We have seen how triangles have interior angles of 180° . This is essential knowledge we want to 'stick' with children. But, how do we teach children about angles in polygons? If we map it out in a table, you may see a pattern.
For each new side, we are essentially adding a new triangle and adding a new triangles means adding 180° to the interior angles.
We may also 'find' the triangles in shapes by choosing a vertex and creating triangles by systematically joining to another vertex.
Making connections between maths is essential to developing a fluid and strong understanding of how concepts work. Using a polygon [square, rectangle or any 4 sided shape] we may show children how they create a 360° angle and the links to a circle.
So far, we have focused on 2D shapes. We now turn to shapes with three dimentions.
3D shapes have volume and surface are and are part of curricula around the world. 3D shapes are often represented by 2D nets. Using manipulatives can be a very effective way of making nets of cubes - encouraging children to find all of the nets of shapes can be a great investigation.
Earlier, we explored the links between interior angles in polygons and angles in a circle. When teaching about circles, we should be careful around their properties. For example, do they have 1 side or 0 sides? And so does a semi-circle have 2 sides or 1 side? That depends on our definition of a side. We have considered them as a straight line on a 2D shape connecting to another side of this definition. A circle, however, has a continuous curved circumference. Here, language matters. We might start and introduce language by drawing circles, labeling them and looking for relationships. It is important to see the circumference, diameter and radius in many different ways to ensure their concepts are clear. For example, always showing the diameter as horizontal or vertical may cause misconceptions around where it may be placed.
Ask: "What do you notice about the relationship between the diameter and the radius?"
Draw attention to the radius being half the size of the diameter in any circle.
Now children have strengthened the connections between shapes, we may begin to deepen understanding through reasoning. For example:
Ask: "What is the area of the rectangle?
Or, deepen children's understanding of circles and knowledge of area of triangles. Knowing and visualising their understanding of triangles being half the area of a polygon.