Addition, Subtraction, Multiplication and Subtraction
Term 1 starting in week 3 :: Estimated time: 5 weeks
- Add and subtract integers
- Common factors
- Common multiples
- Rules of divisibility
- Primes to 100
- Square and cube numbers
- Multiply up to a 4-digit number by a 2-digit number
- Solve problems with multiplication
- Short division
- Division using factors
- Introduction to long division
- Long division with remainders
- Solve problems with division
- Solve multi-step problems
- Order of operations
- Mental calculations and estimation
- Reason from known facts
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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.
Addition Video A reminder of how to add two or more numbers using the column method.
Estimating Angles Estimate the size of the given acute angles in degrees.
Basic Addition A self-marking exercise on addition with increasing levels of difficulty.
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.
Times Tables A collection of activities to help you learn your times tables in only 5 days.
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.
BIDMAS Game An online interactive game celebrating the order of mathematical operations.
Mental Strategies Practise your mental arithmetic skills and learn some new strategies with this self marking exercise.
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
Formal Written Methods Examples of formal written methods for addition, subtraction, multiplication and division.
Rounding Ten Round the numbers to the nearest whole number or the given power of ten.
Clouds Can you work out which numbers are hidden behind the clouds in these calculations?
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?
Column Method for Multiplication Practise your multiplication skills with this exercise that already has the calculation set out for you.
Multitude Arrange the given digits to make three numbers such that the third is the product of the first and the second.
Palindrome Products Use long multiplication and pattern spotting to fill in the table with palindromic products.
Long Division Practise long division with this exercise that
already has the calculation set out for you.
Beat The Clock It is a race against the clock to answer 30 mental arithmetic questions. There are nine levels to choose from.
Division Video A reminder of how to divide one number into another using short or long division.
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.
Temperatures Test your understanding of negative numbers with this self marking quiz about temperatures.
Just In Time Every 10 seconds a new calculation appears on the screen: A dynamic visual aid.
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.
Grid Arithmetic Fill in a multiplication grid with the answers to simple multiplication and division questions.
Rounding Video A reminder of how to round numbers to significant figures, decimal places and to the nearest power of ten.
Negative Numbers Use negative numbers in basic arithmetic and algebraic calculations and word problems.
Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.
Negative Numbers Video Revise how to add, subtract, multiply and divide negative numbers.
Rounding DP A self marking exercise requiring students to round numbers to a given number of decimal places.
Rounding SF A self marking exercise requiring students to round numbers to a given number of significant figures.
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.
Missing Operations Exercise Each box represents a missing operation (add, subtract, multiply or divide). What are they?
Eleven In Your Head Multiply numbers by eleven in your head.
Multi-step Problems Solve multi-step problems in contexts, deciding which operations and methods to use and why.
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.
Numbasics A daily workout strengthening your ability to do the basic mathematical operations efficiently.
Rounding Snap If the last card put down equals the previous card to the nearest whole number then all players race to shout SNAP!
Sum of Three Palindromes Every whole number can be expressed as the sum of three palindromic numbers like this...
Negative Magic Four partially completed magic squares containing negative numbers. Fill in the missing numbers.
Numskull Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.
One Minute Maths A challenge to mentally add numbers together without making the classic place value mistakes.
Partial Pyramids Calculate the missing numbers in these partly completed pyramid puzzles.
Boxed In Numbers The classic dots and boxes game with the addition of some positive and negative numbers which determine your score.
Estimating Percentages Estimate the percentages represented by the diagrams.
If Then What? Deduce multiplication and division results from a related calculation.
Cartoon Scatter Graph Place the cartoon characters on the scatter graph according to their height and age.
Estimating Correlation Practise the skill of estimating the correlation of data on a scatter graph in this self marking exercise.
Correlation Arrange the given statements in groups to show the type of correlation they have.
Pyramid Puzzle Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target?
Quick Can you multiply a number by 1001 in your head? This exercise provides practice in this and other similar challenges.
Short Division Practise short division with this exercise that
already has the calculation set out for you.
Human Scatter Graphs Pupils move to positions in the room according to their data relative to the walls as axes.
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.
Partition Clues Partition numbers in different ways according to the clues given. The higher levels are quite hard!
Perfect Magic Square Arrange the sixteen numbers on the four by four grid so that groups of four numbers in a pattern add up to the same total.
Animal Records Match the values and the units to the animal world records.
Which Operation? Decide which mathematical operation is required then use it to find the answers.
Estimation Golf Play a round of golf using your estimation skills rather than golf clubs.
Heptaphobia Research Use written methods to answer ten arithmetic questions. When you have finished you will find the results of this amazing research.
Cosmic Redshift Investigate the number found by performing an algorithm on a three digit number.
Plotting Scatter Graphs Plot scatter graphs from data representing a number of different everyday situations.
Odd Scatter Out Just by looking at the scatter graphs can you decide which is the odd one out according to their summary statistics?
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.
- Estimating The ability to estimate values is an often overlooked part of Mathematics. Estimating lengths, weights, time, angles and solutions to problems should be practised regularly. Pupils should make sensible estimates of a range of measures in relation to everyday situations. A basic ability to estimate quantities without counting, like when choosing a checkout line at the supermarket, can be called a person’s innate ‘number sense’. Practising this kind of estimating may actually improve a pupil’s ability in other areas of mathematics. This is one of the findings of research published in Psychological Science, a journal of the Association for Psychological Science. Practising estimation can be a lot of fun when presented as a game, challenge or group activity and provides the opportunity for the teacher to introduce variety in the mathematics classroom.
- 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.
- Rounding The objective of rounding is often to get a number that is easier to use, at the cost of making it less precise. This approximation is very important in dealing with answers to mathematical problems and making them relevant to the real world. Rounding to a given number of decimal places or significant figures is required of pupils. See also the "Approximating" Starters. Once the principles of rounding have been understood, a fun way to practise the skills is to play "Rounding Snap".
- Statistics Statistics is the study of the collection, organisation, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments. It also includes describing mathematical relationships between variables and presenting these to an audience in a way that best conveys meaning. See also the topics called Data Handling, Probability and Averages.
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
Square Sequence
Write out as many square numbers as possible in 4 minutes.
2nd Lesson
Blots
The calculations are obscured by ink blots. What do you think the calculations would look like if there were no blots?
3rd Lesson
Division Quickulations
Random division calculations appear on screen every few seconds.
4th Lesson
Eleventh of the Eleventh
Practise multiplying and dividing by eleven in your head.
5th Lesson
Eleven Plus Two
Rearrange the letters in the ex
6th Lesson
Factuples
Spot the factors and the multiples amongst the numbers in the grid.
7th Lesson
Half a Dozen
Six calculations to complete without a calculator.
8th Lesson
Maggots
Do as many of the calculations as possible before the maggots infest!
9th Lesson
Missing digits
Find which digits are missing from the randomly generated calculations.
10th Lesson
Nine Digit Sum
Arrange the digits one to nine to make a correct addition calculation.
11th Lesson
Multiply Quickulations
Random multiplications appear on screen every few seconds.
12th Lesson
No Partner
Find which numbers in a given list do not combine with other numbers on the list to make a given sum.
13th Lesson
Route to Las Vegas
Work out the cheapest way from Los Angeles to Las Vegas by choosing the best route and adding up 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.
