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Multiplication Methods
This timestable multiplication methods blog covers the teaching progression of multiplication in primary schools. It takes you through the different multiplication methods taught in primary maths and includes questions to challenge knowledge and help you practice the various techniques.
What are times tables?
Times tables are a list of multiples of a number. For example, 2, 4, 6, 8, and 10 are all multiples of 2. They are all parts of the two times tables.
What vocabulary is associated with times tables?
The vocabulary used to mean ‘times’ includes:
- multiply
- lots of
- groups of
- sets of?
- multiplied by
- array
- repeated addition
- product
- times table
What are times table facts?
A times table fact is the answer to a multiplication number sentence. Each fact has at least three other facts related to it. When you learn 2 x 4 = 8 you also know 4 x 2 = 8, 8 / 4 = 2, 8 / 2 = 4.
How do I work out a multiplication problem?
Multiplication problems can be solved in many different ways, including using concrete objects, pictorial representations, repeated addition, knowledge of number facts and methods like long multiplication.
Multiplication using Concrete Objects
To build solid foundations in maths knowledge children should be introduced to maths using objects to represent and solve number sentences. These objects can be moved around to show the answer to a question.
Representing the question using objects provides the opportunity for children to arrange those objects into groups before counting them. Manipulating the question in this way allows for a deeper understanding of numbers and their relationship to each other.
Multiplication using Pictorial Representation
To solve a multiplication problem using pictures objects need to be drawn to represent the number sentence.
Predrawn pictures can be provided or children can draw pictures or symbols to represent the number sentence.
Multiplication using Repeated Addition Multiplication
To solve a multiplication problem using repeated addition the same number is added again and again to a total. This can be done by counting in ones or counting in multiples.
Eight groups of two is 8 x 2 or 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2. Can you work out the answer?
If you want to know more about using concrete objects, pictorial representations, or repeated addition to solve multiplication problems have a look at our Year 1 Maths schemes ‘Let’s count in multiples’, ‘Let’s find the total by grouping’ and ‘Let’s share objects equally'.
These ready-to-teach multiplication and division lesson packs all about contain detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 1 multiplication and division Maths National Curriculum objectives.
Multiplication using Number Facts
Using number facts is a great way to solve multiplication problems. By encouraging children to break down number problems and use number facts they know they will develop a greater understanding of numbers. Number facts can include knowledge of times tables, doubles, or rounding.
Knowledge of doubling or rounding and the ten times table is helpful when solving nine multiplied by eight.
9 x 8 = ?
Using the ten times table
Nine multiplied by eight is the same as ten multiplied by eight minus eight.
10 x 8 = 80
so 9 x 8 is the same as
10 x 8 - 8 = 80 - 8 = 72
Using doubles
Nine multiplied by eight is the same as double nine multiplied by four.
9 x 4 = 36
double that to get 9 x 8 = 72
Knowing and using multiple routes to the same answer is a valuable problem-solving skill to have. Which method would you use to work out the answer?
If you want to know more about using number facts and fact families to solve problems have a look at our Year 2 Maths scheme ‘Let’s multiply and divide’.
This ready-to-teach lesson pack on solving multiplication and division problems, contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 2 Maths National Curriculum objectives.
Multiplication using Partitioning
Partitioning numbers are a helpful way to solve multiplication problems, especially if they involve numbers with multiple digits.
Multiplying a 2-digit number by a 1-digit number
To solve seventy-three multiplied by six using partitioning you might separate seventy-three into tens and ones. Then you can multiply seventy (or seven tens) by six and three by six. Finally, you add the two answers together.
73 x 6 = ?
70 x 6 = 420
3 x 6 = 18
420 + 18 = 400 + 20 + 0 + 10 + 8 = 438
73 x 6 = 438
Multiplying a 3-digit number by a 1-digit number
To solve one hundred and twenty-four multiplied by four using partitioning you might separate one hundred and twenty-four into hundreds, tens, and ones. Then you multiply one hundred by four, twenty (or two tens) by four, and four by four. Then you add the three answers together.
124 x 4 = ?
100 x 4 = 400
20 x 4 = 80
4 x 4 = 16
400 + 80 + 16 = 400 + 80 + 10 + 6 = 496
124 x 4 = 496
If you want to know more about using partitioning to solve problems have a look at our Year 3 Maths scheme ‘Multiplying and Dividing’.
