Numbers
Term 2 starting in week 1 :: Estimated time: 2 weeks
- Integers, real and rational numbers
- Work with directed number (review)
- Solve problems with integers
- Solve problems with decimals
- HCF and LCM (review)
- Adding and subtracting fractions (review)
- Multiplying and dividing fractions (review)
- Solving problems with fractions
- Numbers in standard form (review)
For higher-attaining pupils:
- Understand and use surds
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Activities for pupils
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.
Addition Video A reminder of how to add two or more numbers using the column method.
Number Grids Investigate the properties of number with these interactive number grids.
Basic Addition A self-marking exercise on addition with increasing levels of difficulty.
Prime Numbers Video A reminder of what prime numbers and composite numbers are.
Number Line Banner A printable banner (multiple A4 sheets) of a colourful number line for the classroom wall.
Number Line This number line visual aid is designed to be projected onto a whiteboard for whole class exposition.
Prime Numbers Jigsaw Interactive jigsaw puzzles of different types of grids containing prime numbers.
Formal Written Methods Examples of formal written methods for addition, subtraction, multiplication and division.
Finding Prime Factors A straight forward explanation from SLEP
Prime Path Pace The objective is to find a continuous path of prime numbers in the shortest time.
Factor Trees Create factor trees to find the prime factors of the given numbers.
Decimal Plus Video Learn the written methods for adding and subtracting decimal numbers. This video is to help you do the online, self-marking exercise.
Flabbergasted Game This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.
Beat The Clock It is a race against the clock to answer 30 mental arithmetic questions. There are nine levels to choose from.
Fractions Video So many people can't remember how to add, subtract, multiply and divide fractions so here is a reminder.
Discombobulated A fun game requiring you to find numbers which add up to the target number as quickly as possible.
Least Common Multiple A cartoon from Smile and Learn with very easy examples of how to find the LCM of two numbers.
Product of Primes Match the primes that multiply to give the products. A drag and drop activity.
Prime Labyrinth Find the path to the centre of the labyrinth by moving along the prime numbers.
Arithmagons Find the missing numbers in these triangular, self-checking puzzles and discover the wonders of these fascinating structures.
Decimal Plus Practise mental and written methods for adding and subtracting decimal numbers.
Multiplying and Dividing Decimals A straight forward, no nonsense demonstration of the methods of multiplying and dividing decimals.
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.
Fractions A series of self-marking exercises on adding, subtracting, multiplying and dividing fractions.
Boxed In Fractions The classic dots and boxes two-player game with the addition of some fractions which determine your score.
Fractionagons Calculate the missing fractions in these partly completed arithmagon puzzles.
Negative Numbers Use negative numbers in basic arithmetic and algebraic calculations and word problems.
Negative Numbers Video A video showing how to how to add, subtract, multiply and divide negative numbers.
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?
Mixed Numbers Revise the methods for adding, subtracting, multiplying and dividing mixed numbers (fractions) by watching this video.
Mixed Numbers A self marking quiz about the application of the four operations to mixed numbers.
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.
Numbasics A daily workout strengthening your ability to do the basic mathematical operations efficiently.
Mental Maze Choose the correct operations to get through the maze and achieve the given target.
Number Skills Inventory A checklist of basic numeracy techniques that every pupil should know.
Standard Form Test your understanding of standard form (scientific notation) with this self-marking quiz.
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.
Thai Restaurant Calculate the restaurant bills for each of the tables in the Thai Restaurant.
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.
Powten Practise multiplying and dividing by powers of ten without using a calculator.
Quickulations A mental arithmetic visual aid that displays random calculations then after a few seconds displays the answers.
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.
Bidmaze Find your way through the maze encountering mathematical operations in the correct order to achieve the given total.
Expedite Drag the numbered cards to produce a multiplication fact. Complete twenty mixed times tables questions to earn a trophy.
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.
Heptaphobia Research Use written methods to answer ten arithmetic questions. When you have finished you will find the results of this amazing research.
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.
Surds A self-marking exercise on calculating, simplifying and manipulating surds (also known as radicals).
Number Systems Place the numbers in the correct sets in this concentric circles Venn diagram.
