Basic Number, factors and multiples (2 year teaching) (8300 - Higher - Number)

Topic:Basic number, factors and multiples

Specification references (in recommended teaching order)

Specification content Specification notes
N1
  • Order positive and negative integers
  • Use the symbols =, ≠, <, >, ≤, ≥

  • including use on a number line
  • know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary

N2
  • Apply the four operations, including formal written methods, to integers – both positive and negative
  • Understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)

  • Including questions set in context
  • Knowledge of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit and balance, income tax, VAT and interest rate

N3
  • Recognise and use relationships between operations including inverse operations (e.g. cancellation to simplify calculations and expressions)


N14
  • Estimate answers
  • Check calculations using approximation and estimation, including answers obtained using technology

  • including evaluation of results obtained

N4
  • Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation, and the unique factorisation theorem

  • prime factor decomposition including product of prime factors written in index form

N5
  • Apply systematic listing strategies and the use of the product rule for counting

  • including using lists, tables and diagrams


The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

Teaching resources

Teaching resources - see below
Downloadable resource in format. 29/08/2014

Adding and Subtracting Positive and Negative Integers
A teacher guide which outlines four different models for adding and subtracting positive and negative integers.19/05/2015
Co-primes: Teacher Notes
Teacher notes which guide an investigation into co-prime numbers.19/05/2015

Arrange the Digits
Students must use the digits 1-9 to make 3 three-digit numbers which sum to a number as close as possible to 1500.19/05/2015
Calc - a - Hundred
Students work in pairs to carry out operations on calculators to produce a total as close as possible to 100.19/05/2015
Can you find a perfect number?
An introduction to the idea of a 'perfect' number, from which students must investigate to find other perfect numbers and consider other properties involving factors.19/05/2015
HCF and LCM
Activities involving HCF and LCM with demanding 2 or 3 digit numbers.19/05/2015
HCF, LCM, Product of Prime Factors tarsia
A tarsia card sorting activity which forms a hexagon. Questions involve prime factor decomposition, HCF and LCM. You will need to register for a TES account to access this resource, this is free of charge.19/05/2015
Inequalities
Choosing the correct inequality symbol to place between pairs of numbers. Some pairs include negative numbers. 19/05/2015
Metric Numbers
An overview of the prefixes used for very large and very small numbers, followed by 10 questions involving these prefixes.19/05/2015
Number Line
Positioning and ordering positive and negative integers on a number line.19/05/2015
Prime Factorization
Prime numbers interactive worksheet. An introduction to prime factorization, followed by six questions assessing understanding.29/08/2014

Arrange the Digits
Students must use the digits 1-9 to make 3 three-digit numbers which sum to a number as close as possible to 1500.19/05/2015
Weekly Problem 16 - 2006
A student investigation which requires consideration of multiples.19/05/2015

Inverse Operations Worksheet
A series of puzzles which students must solve by using inverse operations. You will need to register for a TES account to access this resource, this is free of charge.19/05/2015
Prime Factorization
Prime numbers interactive worksheet. An introduction to prime factorization, followed by six questions assessing understanding.29/08/2014

Playing connect three
A game for pairs of students which allows investigation of addition and subtraction of positive and negative integers. 19/05/2015
Venn Multiples
An interactive website in which students must place numbers in the correct area of the Venn diagram, depending on what they are multiples of. The activity can be varied by changing the required multiples.19/05/2015

Eratosthenes' Sieve
Online demonstration which uses the principles of Eratosthenes' Sieve to identify the prime numbers between 1 and 100.19/05/2015

Collecting Data - Organising Data - Repeating Numbers - Problem Sheet
Downloadable resource in doc format. 01/02/2010
Ratio and Proportion - Golf - Golf Scores - Problem Sheet and Answers
Downloadable resource in doc format. 07/05/2010
Ratio and Proportion - Golf - Holes and Distances - Supplementary Resource
Downloadable resource in xls format. 08/05/2010
Ratio and Proportion - Golf - Par Cards - Supplementary Resource
Downloadable resource in xls format. 09/05/2010
Ratio and Proportion - Maths and Golf - Lesson Plan
Downloadable resource in doc format. 10/05/2010

Topic Tests

8300 GCSE Higher Arithmetic (including fractions) Mark Scheme
Downloadable resource in pdf format. 09/09/2022
8300 GCSE Higher Arithmetic (including fractions) Topic Test
Downloadable resource in pdf format. 09/09/2022
8300 GCSE Higher Product of Primes (HCF and LCM) Mark Scheme
Downloadable resource in pdf format. 09/09/2022
8300 GCSE Higher Product of Primes (HCF and LCM) Topic Test
Downloadable resource in pdf format. 09/09/2022
8300 GCSE Higher Types of Number Mark Scheme
Downloadable resource in pdf format. 09/09/2022
8300 GCSE Higher Types of Number Topic Test
Downloadable resource in pdf format. 09/09/2022

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