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# Topic 3 Year 7 Mathematics

 Mathematics Topic Factors and multiples No of lessons 8 When is it happening Term 1 Year 7 What will students learn In this unit students are given the opportunity to explore the ‘structure’ of the natural numbers. Students will be introduced to factors, multiples and important sets of numbers such as prime numbers, square numbers and cube numbers. Once the fundamental concepts have been introduced students are given the opportunity to develop their understanding, conjecture, problem solve and generalise in a series of structured tasks Key Knowledge that students should know at the end of 'Topic' This is the knowledge that students will meet for the first time in this topic Use factor pairs to find all factors of an integer Recognise primes and square numbers Investigate the structure of square numbers Explore different ways of constructing square numbers Developing a new representation to reveal the structure of positive integers Using the “lot of” representation to find the factors of an integer Using the “lot of” representation to express an integer as a product of two or more of its factors Explore a geometric application of factors Define the ‘common multiples’ of a set of integers. Use Venn Diagrams to categorise multiples of two or more numbers. Express the multiples of a number using algebra. Explore patterns involving multiples in number grids Identify the prime numbers in a 6-column number grid using a sieve algorithm. Deduce that prime numbers greater than 3 can be written as 6n+1 or 6n-1. This is knowledge that students may have met before but will need to deepen their understanding Using arrays to represent integers Commutativity of multiplication Using arrays to represent integers Multiplying a two-digit number by a one digit number Recognising square numbers Finding factors of integers Associativity of multiplication Experience identifying factors of numbers Draw and recognise regular polygons Constructing multiplicative models Experience with multiples as 'times tables' Experience with times tables Using algebraic notation to represent a variable integer Identify prime numbers Represent multiples as the product of integers Using algebraic notation to represent a variable integer Key Skills that students should be able to demonstrate at the end of 'Topic' This is the skills  that students will meet for the first time in this topic Be able to list the factors of integers supported by appropriate representation Experience decomposing and organising numbers based on their factors Be able list and organise common multiples for sets of integers Experience representing and explaining patterns in common multiples This is skills that students may have met before but will need to develop Understand the multiplication times table Understand the factor properties of integers, prime numbers and square numbers Understand any set of integers as having a repeating pattern of common multiples Key vocabulary that students should know and understand Factor, Multiple, Decomposition, Product The Big Question How many different polygons can I draw on dotted paper. Explore what happens as you vary the number of dots. Key questions that students should be able to answer at the end of the 'Topic' Do I understand what factors are and how to work them out? Can I work out all factors of  any given number. Do I understand square numbers? Am I able to write down a number as a product of its factors? Am I able to write down all the common factors of 18 and 24. If you can draw a regular hexagon in a ring, what other regular shape can you definitely draw? Do I understand how to work out multiples ? Can I write down the lowest common multiple of 2 numbers? Do I understand what a prime number is? Can I write down all prime numbers less than 100.