Learning Paths
Each learning path is one chapter: a guided route through a topic, one small course at a time. Pick a class to see its chapters in order.
Chapter 1
Rational and Irrational Numbers, Exponents and Radicals
You have counted with 1, 2, 3, and you have used fractions and decimals. Are there numbers that are neither? Yes. The length of the diagonal of a square with a side of 1 is one of them, and no fraction can write it. In this chapter we sort the numbers into families, we meet the irrational numbers, and we place every real number on the number line. Then we learn how to add, multiply and rationalise them, and how to work with fractional powers. We use Python to see the digits.
2 courses
Chapter 2
Divisibility, HCF and LCM, Rational and Irrational Numbers
Every whole number above 1 is built from primes in exactly one way. This one fact finds the HCF and the LCM of any numbers, and it proves that a number such as the square root of 2 can never be written as a fraction. In this chapter you break numbers into primes, solve problems about bells, tiles and buses with the HCF and the LCM, and learn how to prove that a number is irrational. Python checks your work and finds patterns in thousands of numbers.
2 courses