The four basic mathematical operations are:
Adding two (or more) numbers means to find their sum (or total). The symbol used for addition is '+'.
For example, 5 + 10 = 15
This is read as five plus ten is equal to fifteen or simply, five plus ten is fifteen.
Find the sum of 9 and 8.
9 + 8 = 17
Addition of Large Numbers
To add large numbers, list them in columns and then add only those digits that have the same place value.
Find the sum of 5897, 78, 726 and 8569.
- Write the numbers in columns with the thousands, hundreds, tens and units lined up.
- 7 + 8 + 6 + 9 = 30. Thus, the sum of the digits in the units column is 30. So, we place 0 in the units place and carry 3 to the tens place.
- The sum of the digits in the tens column after adding 3 is 27. So, we place 7 in the tens place and carry 2 to the hundreds place.
- The sum of the digits in the hundreds column after adding 2 is 22. So, we place 2 in the hundreds place and carry 2 to the thousdands place.
Subtracting one number from another number is to find the difference between them. The symbol used for subtraction is '–'. This is known as the minus sign.
For example, 17 – 8 = 9
This is read as seventeen take away eight is equal to nine (or seventeen take away eight is nine). Also, we can say that 17 minus 8 is 9.
Subtract 9 from 16.
16 – 9 = 7
Subtraction of Large Numbers
To subtract large numbers, list them in columns and then subtract only those digits that have the same place value.
Find the difference between 7064 and 489.
- Use the equals addition method or the decomposition method.
- Line up the thousands, hundreds, tens and units place values for the two numbers when placing the smaller number below the larger number as shown above.
Multiplication means times (or repeated addition). The symbol used for multiplication is '×'.
For example, 7 × 2 = 14
This is read as seven times two is equal to fourteen or simply, seven times two is fourteen.
To multiply a large number with another number, we write the numbers vertically and generally multiply the larger number with the smaller number.
A product is the result of the multiplication of two (or more) numbers.
Calculate 765 × 9.
Write the smaller number, 9, under the larger number, 765, and then calculate the multiplication.
- 9 × 5 = 45. So, place 5 units in the units column and carry the 4 (i.e. four tens) to the tens column.
- Calculate 9 × 6 and then add 4 to give 58 (i.e. 58 tens). Then place 8 in the tens column and carry 5 to the hundreds column.
- Finally multiply 7 by 9 and add 5 to give 68 (i.e. 68 hundreds). Write this number down as shown above.
- To multiply two large numbers, write the numbers vertically with the larger number generally being multiplied by the smaller number which is called the multiplier.
- We use the 'times table' to find the product of the larger number with each digit in the multiplier, adding the results.
- Remember to add a zero for every place value after the multiplying digit. For example, if the multiplying digit is in the hundreds column, add two zeros for the tens column and for the units column.
Calculate 38 × 70.
- Multiplying 38 by 70 is quicker than multiplying 70 by 38 as 70 contains a zero.
- A zero is placed in the units column. Then we calculate 7 × 38 as shown above.
Calculate 385 × 500.
- Multiplying 385 by 500 is quicker than multiplying 500 by 385 as 500 contains two zeros.
- A zero is placed in the units column and also the tens column. Then we calculate 5 × 385 as shown above.
Calculate 169 × 68.
- To multiply 169 by 68, place 68 below 169.
- Then we calculate 8 × 169 and 60 × 169 as shown above.
Division 'undoes' multiplication and involves a number called the dividend being 'divided' by another number called the divisor. The symbol used for division is '÷'.
- As division is the inverse of multiplication, start by dividing 4 into the column furthest to the left.
- 6 ÷ 4 = 1 and 2 is the remainder.
- Clearly, the remainder 2 is 200 (i.e. 20 tens); and we can carry this into the tens column to make 29.
- Now, 29 ÷ 4 = 7 with a remainder of 1. Clearly, the remainder of 1 is 10 (i.e. 10 units) and we carry this into the units column to make 12.
