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Number Theory — DrFrost Y7 Lesson Notes

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Number Theory — DrFrost Y7 Lesson Notes

Authors: DrFrost Maths, Jasmine Vincent Year: 2024–2025 Venue: DrFrost Learning Platform Link: https://www.drfrost.org/downloadables.php (rid=5, noid=8) Tags: papers math y7 number-theory education drfrost Created: 2026-05-30 Last Updated: 2026-05-30

Summary

This collection covers the Year 7 number theory curriculum: identifying multiples, factors, and prime numbers, prime factorisation using factor trees and index notation, finding the highest common factor (HCF) and lowest common multiple (LCM) using both listing and prime factorisation methods, divisibility rules, and applying these concepts in problem-solving contexts. Approximately 15 individual lesson packs are included.

Core Ideas

  • A prime number has exactly two distinct factors: 1 and itself (so 1 is not prime)
  • Every integer greater than 1 can be expressed as a unique product of prime factors
  • The HCF of two numbers is the largest integer that divides both exactly
  • The LCM of two numbers is the smallest integer that is a multiple of both
  • Divisibility rules provide quick checks for whether one number divides another
  • The number of factors of a number can be determined from its prime factorisation

Teaching and Assessment Focus

  • Use the Sieve of Eratosthenes for a visual introduction to prime numbers
  • Teach factor trees before moving to formal prime factorisation notation
  • LCM and HCF by prime factorisation is preferable to listing once students are confident
  • Divisibility rules from 2 to 11 form a toolkit for checking answers
  • Apply LCM to problems involving synchronised events
  • Apply HCF to problems involving splitting items into equal groups

Key Resources

  • Yr7-NumberTheory.pptx (82 slides) — Comprehensive unit including all topics
  • Multiples, Factors and Primes — Lesson + 6 exercises + prerequisite checks
  • Prime Factorisation of a Number — Lesson + exercise
  • LCM and HCF by Prime Factorisation — Lesson + exercise
  • Common Factors and the HCF — Lesson + 4 exercises/gap fills
  • Common Multiples and the LCM — Lesson + 3 exercises
  • Divisibility Tests — Lesson + 2 exercises
  • Properties of a Number Based on Prime Factorisation — Lesson + exercise
  • Solving Problems involving HCF and LCM — Lesson + 3 exercises
  • All in One — LCM & HCF Parts I & II — Standalone worksheets
  • Year 7 Number Theory QQQ — Quick quiz questions
  • Number Grids — Extension for maths challenge students

Sources

  • drfrost-downloads/Yr7-NumberTheory.pptx
  • drfrost-downloads/PrimeFactorisation-Lesson.pptx
  • drfrost-downloads/PrimeFactorisation-Ex.pdf

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