Some Sums and Products Number puzzles involving adding, multiplying and problem solving
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Arithmetic The ability to perform mathematical calculations is still very important despite our hi-tech environment. Good numeracy skills support the understanding of more advanced mathematical concepts at all levels. Mathematicians still consider mastery of the manual algorithms to be a necessary foundation for the study of algebra and computer science. Pupils should have a good grasp of the meaning of numbers and use their understanding of place value to multiply and divide whole numbers and fractions. They should be able to order, add and subtract negative numbers in context. They should use all four operations with decimals rounding answers where required. They should be able to solve simple problems involving ratio and direct proportion and calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate. See also the Mental Methods topic and our Number Skills Inventory.
- Decimals Working with decimals, for most pupils, presents little difficulty if the pupils have confidence working with whole numbers. The topic of decimals provides an extension to the place value system with the addition of tenths, hundredths, thousandths etc. For many pen and paper multiplication and division calculations the decimal numbers can be considered as whole numbers then the answers adjusted accordingly. So 2.4 x 2.34 can be considered as 24 x 234 รท 1000. The numbers are multiplied by ten and one hundred respectively then the answer needs to be divided by the ten and one hundred to compensate. Pupils should use their understanding of place value to round decimal numbers. They should also use decimal numbers in the context of measures and money. This topic also contains activities which encourage pupils to investigate and explore the properties of decimal numbers and gain a better understanding of them.
- 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.
- Fractions A fraction is a part of a number. Fractions are either vulgar or decimal. Vulgar fractions can be proper, improper or mixed. Equivalent fractions have the same value. Pupils, at all stages of their learning, should practise using fractions. From dealing with halves, the most basic fraction, to manipulating algebraic fractions containing surds, this topic is always relevant. Proficiency also depends on reasonable numeracy skills particularly the multiplication tables and finding the lowest common multiple of two numbers. Pupils also need to be able to convert vulgar fractions to decimals and percentages and vice versa. Be wary of teaching the 'rules' for manipulation fractions by rote. Pupils need to understand the reason why and the time-honoured key to understanding starts with the imaginary pizza and the much-used fraction wall.
- 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.
- Mental Methods Though using pencil and paper are as useful as having up-to-date technology skills, there is no substitute for strategic mental methods for working out calculations and solving problems. The activities in this topic are designed to improve pupils' abilities to use their brains. Calculating 'in your head' can be a difficult task. If you cannot remember what you have worked out or simply do not know how to solve a problem then it can be very challenging and frustrating. It is important to learn and practise mental arithmetic and using mathematical patterns, you can dramatically improve the speed and accuracy of your mental mathematics. See also the Arithmetic topic and our Number Skills Inventory.
- Negative Numbers A negative number is a real number that is less than zero. Such numbers are often used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are also used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. Here are some activities designed to strengthen a pupil's understanding of negative numbers.
- 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.
- Tables Times Tables is the common term referring to the multiples of numbers 2 to 12 (or 2 to 10). Having a quick recall of these tables is an important pre-requisite for studying other aspects of mathematics and for coping with personal finance and other area of everyday live involving numbers. People of any age can improve their skills in recalling table facts. They should learn then as they would learn a song or a dance. You need to know your times tables forwards, backwards and all mixed up. Spend time learning them well and you'll reap the benefits in future. Here on this website we have developed many activities that help pupils learn their times tables and as then revise them in different ways so that the recall becomes easier and easier. Some of the activities are games and quizzes while others help pupils spot the patterns in the times tables in many different ways. Here's a plan for learning a new times table in only five days!
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Happy New Year
Work out the date for various given amounts of time after the beginning of the year.
2nd Lesson
Not Multiples
Write down the numbers from a list which are not multiples of a given number.
3rd Lesson
Register
When the register is called answer with a multiple of 7.
4th Lesson
Recurring Decimal
Use your calculator to find which whole number divided by another whole number gives a recurring decimal.
5th Lesson
Digital Lights
Questions about the Small LEDs used to make up the digits on a calculator display.
6th Lesson
Happy Numbers
To find out whether a number is happy or not, square each of its digits, add the answers and repeat. If you end up with 1 the number is happy! How many other happy numbers can you find?
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.
