M1.          (a)     (8, 7)           Do not accept (7, 8).
Accept co-ordinates written on diagram with or without commas and brackets, eg:
•    (8 7)
•    8 7
•    8,7
1

(b)     (5, 3)           Do not accept (3, 5).
Accept co-ordinates written on diagram with or without commas and brackets, eg:
•    (5 3)
•    5 3
•    5,3
1
[2]

 

M2.          (a)     (2, 1)
Both the numbers must be correct and in the correct order.
Acceot (2, 1) on diagram with or without comma and brackets.
1

(b)     Explanation which either implies that B has the coordinates (12, 6)
OR that (11, 5) cannot be on the line because of the general
relationship between the points, eg:
•    ‘Because it’s 12, 6’
•    ‘If you count up in 2’s and 1’s it doesn’t come to 11, 5’
•    ‘The first numbers are always even’
•    ‘First should be twice the second number’
Do not accept arbitrary or vague reasons, such as:
‘She miscounted’;
‘Because the bottom line doesn’t go up to 11’;
‘Because it’s in a pattern’.
1
[2]

 

M3.          (3, 5)
Do not accept (5, 3).
[1]

 

M4.          (10, 7) (12, 7) (10, 10)
All correct, in any order for 1 mark.
[1]

 

M5.          (3, 11)
Coordinates must be written in the correct order.
Accept correct answer written on the diagram, with or without brackets or commas.
[1]

 

M6.          (4, 3)
Coordinates must be written in the correct order.
Accept (6, 3), (4, –1) or (6 –1)
Accept answers written on the diagram, with or without brackets and commas.
[1]

 

M7.          (4, 6)
Both numbers must be correct for the award of the mark.
Accept correct answers written on the diagram with or without brackets.
Coordinates must be written in the correct order.
[1]

 

M8.          (a)     (0, 10)
Coordinates must be written in the correct order.
Accept unambiguous answers written on the diagram.
1
(b)     (10, 20)
If the answer for 15a is (10, 0) AND the answer to 15b is
(20, 10), award ONE mark only, in the 15b box.
1
[2]

 

M9.          (5, 2)
Coordinates must be written in the correct order.
Accept unambiguous answers written on the diagram.
[1]

 

M10.          Diagram completed as shown:

Accept slight inaccuracies in drawing
[1]

 

M11.(2, 4)
[1]
Question Requirement Mark Additional guidance

 

E1.          Co-ordinates
The two questions involving co-ordinates were not well answered even by children achieving Levels 4 or 5 overall. Test A question 13 required children to understand that points are related by their co-ordinates and to use the given co-ordinates to calculate the co-ordinates of other points on the same shape. The example below illustrates a strategy used successfully by some children. He used the given co-ordinates and the axes as the basis for working out the co-ordinates of points B and M. Several children recognised that the y co-ordinate of the halfway point, M, had to be the same as those of points C and D but were unable to determine the x co-ordinate.

E2.          Children at all levels were more successful in the co-ordinates questions on the tests in 1997 compared with 1996. More children attempted the questions. The reasoning offered to explain why a given co-ordinate (11,5) could not be on the line shown, was in some cases remarkably clear: Because the first number goes up by two and the last one goes up one so the correct answer is (12,6); there is the same space between each dot and the x co-ordinates go up in even numbers and 11 is an odd number; Because 5 is not half of 11 and all the rest are half of one another.

E8.          Target Level: 4
The focus of this question is coordinates in the first quadrant. Pupils are required to understand the properties of a square in order to use given coordinates to work out other coordinates.
Performance
•    Two-thirds of pupils working at level 4 gave the correct coordinates for point B. Over 90% of pupils working at level 5 and more than 20% of those working at level 3 were also correct.
•    Of those children working at levels 4 and 5, similar percentages gave the correct coordinates for point C. Children working at level 3 had less success than for point B, with over 15% giving the correct coordinates.

Common errors and misconceptions
•    Over 10% of pupils working at level 4 reversed the x and y coordinates to give an answer of (10, 0) for point B, and a similar percentage made a similar error for point C to give an answer of (20, 10). Over 5% of pupils working at levels 3 and 5 also made this error. However, few pupils consistently reversed the coordinates for both parts of the question. Those that did this were presumably able to reason correctly but were unable to record the coordinates in the correct order.
•    Over 5% of pupils working at level 4 and more than 15% of those working at level 3 gave an answer of (10, 10) for point B, the same coordinates as point A.

•    Nearly 10% of pupils working at levels 3 and 4 gave an answer of (20, 20) for point C. These pupils may have seen the coordinates as increasing in sequence: (0, 0), (10, 10), (20, 20). Another possibility is that they thought that, for diagrams involving squares, each value in a pair of coordinates should be the same.
•    The nature of the errors made by pupils often varied between parts (a) and (b). This suggests that many pupils were not secure in their understanding of or reasoning with coordinates.

E9.          Target Level: 4
Curriculum Coverage (POS ref: Ma3/3c, 2b; 2/4e)
This question assesses pupils’ ability to plot and read coordinates in the first quadrant. They are also required to demonstrate their knowledge of the properties of a rectangle in order to work out the coordinates of one vertex given the vertices of the others.

Performance
More than 70% of pupils working at level 4 gave the correct coordinates, as did 95% of those working at level 5 and over 40% of those working at level 3.
Common errors and misconceptions
•    Around 5% of pupils working at both levels 3 and 4 gave an answer of (5, 6). These pupils may have reversed the order of their coordinates when plotting D, at (4, 3) rather than (3, 4). They then formed a square with C at (6, 5), reversing these coordinates also.

Methods
About 80% of pupils annotated the grid, with those working at level 5 the most likely and those at level 3 the least likely to make annotations.
Of those who annotated the grid, pupils working at the higher levels were most likely to mark two points on the grid without joining points, while pupils working at level 3 were most likely to attempt to draw a shape by joining points on the grid. Both these methods were commonly used by pupils who reached the correct answer.

 
Resource currently unavailable.