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- Find and use multiples
- Identify factors of numbers and expressions
- Recognise and identify prime numbers
- Recognise square and triangular numbers
- Find common factors of a set of numbers including the HCF
- Find common multiples of a set of numbers including the LCM
- Write a number as a product of its prime factors
- Make and test conjectures
- Use counterexamples to disprove a conjecture

For higher-attaining pupils:

- Use a Venn diagram to calculate the HCF and LCM

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Prime Pips in Pots This is a version of Wari, one of the oldest known games to still be widely played today. It involves small prime numbers.
- Number Grids Investigate the properties of number with these interactive number grids.
- Prime Numbers Video A reminder of what prime numbers and composite numbers are.
- Prime Numbers Jigsaw Interactive jigsaw puzzles of different types of grids containing prime numbers.
- Finding Prime Factors A straight forward explanation from SLEP
- Factor Trees Create factor trees to find the prime factors of the given numbers.
- Flabbergasted Game This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.
- Prime Labyrinth Find the path to the centre of the labyrinth by moving along the prime numbers.
- Convoluted Find the runs of four multiples in order as quickly as you can.
- Connect 4 Factors This a game for one or two players. The winner is the first to line up four numbers with a common factor.
- Pick The Primes Pick the prime fruit from the tree as quickly as possible. Practise to improve your personal best time.
- HCF and LCM Video Learn different methods for finding the highest common factor and lowest common multiple of two or three numbers.
- HCF and LCM Practise finding the highest common factor (H.C.F), sometimes called the greatest common divisor, and the lowest common multiple (L.C.M) of two numbers.
- HCF and LCM Calculator A demonstration of how to find the highest common factor (HCF or GCD) and the lowest common multiple (LCM) of two numbers.
- Factor Trees Challenge Can you determine the unique digits that will complete these factor trees?
- Venn Diagram Place each of the numbers 1 to 16 on the correct regions on the Venn diagram.
- Dump-A-Dice Race An online board game for two players involving prime and square numbers and making choices.
- Number Skills Inventory A checklist of basic numeracy techniques that every pupil should know.
- Divisibility Test Practise using the quick ways to spot whether a number is divisible by the digits two to nine.
- Divisibility Tests 2-12 A visual aid designed to be projected in the classroom. Here you can find the quick ways of telling whether a number is exactly divisible by the numbers two to twelve.
- Prime Pairs Game A game for two players who take turns to select two numbers that add up to a prime number.
- Goal Products Arrange the numbered footballs on the goal posts to make three, 3-number products that are all the same.
- Divisibility Tests Worksheet This worksheet contains a list of the divisibility tests along with a fill-in-the-table exercise.
- Scallywags and Scoundrels Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.
- Three Prime Sum A self-marking challenge to write each of the given numbers as the sum of three prime numbers.
- Product Square Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products.
- What Are They? An online exercise about sums, products, differences, ratios, square and prime numbers.
- Satisfy Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.
- Three Ways Find three different ways of multiplying four different digits together to get the given target number. There are nine levels for this online challenge.
- Snooker Investigation Investigate a special snooker table with only four pockets. Which pocket will the ball fall into for various sized snooker tables?
- Prime Square Drag the numbers into the red cells so that the sum of the three numbers in each row and each column is a prime number.
- Doughnut Dissection A puzzle to find four different ways of making 900 by multiplying together three different numbers.
- Delightfully Divisible Arrange the digits one to nine to make a number which is divisible in the way described.
- Sieve of Eratosthenes A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.
- Square and Cube Roots Find square roots and cube roots by first calculating the prime factorisation of a number.

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Factors A factor is a whole number that divides exactly into another whole number. We say the first number is a factor of the second number. Prime numbers only have two factors, one and themselves. After becoming familiar with times tables pupils then practise using this knowledge by recognising factors of numbers. There are well known and some less well known divisibility tests that are of some use in solving more complex number problems. Pupils need to know how to find the highest common factor (HCF) of two or more numbers either mentally or using a pen and paper strategy so that they can correctly manipulate fractions and algebraic expressions.
- LCM LCM stands for lowest common multiple or least common multiple. The LCM of two (or more numbers) is the smallest number that both of the numbers divide into exactly. Being able to find the LCM is useful when trying to find a common denominator when adding two fractions together. The LCM also describes the points when two (or more) periodic repetitions coincide. HCF stands for highest common factor which is also known as the greatest common factor. The HCF of two (or more) numbers is the largest number that divides into the two numbers exactly. Being able to find the HCF is useful in everyday organisational tasks and also when factorising algebraic expressions.
- Number Spotting patterns is an important skill in many areas of life. The world of numbers contains many fascinating patterns and understanding them enables better problem solving strategies. From seeing patterns in the multiples of numbers shaded in a hundred square to spotting the recurring sequences of digits in decimal numbers there is a great deal for pupils to be introduced to. This topic includes even, odd, prime, triangular, perfect, abundant, square and cube numbers. It uses factors and multiples to find solutions to real life problems and encourages number connections to be investigated for pleasure. There are a lot of puzzles, challenges and games too. See also the Mental Methods topic and our Number Skills Inventory.

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

Recognise odd, even, square, prime and triangular numbers.

A starter about sums, products, differences, ratios, square and prime numbers.

A game based around the concept of factors and abundant numbers.

An activity designed to address common misconceptions.

A puzzle about the lifts in a hotel which serve floors based on the day of the week.

If each number in a sequence must be a factor or multiple of the previous number what is the longest sequence that can be made from the given numbers?

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.