complete the pattern in all four quadrants? What do you need to do?
10 675 Use co-ordinates and etend to quadrants. Page Draw this shape on the grid: y (,) (,) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (,) Reflect the shape in the -ais. Write down the co-ordinates of the reflection. (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) Now reflect the first shape in the y-ais. Write down the co-ordinates of this reflection. (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) 5 Can you complete the pattern in all four quadrants? What do you need to do?
11 675 Use co-ordinates and etend to quadrants. Page Name these quadrilaterals. Mark the parallel lines in them with arrows. Colour the perpendicular lines (those at right angles to each other). A B C D E F G H
12 675 Use co-ordinates and etend to quadrants. Page Two points at the top of a diagram are joined to two points at the bottom. Put a dot where the lines intersect. How many intersections are there? Why, just one of course! How many intersections are there when there are three points at the bottom of the diagram? Number of points at the bottom Number of intersections Continue this for four points at the bottom, five points and so on. Keep going until you have si points at the bottom. Put your results in the table. What pattern do you notice? Can you complete the pattern for up to ten dots without drawing the diagrams?
13 675 Use co-ordinates and etend to quadrants. Page Answers Page B(,) C(,) D(5,5) F(,) G(,) I(,) J(,) L(,) Page Shape is a sailing boat with sail displaced to the right. (,) ( 5,) (,) (,) (,) (,) (,5) (,) ( 6,) (,5) (Not necessarily in this order) Page 6 The drawing is a simplified digger. Page 9 (,) (,) (,) (,) (,) (,) (,) (, ) (, ) (, ) (, ) (, ) When the shape is reflected in the y-ais, the first number in each co-ordinate becomes negative. When the shape is reflected in the -ais, the second number in each co-ordinate becomes negative. To complete the pattern either a) the first reflection must be reflected in the -ais or b) the second reflection must be reflected in the y-ais. Page (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (,) To complete the pattern either a) the first reflection must be reflected in the y-ais or b) the second reflection must be reflected in the -ais. Page A Rectangle B Square C Trapezium D Parallelogram E Parallelogram F Trapezium G Rhombus H Kite Page 8 The shape is a heagon. (,) ( 5,) ( 5,) (,) (,) (,) (, ) (5, ) (5, ) (, ) (, ) (, ) When the shape is reflected in the y-ais, the first number in each co-ordinate becomes negative. When the shape is reflected in the -ais, the second number in each co-ordinate becomes negative. Page Number of points Number of intersections
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