The KS3 DT curriculum requires students to be able to design for themselves from their own experience or for clients, learning appropriate skills in working with different materials. This task provides a context for this which can also be linked to the KS3 maths curriculum, drawing nets in 2-d which can be folded up into 3-d objects.
Creating 3-d objects from a 2-d design or plan is a topic covered in both maths and DT thus providing a good context for cross-curricular work. The pencil case could be initially designed in DT, focusing on the design process. At a convenient point later, the net could be drawn and tested in maths through making a paper prototype. The design would then be taken back into the DT lesson for making the final product, covering issues such as appropriate materials and the skills necessary to work with them.
Have a collection of cardboard boxes available for students to use to stimulate ideas and to help them with making the link between the 3-d object they want to finish up with, and the 2-d net.
The net of a prism (which is a 3-d shape with a constant cross-sectional area) consists of two end pieces which determine the shape of the prism (so circles for a cylinder, squares for a cuboid, hexagons for a hexagonal prism, etc) and a rectangle. The rectangle is wrapped round the two end pieces.
This means that the rectangle needs to have a length equal to the perimeter of the end pieces. Students will know how to find the perimeter of a square. Finding the perimeter (circumference) of a circle is covered in KS3, but it would be as well to check when this topic is covered at your school. Perimeters of other shapes, such as triangles, hexagons and octagons is best done by accurate measurement at this stage.
There are techniques for drawing a regular triangle (equilateral) and hexagon. To draw an equilateral triangle or a regular hexagon, start with a circle, marking one vertex. Keeping the compasses set to the same radius, put the point on the marked vertex and make two marks on the circle on either side. Repeat with one of the new marks, and continue until there are 6 equally spaced marks around the circle. Join all 6 marks to make a hexagon, join alternate marks to make a triangle. The most straight-forward way to draw an octagon (which will then not be regular, since the sides will not all be the same length) is to use squared paper.
Some students will see very quickly what shapes need to be put together to make a cylinder or a prism with a polygonal cross-section, others will struggle to see the relationship between the 3-d object they want and the 2-d net. Providing a collection of cardboard boxes in different sizes and shapes which they can open out will help with this.
Even when they have worked out what shape pieces they require, some will struggle with working out which lengths need to be equal. Again a collection of boxes which they can measure will help.