- Finally, 12 ÷ 4 = 3.
- The four basic mathematical operations are:
- Adding two (or more) numbers means to find their sum (or total).
- Subtracting one number from another number is to find the difference between them.
- Multiplication means times (or repeated addition). A product is the result of the multiplication of two (or more) numbers.
- Division 'undoes' multiplication.
basic operations, addition, sum, total, subtraction, difference, minus sign, equals addition method, decomposition method, multiplication, times, repeated addition, product, division, dividend, divisor, quotient, remainder
This list consists of visual resources, activities and games designed to support the new curriculum programme of study in Years Five and Six. Containing tips on using the resources and suggestions for further use, it covers:
Year 5: Add and subtract whole numbers with more than 4 digits, including formal written methods, add and subtract numbers mentally with increasingly large numbers, use rounding to check answers and determine levels of accuracy, solve addition and subtraction multi-step problems in contexts.
Year 6: Perform mental calculations, including with mixed operations and large numbers, use knowledge of the order of operations to carry out calculations involving the four operations, solve addition and subtraction multi-step problems in contexts, solve problems involving addition, subtraction, multiplication and division, use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.
Visit the primary mathematics webpage to access all lists.
Links and Resources
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The activities in this pack are designed for use as lesson starters or plenaries, but some could also be extended into a longer activity. The activity on page 8 is a ready-made chain game which could be used with the whole class to practise mental addition and subtraction. Classes could set themselves a time limit in which to complete it and improve on this each time. Blank cards are provided for teachers to write in extra questions to help differentiate the activity. The cards are at the end of the file.
This resource offers many activity ideas, games and worksheets which practise different areas of mathematics.
Topic 17 introduces four-digit subtraction, including the exchange of a thousand for ten hundreds.It offers investigations and worded problems and a checking system for subtraction.
The workbook and answer book can be found here.
By Years Five and Six, children will have encountered many different ways of carrying out subtraction. This video shows examples of subtraction methods used within a Year Six class. It includes examples of finding the difference by counting on, along a number line and in a column. It also shows an interesting method where column subtraction is done without borrowing but by using negative numbers.
This interactive resource is a great way of helping children understand the process of column subtraction. Three digit numbers are partitioned and place value counters are used before carrying out the column subtraction. This is a useful step when moving children towards a more formal written method for subtraction. Make your own place value counters and use them in class. A great aid for children struggling with column subtraction or for the whole class, dependent on specific class needs.
There are examples of expanded subtraction and column subtraction both with and without borrowing.
This book provides a wealth of games which practise many aspects of mathematics. Aimed at children working within the curriculum levels 3-6.
Jumble (sheet 18) practises mixed number operations.
Stopper (sheet 23) practises adding several single-digit numbers.
Snowman (sheet 25) practises addition and subtraction
of three-digit numbers.
Add and Match (sheet 32) practises adding sets of three single-digit numbers, aiming to make equal totals.
Go further with Number Skills provides 40 more activity sheets which are a great addition to many lessons.
This article from NRICH discusses ways in which teachers may develop children's problem solving skills. It provides ideas and links which would benefit a teacher's own practice or could be used as a basis of a staff training session.
Here are nine challenges from NRICH which support Addition and Subtraction at KS2.
Addition pack one contains fifteen work cards with activities on simple counting, number bonds to ten, addition using money and adding two digit numbers.
Addition pack two contains eleven work cards with slightly more challenging activities. Students are required to add two digit numbers which require a digit to be carried, know number bonds up to a hundred, to find multiples of ten and to be able to use a calculator to solve more challenging problems.
Addition pack three contains nine work cards in which the degree of challenge is greater. Students are required to add simple decimals, solve more challenging puzzles and add larger decimal numbers using money as the context.
This resource contains one pack of games, investigations, worksheets and practical activities supporting the teaching and learning of subtraction.
The six work cards provide activities covering subtracting two digit numbers using physical apparatus, and using the column method.