Maths Subject Knowledge: Understanding Numbers

Syllabus

• Week 1

  Number systems

  • Understanding numbers

    Over the next four weeks we will explore the properties of a range of numbers, connections between different number types, and delve into different number systems. We start by looking at the origins of our number systems.

  • Place value systems

    The denary number system is the one we most commonly use. Here we look at the underlying principles and the place value system.

  • Other number bases

    We've looked at base 10, now we look at how it's possible to work with other number bases. This is particularly important in computing.

• Week 2

  Multiples, factors and primes

  • Grouping numbers

    This week we look at how numbers are grouped, in particular through times tables. This leads us into exploration of multiples, factors, and primes.

  • Patterns of divisibility

    In the next steps we explore whether the last digit in numbers shows us whether that number is exactly divisible by another. There are some interesting links to error checking used in real life.

  • Multiples and factors

    Lowest common multiples and highest common factors are used across areas of mathematics. In these steps we clarify what they mean and how they can be used.

  • Prime numbers

    Prime numbers is a group of numbers that many people have heard of. How would you define what a prime number is and how might you find them?

• Week 3

  Negative numbers and exact numbers

  • Negative numbers

    So far in the course we have only looked at positive whole numbers. How do calculations work with negative numbers and what patterns might there be?

  • Negative numbers: addition and subtraction

    We'll now look at the different ways you can teach addition and subtraction of negative numbers.

  • Negative numbers: multiplication and division

    Moving on from addition and subtraction, you'll now explore a couple of approaches for multiplying and dividing by negative numbers.

  • Order of operations

    The agreed system for processing calculations is the order of operations. Without an order, chaos reigns!

  • Approximation and exact answers

    In the final part of this week we look at representing approximations and different forms of exact answers using irrational numbers.

• Week 4

  Number sequences

  • Introducing number sequences

    Our final week of the course looks at number sequences and different activities that link numbers together.

  • Types of sequences

    There are two main types of mathematical sequence studied in school: arithmetic and geometric. We start though with a sequence you may have heard of before: Fibonacci.

  • Characterising numbers

    In the final part of this course we look at square, triangle, perfect and happy numbers.

  • Reviewing your professional development

    Review your professional development and plan your next steps to sustain and develop the way you plan for learning.

Who will you learn with?