multiplication

Why is multiplication important?

Multiplication is a basic maths skill that is important for students to continue their complete maths understanding. Without proper teaching tools and methods, students often struggle to understand this concept. How and when should they multiply? And what does multiplication mean?

If a student doesn't understand what, how and why they are doing any particular maths equation, it is hard for them to retain or remember what they are being taught. To multiply means to "fast add" or skip count, and it's a fairly simple manoeuvre. 

However, like with all maths concepts, the foundational concepts of Place Value, addition and subtraction must first be completely understood by your student. 

What is multiplication?

Multiplication is the process or skill of multiplying. It is also referred to as fast adding or skip counting. However, as simple as the definition may be, teaching multiplication is usually not as easy as it seems. 

The following is a simple example of multiplication:

3 × 7 is the same as 7 + 7 + 7 = 21

5 × 6 is the same as 6 + 6 + 6 + 6 + 6 = 30

As you can see, by "fast adding" and skipping the middle numbers, you can add up the total value of the numbers and find the answer much quicker. However, most students struggle with this concept. Why are there so many numbers? Where did they come from? And how do I know that I've gotten the correct answer?

By teaching multiplication using these simple methods, you will be able to confidently teach your students maths skills they can use in everyday life situations, further study, employment opportunities and their ongoing careers. It's definitely worth getting right!

Is multiplication important for maths?

The ability to know how and when to multiply numbers to achieve your desired answer is an essential maths skill for any student. Multiplication is part of the basic operations of maths and therefore is a key concept to master.

Here are the four basic maths operations:

+ Addition, Add, Sum, Plus, Increase, Total
− Subtraction, Subtract, Minus, Less, Difference, Decrease, Take Away, Deduct
× Multiplication, Multiply, Product, By, Times, Lots Of
÷ Division, Divide, Quotient, Goes Into, How Many Times

As you can see, multiplication is taught after addition and subtraction has been mastered by your student. This is an important piece to note.

After these basic maths operations are taught, the student continues learning more advanced maths concepts such as fractions, geometry, angles, algebra and calculus level mathematics. If students haven't understood the four basic maths operations fully, they will struggle ongoing. If students are left alone to struggle with maths, they will get poor maths results and end up hating maths. Sound familiar? 

multiplication

How do you teach multiplication?

The most simple and effective way to teach multiplication is through using multisensory methods. Multisensory means "using a variety of senses" and by engaging the tactile experience of your student to learn maths, concepts become much easier and much more understandable to teach.

There are four types of learning styles based on the VARK model. By teaching maths using all four senses and styles, your student will be able to learn, understand and integrate what they are being taught in a much more effective manner. 

  • Visual learner: meaning your student will remember pictures, images and what they see through their eyes
  • Auditory learner: meaning your student will remember what you speak to them, how you explain concepts, and what was heard by their ears
  • Reading and writing learner: meaning your student will learn through what they read and write down
  • Kinaesthetic learner: This means your student will learn, remember, recognise and integrate with a hands-on, tactile experience of what is being taught

Traditionally, maths isn't taught using multisensory methods. At one point in the classroom, cuisenaire rods were used to teach maths. That's a strategy that worked well, and most people remember them from school! However, for some reason these were taken out of the school curriculum and maths went back to being taught purely in an abstract form through formulas and rote learning. However, when students have nothing to base these abstract numbers from, no understanding or foundational awareness of numbers, they will continue to struggle with maths.

Most teachers, when they realise their students are still finger counting and struggling with Place Value after they have been in class for several years, don't know what to do. When students are constantly getting poor maths results and aren't able to understand simple concepts, there's something wrong in the way maths is being taught.

By using specific multisensory, tactile teaching methods, your student will be able to understand how numbers work and how they relate to each other. They will understand Place Value, and the value of each number, and be able to successfully navigate maths.
Teaching each concept sequentially will further support your student to build on their understanding of the previous concept and confidently move forward. It's a game changer!

Multiplication must be taught sequentially

The most important part about teaching multiplication is that it must be taught sequentially. That means your student needs to have mastered Place Value, addition and subtraction, and be able to easily identify numbers and recognise their corresponding value. 

Let me show you what I mean with a simple example:

Multiply 6 x 9 and write the correct answer.

If the student cannot recognise 6 is different to a 9, they will struggle with this question. If they do not understand Place Value properly, the correct answer of 54 may be written as 45, or 540. The student will also not be able to properly complete this question if they do not understand addition - which comes before multiplication. 

Fast adding, skip counting and multiplication are all the same thing. It means you are wanting 6 pieces 9 times (6 x 9) and instead of counting 1, 2, 3, 4, 5, 6 ....10.....15" you are counting quickly and getting to the answer faster by multiplying. 

multiplication

In the Math-U-See program, we teach multiplication by using these coloured blocks and introducing the concept of making rectangles or squares. Rectangles have dimensions and these are the numbers 5 across one side of the rectangle and 6 down, as shown in the example above. By using these hands-on blocks to show numbers, it becomes very easy for the student to see and understand this concept. 

If you want to know more about how to teach multiplication using rectangles, here's a short video. This specific method, paired with the coloured blocks, is used throughout the Math-U-See program to teach multiplication, fast adding and support confidence with maths.

Want to check your student's maths understanding?

Before going any further with maths, it's a good idea to check what your student knows and what they don't know. By taking a clear snapshot of their current understanding, you'll know where to start to fill in those gaps of knowledge, and how to support your student as they continue learning maths. 

Here's a simple diagnostic test to check your student's maths knowledge:

multiplication

Looking for extra support to teach maths?

Most teachers struggle with teaching their students maths concepts. It's a well known fact that maths is hard to teach, and even harder for students to understand. But that doesn't have to be the case - in fact, maths can be easy when taught using simple, multisensory methods. 

When numbers become tactile and can be seen, felt and experienced by the student, they are able to understand maths in a much more integrated way. By using key strategies to teach foundations first and progress sequentially, concepts that students notoriously struggle with until much later into highschool such as Place Value become simple to teach. 

Because of the high demand, we have put together a series of teacher-specific trainings to support educators to become confident about teaching maths. Perfect for primary and highschool teachers, tutors and intervention specialists when teaching multiplication and other maths concepts. 

What are the most challenging moments in your classroom or learning area when teaching your students? And what are the most rewarding moments you have? Let us know in the comments below

Good luck teaching happy students!

Esther White

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