Y10 Foundation: Topic 12 AND 13: Number patterns and sequences; powers, roots and indices

Objectives:

    • Understand and use negative numbers in context, eg thermometers
    • Find: squares; cubes; square roots; cube roots of numbers, with and without a calculator (including the use of trial and improvement)
    • Understand odd and even numbers, and prime numbers
    • Find the HCF and the LCM of numbers
    • Write a number as a product of its prime factors, eg 108 = 2 × 2 × 3 × 3 × 3
    • Interpret standard index form from a calculator display
    • Add, subtract, multiply and divide numbers in standard form using a calculator

    • Generate simple sequences of odd or even numbers
    • Find the missing numbers in a number pattern or sequence
    • Find the nth term of a number sequence
    • Find whether a number is part of a given sequence
    • Continue a sequence derived from diagrams

    • Use a calculator to produce a sequence of numbers

Prior Knowledge:

    • Number complements to 10 and multiplication/division facts
    • Use a number line to show how numbers relate to each other
    • Recognise basic number patterns
    • Experience of classifying integers

    • Know about odd and even numbers
    • Recognise simple number patterns, eg 1, 3, 5, ...
    • Writing simple rules algebraically
    • Raise numbers to positive whole number powers

Key Vocabulary:

  • Copy and paste here.

Differentiation & Extension:

    • Calculator exercise to check factors of larger numbers
    • Further work on indices to include negative and/or fractional indices
    • Use prime factors to find LCM
    • Use a number square to find primes (sieve of Eratosthenes)
    • Calculator exercise to find squares, cubes and square roots of larger numbers (using trial and improvement)

    • Matchstick problems
    • Sequences of triangle numbers, Fibonacci numbers, etc

Using & Applying ideas:

  • Collaborate here.

NOTES
    • All of the work in this unit is easily reinforced by starter and plenary activities
    • Oral discussion should be used to ensure recognition of odd and even numbers
    • Calculators are only used when appropriate

    • Emphasise good use of notation, eg 3n means 3 × n
    • When investigating linear sequences, students should be clear on the description of the pattern in words, the difference between the terms and the algebraic description of the nth term
    • The cube (and cube root) function on a calculator may vary depending on make


Teaching & Learning Resources:


3D Shapes Resources