Year-5-Solve-Problems-with-Coordinates-TPP.pptx

Maths

1. MATHS Solve Problems with Coordinates Y5

2. Solve Problems with Coordinates Key Information Coordinates are a set of values that show an exact position. We use a pair of numbers separated by a comma and written inside brackets to describe position on a grid, for example, (4, 5). The first number describes the position along the x-axis and the second describes the position along the y-axis . The first quadrant is the upper right-hand section of a graph, where both x and y have positive values.

3. Solve Problems with Coordinates Let’s start with a question about plotting coordinates, which is linked to the new learning later in this lesson. 

4. Solve Problems with Coordinates What shape have you made? 1 2 3 4 5 5 4 3 2 1 x y (4, 4) (4, 1) (1, 1) Plot the given coordinates on the grid below.

5. Solve Problems with Coordinates What shape have you made? A right-angled triangle 1 2 3 4 5 5 4 3 2 1 x y (4, 4) (4, 1) (1, 1) Plot the given coordinates on the grid below.

6. Solve Problems with Coordinates Now that we are ready to move on, we can learn about problem solving with coordinates.

7. Solve Problems with Coordinates When there are no numbered scales, we must use any given information to help us work out missing coordinates. x C A D B y (4, 3) Here is a coordinate grid without the numbered scale for the axes.

8. Solve Problems with Coordinates Follow-up question How can we use the coordinates of vertex A to work out the coordinates for vertex B? x C A D B y (4, 3) On this grid, we are given the coordinates of vertex A.

9. Solve Problems with Coordinates This is because vertex A and vertex B are in line with each other. We can count the grid lines from 0 to check. x C A D B y ( 4 , 3) 4 ( 4 , ) We know that the x coordinate of vertex A is 4, so the x coordinate of vertex B is also 4.

10. Solve Problems with Coordinates Follow-up question How can we use the grid to help us work out the y coordinate of vertex B? x C A D B y (4, 3) (4, ) We now need to work out the y coordinate of vertex B.

11. Solve Problems with Coordinates As the scale increases by 1 each time, the y coordinate of vertex B must be 1. This also means that vertex D has a y coordinate of 1. x C A D B y (4, 3) (4, 1 ) 1 We can draw a line from vertex B to the y-axis to work out the missing coordinate.

12. Solve Problems with Coordinates Follow-up question How could we use knowledge of shape to help us work out the x coordinate of vertex D? x C A D B y (4, 3) (4, 1) ( , 1) We can now work out the x coordinate of vertex D.

13. Solve Problems with Coordinates If the difference between the y coordinates of vertices A and D is 2, then this will be the same for the x coordinates of vertices C and D. x C A D B y (4, 3) (4, 1) ( , 1) As the shape is a square, we know that the vertices are an equal distance apart on both axes.

14. Solve Problems with Coordinates Follow-up question What are the coordinates of vertex C? x C A D B y (4, 3) (4, 1) ( 2 , 1) This means that the x coordinate of vertex D is 2.

15. Solve Problems with Coordinates x C A D B y (4, 3) (4, 1) (2, 1) ( 2, 3 ) The x coordinate is 2 and the y coordinate is 3.

16. Solve Problems with Coordinates A B C (3, 4) x y Use the given information to work out the missing coordinates of the triangle below.

17. Solve Problems with Coordinates Vertex B = (2, 2) Vertex C = (4, 2) A B C (3, 4) x y Use the given information to work out the missing coordinates of the triangle below.

18. Solve Problems with Coordinates A B (1, 4) Follow-up question The perimeter of a rectangle is 12 cm. How can we work out the missing coordinates of the other vertices? (1, 2) x y 1 cm We can also use coordinate grids to work out missing coordinates when we are given the area or perimeter of a shape.

19. Solve Problems with Coordinates The coordinates of vertex C are (5, 4) and vertex D are (5, 2). A C B D (1, 4) (1, 2) x y 1 cm We can a perimeter of 12 cm and then find vertices C and D.

20. Solve Problems with Coordinates D A C B (3, 5) (2, 1) x y Follow-up question How can we use the given information to work out the x coordinate of vertex B? Sometimes, we may need to use given information to find missing coordinates when we don’t have a grid. For example:

21. Solve Problems with Coordinates Follow-up question How can we use the given information to work out the y coordinate of vertex B? D A C B (3, 5) (2, 1) x y ( 3 , ) We know that the x coordinate of vertex B is 3. This is because the x coordinates of vertices A and B are in line with each other.

22. Solve Problems with Coordinates Follow-up question What are the missing coordinates of vertex D? D A C B (3, 5) (2, 1 ) x y (3, 1 ) We know that the y coordinate of vertex B is 1. This is because the vertices of B and C are in the same place on the y-axis .

23. Solve Problems with Coordinates D A C B (3, 5) (2, 1) x y (3, 1) (2, 5) The missing coordinates are (2, 5). The x coordinate is the same as vertex C and the y coordinate is the same as vertex A.

24. Solve Problems with Coordinates A C x y (4, 4) (4, 2) (3, 3) D B Use the given information to work out the missing coordinates of B.

25. Solve Problems with Coordinates Vertex B = (5, 3) A C x y (4, 4) (4, 2) (3, 3) D B ( 5 , 3 ) Use the given information to work out the missing coordinates.

26. Solve Problems with Coordinates x y (4, 8) (4, 4) (10, 4) (10, 8) Sometimes, the scale does not go up in 1s. In the example below, the scale increases in 2s.

27. Solve Problems with Coordinates Now that we can problem solve with coordinates, let’s apply our learning to some problem-solving and reasoning questions.

28. Solve Problems with Coordinates Is Ruby correct? Explain her mistake. B C A D y (0, 4) (0, 0) The coordinates of vertex B are (2, 2) and (0, 4) for vertex C. x Ruby is working out the missing coordinates of the shape below. She says,

29. Solve Problems with Coordinates Is Ruby correct? Explain her mistake. Ruby is both correct and incorrect… B C A D y (0, 4) (0, 0) The coordinates of vertex B are (2, 2) and (0, 4) for vertex C. x Ruby is working out the missing coordinates of the shape below. She says,

30. Solve Problems with Coordinates Is Ruby correct? Explain her mistake. Ruby is both correct and incorrect because the coordinates of vertex B are correct. However, she has confused the x and y coordinates of vertex C. The correct coordinates are (4, 0). B C A D y (0, 4) (0, 0) The coordinates of vertex B are (2, 2) and (0, 4) for vertex C. x Ruby is working out the missing coordinates of the shape below. She says,

31. Solve Problems with Coordinates Here is a compound shape drawn onto a coordinates grid. What could the coordinates of vertices B, D and F be? Find three possibilities.

32. Solve Problems with Coordinates Various answers, for example: Vertex B = (10, 8); Vertex D (8, 6); Vertex F (4, 2) Vertex B = (25, 20); Vertex D (20, 15); Vertex F (10, 5) Here is a compound shape drawn onto a coordinates grid. What could the coordinates of vertices B, D and F be? Find three possibilities.