This ready-to-teach lesson pack introduces the concept of multiplying 2-digit numbers by a 1-digit number using partitioning. It contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 3 Maths National Curriculum objectives.
The Grid Method Multiplication
The grid multiplication grid method is a more formal way to solve multiplication problems than the partitioning method shown above. This method builds on your knowledge of partitioning.
Can you solve 53 x 8 using the grid method? Use the example below to help you.
If you want to know more about using the grid method to solve problems have a look at lesson 5 of our Year 3 Maths scheme ‘Using Times Tables’.
This ready-to-teach lesson pack introduces the grid method to solve multiplication problems. It contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 3 Maths National Curriculum objectives.
Informal Partitioning Multiplication
Informal partitioning is a way to solve multiplication problems by partitioning. This version of partitioning requires a good understanding of place value and partitioning because fewer steps are recorded.
Can you solve 39 x 6 using the expanded method? Use the example below to help you.
Solve 53 x 7 using informal partitioning
If you want to know more about using informal partitioning to solve problems look at lesson 3 and lesson 4 our Year 4 Maths scheme ‘Seeing Doubles’.
This ready-to-teach lesson pack introduces the concept of multiplying 2-digit numbers by a 1-digit number using informal partitioning. It contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 4 Maths National Curriculum objectives.
Multiplication using The Expanded Method
Partitioning numbers is a helpful way to solve multiplication problems involving numbers larger than 1-digit numbers.
Can you solve 73 x 9 using the expanded method? Use the example below to help you.
If you want to know more about using partitioning to solve problems look at lesson 2 of our Year 4 Maths scheme ‘Multiplication and Division Methods’.
This ready-to-teach lesson pack introduces using the expanded method (and lots of other methods!) to solve multiplication problems. It contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 4 Maths National Curriculum objectives.
Short Multiplication Method
Short multiplication methods can be used to multiply any number by a one-digit number. Working from right to left, the ONES, TENS, HUNDREDS, and so on are multiplied. If the product of sum is more than 9 the number is carried.
Can you solve 95 x 6 using the expanded method? Use the example below to help you.
If you want to know more about using short multiplication to solve problems explore lesson 4 of our Year 4 Maths scheme ‘Multiplying Doubles and Digits’.
This ready-to-teach lesson pack introduces using short multiplication to solve multiplication problems. It contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 4 Maths National Curriculum objectives.
Long Multiplication Method
Long multiplication, or formal multiplication, is a helpful way to solve multiplication problems when both numbers are larger than 1-digit numbers. Long multiplication is similar to short multiplication except that more than one set of multiplications need to be completed. Just as before, you start with the ones, then the tens, and so on, and you carry the numbers if the product is more than 9.
Can you solve 395 x 52 using the expanded method? Use the example below to help you.
If you want to know more about using long multiplication to solve problems look at lesson 4 of our Year 5 Maths scheme ‘Formal Multiplication’.
This ready-to-teach lesson pack introduces using long multiplication to solve multiplication problems. It contains detailed planning, informative teaching slides, and engaging worksheets all designed to cover Year 5 Maths National Curriculum objectives.
Download these FREE multiplication resources and times tables games
These free multiplication resources can help you become more confident with your times tables.
These Times Table Grids and Multiplication Squares can help you learn and practice multiplication tables. The free pack includes a completed multiplication grid, a blank multiplication grid, a mixed-up multiplication grid, and a multiplication grid with missing numbers.
These Times Table Cubes can help you learn and practice the 2 times table to the 12 times table.
This Times Table Booklet is a fun way to check and develop your knowledge of multiplication facts up to 12 x 12.
This Times Table Chart is a great reference point when learning multiplication facts up to 12 x 12.
This Multiplication Wheel resource is a fun way for your class to practice their times table knowledge, as well as self-check their answers.
This Multiplication Make a Square Game is a fun way to practice multiplication skills.
Want ready-to-teach Maths lesson packs?!
We’ve got loads of downloadable Maths lesson packs. Each pack comes with lesson plans, slide show presentations and worksheets. View our full collection of Multiplication and Division lesson packs and learn how to get the most out of our resources.
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