10.0.1 What to Expect in this Unit

This unit should take around 14 hours to complete. In this unit you will learn about:

  • Writing very small and very large numbers.
  • More on working with exponents.
  • The roots of numbers.
  • Scale diagrams.
  • Math language and notation for shapes.
  • Perimeter and area of simple shapes.
  • Calculating the volume of simple solids.
  • Further appreciate that drawing diagrams or working with models can help solve problems.

You learned about measurement in Unit 5, where mathematical units were introduced. Section 10.1 extends those ideas by considering measuring very small things (viruses, bacteria, or germs) and very large things (galaxies, distances in the universe), and shows how these measurements can be written using scientific notation. It also explains some important mathematical techniques in working with exponents, which you met in Unit 4.

One of the difficulties in considering very large or very small things is in visualizing them. Section 10.2 explores scale diagrams to help with this. These allow you to represent large areas, such as a road network on paper in the form of a map. This also builds on the ideas of ratio from Unit 8.

Section 10.3 introduces some basic properties of shapes, such as triangles, rectangles, and circles, and also introduces new vocabulary relating to these. Sections 10.4 and 10.5 then introduce perimeters and areas of various shapes, including circles, and uses this knowledge to solve a practical problem.

Section 10.6 extends these ideas to volumes: How much will that box hold? How much water do I need for the fish tank?

The study skills in this chapter concentrate on understanding and using new notation and vocabulary, and extending your problem solving strategies. (Remember to add the new vocabulary to your math notebook glossary as you come across it.) One of the problem solving strategies you have already used is drawing a diagram to help you to visualize a problem, and this unit looks at the use of diagrams and models in more detail. Problems can be tackled in a variety of different ways, and deciding which approach is most appropriate in a particular situation is important. To illustrate this, in Section 10.5 we consider which mathematical technique is best in a medical emergency!

Practice Quiz

Check your understanding of geometric shapes and sizes before you start by giving the Unit 10 pre quiz a try, then use the feedback to help you plan your study.

The quiz does not check all the topics in the unit, but it should give you some idea of the areas you may need to spend most time on. Remember, it doesn’t matter if you get some or even all of the questions wrong—it just indicates how much time you may need for this unit!

Click here for the pre quiz. [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

10.1 Big and Small