Completing a four-sided figure on a grid is in the Primary 5 Parallelogram, Rhombus and Trapezium chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
Count squares, across then up. A to C is 4 squares right and 2 squares up.
For a parallel side, walk the same run and rise from B. Twice as long means 8 squares right and 4 up.
Read the coordinates of the end point: Y is at 10, 5.
For a right angle, swap run and rise: R S is 4 left, 3 up, so a quarter turn is 3 right, 4 up.
Choose the side the question wants. The square must not overlap the rhombus, so build it 3 right and 4 up.
A parallel side is the same run and the same rise. A right angle is those two swapped. And the question says which side of the line.
Worked example, step by step
From the lesson: Drawing on a grid
The dot grid below has A at (2, 3) and B at (8, 5). Draw the trapezium ABCD, in which DC is parallel to AB, AD is at right angles to AB, and AD and DC are each half as long as AB. D is above the line AB. Write down the coordinates of C and D.
AB runs 6 squares right and 2 squares up
half of AB is 3 squares right and 1 square up
AD is at right angles to AB and half as long, so AD runs 1 square left and 3 squares up
A is at (2, 3), so D is at (1, 6)
DC is parallel to AB and half as long, so DC runs 3 squares right and 1 square up
D is at (1, 6), so C is at (4, 7)
AB and DC are parallel and of different lengths, so ABCD is a trapezium, and the angles at A and at D are right angles
Ans: The answer is D at (1, 6) and C at (4, 7).
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
Question 1 of 10 · Basic · free to tryThe grid below is a 1-cm square grid. The sides PQ and QR of a rhombus PQRS…The grid below is a 1-cm square…
The grid below is a 1-cm square grid. The sides PQ and QR of a rhombus PQRS have been drawn on it, with P at (1, 4), Q at (5, 1) and R at (9, 4). Complete the rhombus PQRS and write down the coordinates of S.
QR runs 4 squares right and 3 squares up, so QR is the same length as PQ
in a rhombus SR is parallel to PQ and the same length, so S is 4 squares left and 3 squares up from R
R is at (9, 4), so S is at (5, 7)
PS runs 4 squares right and 3 squares up from P and reaches the same point, so all four sides are equal and PQRS is a rhombus
Answer: S at (5, 7)
For parents
How do you answer P5 drawing shapes on a grid questions?
Primary 5 children complete a parallelogram, rhombus or trapezium on a square or dot grid, using the properties of each shape.
What your child learns here
Primary 5 children complete a parallelogram, rhombus or trapezium on a square or dot grid, using the properties of each shape. This page also revisits the rectangles, squares and right-angled triangles of earlier years, all drawn by counting squares.
A slanting side is described by how many squares it goes across and how many it goes up or down.
A side parallel to it and just as long repeats the same two counts from a new starting point.
A side at right angles swaps the two counts and turns one of them round.
A side twice as long doubles both counts; a side half as long halves both.
Every corner sits on a grid point, so its place can be named and checked.
Does the answer make sense?
In Question 1, PQ goes 4 squares right and 3 squares down, so RS must go 4 squares left and 3 squares up from R, landing on (5, 7). From P to S is then 4 right and 3 up, the same two counts as every other side, so all four sides of PQRS are equal.
How to practise these questions
Question 1, free to everyone, gives the sides PQ and QR of rhombus PQRS on a 1-cm square grid, with P at (1, 4), Q at (5, 1) and R at (9, 4), and your child completes the rhombus and gives the position of S. The Basic questions train finishing a rhombus, a right-angled isosceles triangle, a rectangle or a square from the sides already drawn. The Intermediate questions add a side twice as long as another, or a side at right angles. The Challenge questions set two conditions at once, such as a square that must not cover another shape, or ask for every possible fourth corner. Your child marks each drawing against the answer; if one goes wrong, open its worked solution and recount the squares side by side.
Questions parents ask
Is drawing on a grid in the Primary 5 syllabus? Yes, as part of the properties of the parallelogram, rhombus and trapezium. Drawing rectangles and squares comes a year earlier, in Primary 4.
Does my child need to know coordinates? Coordinates are not a Primary 5 topic. A pair such as (5, 7) only names a grid point, counted across from the left and then up from the bottom, so an answer can be checked.
How can my child check a finished shape? Count the squares along each side, across and then up or down. Opposite sides of a parallelogram must give the same two counts, and in a rhombus every side covers the same two numbers in some direction.
