Solving problems with multiplication and division
Term 2 starting in week 3 :: Estimated time: 3 weeks
- Properties of multiplication and division
- Understand and use factors
- Understand and use multiples
- Multiply and divide integers and decimals by powers of 10
- Convert metric units
- Use formal methods to multiply integers
- Use formal methods to multiply decimals
- Use formal methods to divide integers
- Use formal methods to divide decimals
- Understand and use order of operations
- Solve problems using the area of rectangles and parallelograms
- Solve problems using the area of triangles
- Solve problems using the mean
For higher-attaining pupils:
- Multiply by 0.1 and 0.01
- Solve problems using the area of trapezia
- Explore multiplication and division in algebraic expressions
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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.
Paradox Arrange the mathematical statements so as not to create a paradox.
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.
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.
Basic Subtraction A self-marking exercise on subtraction with increasing levels of difficulty.
Number Line This number line visual aid is designed to be projected onto a whiteboard for whole class exposition.
BIDMAS A self marking exercise testing the application of BIDMAS, an acronym describing the order of operations used when evaluating expressions.
Basic Multiplication A self-marking exercise on multiplication with increasing levels of difficulty.
Basic Division A self-marking exercise on dividing numbers of up to four digits by one or two-digit whole numbers using the formal written methods of short and long division
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.
Clouds Can you work out which numbers are hidden behind the clouds in these calculations?
Factor Trees Create factor trees to find the prime factors of the given numbers.
BIDMAS Video A reminder of the order of operations often referred to as BIDMAS, BODMAS or PEMDAS.
Broken Calculator Some of the buttons are missing from this calculator. Can you make the totals from 1 to 20?
Chain Challenge How fast can you perform all of the given operations without using a calculator?
Palindrome Products Use long multiplication and pattern spotting to fill in the table with palindromic products.
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.
Division Video A reminder of how to divide one number into another using short or long division.
Product of Primes Match the primes that multiply to give the products. A drag and drop activity.
Equatero Find the expression from a series of guesses and clues.
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.
Area and Perimeter Show that you know the area and perimeter formulas of basic shapes.
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.
Cracked Clock Quiz A self marking set of ten mathematical questions about a clock which cracked!
Yohaku Puzzles Fill in the blank spaces so that the cells give the sum or the product shown in each row and column.
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 Revise 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.
Make an expression Use the digits given to form an expression equivalent to the given total.
Masad For each pair of numbers subtract the sum from the product then divide the result by 20 without a calculator.
HCF and LCM Video Learn different methods for finding the highest common factor and lowest common multiple of two or three numbers.
Missing Operations Exercise Each box represents a missing operation (add, subtract, multiply or divide). What are they?
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.
Estimating Estimation is a very important skill. Use this activity to practise and improve your skills.
Multiplication Video A reminder of how to multiply two numbers using the column method or long multiplication.
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.
Number Skills Inventory A checklist of basic numeracy techniques that every pupil should know.
Numskull Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.
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.
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.
Subtraction Video A reminder of how to subtract one number from another using the column method.
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.
Partition Clues Partition numbers in different ways according to the clues given. The higher levels are quite hard!
Product Square Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products.
Satisfy Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.
Which Operation? Decide which mathematical operation is required then use it to find the answers.
Converting Standard Units Converting measurements of length, mass, volume and time from one unit of measure to another.
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.
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.
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.
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.
- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- 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.
- 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.
- 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
A Thousand and One
Develop a quick way of mentally multiplying any number by 1001.
2nd Lesson
All for 100
Can you write an ex
3rd Lesson
Broken Calculator (2 and 3)
Make the numbers 1 to 10 using only the keys on the broken calculator.
4th Lesson
All The Nines
Add up all the multiples of nine in an elegant way.
5th Lesson
Multiply, Add, Subtract and Divide
For each pair of numbers subtract the sum from the product then divide the result by 20 without a calculator.
6th Lesson
Six Discrimination
An activity involving a calculator which is missing the six button. Can you evaluate the given expressions without using the six?
7th Lesson
Two Pots Make Four
Make exactly four litres given a seven litre jug and a five litre jug.
8th Lesson
Alphanumbetical
A challenge to find the number which when written as a word has all the letters in alphabetical order.
9th Lesson
Strange Tables
A challenge to learn an unfamiliar times table involving decimals.
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.
