National curriculum content

• Describe positions on the full co-ordinate grid (all four quadrants)
• Draw and translate simple shapes on the co-ordinate plane, and reflect them in the axes

Lesson objectives

1. The first quadrant
2. Four quadrants
3. Translations
4. Reflections

What we want children to know

• Read and plot co-ordinates in the first quadrant
• Draw shapes on a 2D grid from given co-ordinates
• Write co-ordinates for shapes without plotting the points
• Read and plot co-ordinates in all four quadrants
• Draw shapes from co-ordinates given
• Become fluent in deciding which part of the axis is positive or negative
• Develop understanding of how to find the length of a line by using the co-ordinates of its two end points
• Translate shapes in all four quadrants
• Describe translations using directional language, and use instructions to draw translated shapes
• Reflect shapes in four quadrants using both the x-axis and y-axis. Use knowledge of co-ordinates to ensure that shapes are correctly reflected
   

What skills we want children to develop

Use knowledge to solve Reasoning and Problem Solving questions such as:

Working backwards

Two triangles have the following co-ordinates:

Triangle A: (3, 5)   (7, 5)    (4, 7)

Triangle B: (3, 1)  (7, 1)   (4, 3)

Describe the translation of triangle A to B and then from B to A.

Possible answers

Follow the clues. What could the missing co-ordinates of the shape be?

• The shape is a regular polygon
• The shape crosses all four quadrants
• At least three points have 0 in their co-ordinates
• One of the points is (10,10)

True or false?

Dexter has translated the rectangle ABCD 6 units down and 1 unit to the right to get to the yellow rectangle.

Explain your reasoning.   

Mathematical Talk

• Which axis do we look at first?
• Does joining up the vertices already given help you to draw the shape?
• Can you draw a shape in the first quadrant and describe the co-ordinates of the vertices to a friend?
• If (0,0) is the centre of the axis (the origin), which way do you move along the x-axis to find negative co-ordinates?
• Which way do you move along the y-axis to find negative co-ordinates?
• Which point are you going to look at when describing the translation?
• Does each vertex translate in the same way?
• How is reflecting different to translating?
• Can you reflect one vertex at a time? Does this make it easier to reflect the shape?
• Which axis are you going to use as the mirror line?