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

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

## Objectives:

nth term of a number sequencePrior Knowledge:## Key Vocabulary:

## Differentiation & Extension:

## Using & Applying ideas:

NOTESnmeans 3 ×nnth term## Teaching & Learning Resources:

3D Shapes Resources