There are 3 free PDF different worksheets available depending upon the child’s level of difficulty.
Before we do detail the contents of what’s inside each of the math worksheets, let’s look at how best we can teach this mathematical concept of multiplication.
How do you start teaching multiplication?
The concept of multiplication is better understood once your child already has a grasp on the concept of addition.
The concept of addition helps to determine the total of a cluster of objects (or no objects), whereas multiplication helps to determine the sum total where clusters of objects are equal sizes.
Concrete Example
Where possible start with a concrete or tangible example.
For example:
If I have 3 apples in each box and there are 3 boxes, how many apples do I have altogether?
If children are familiar with addition they would answer the word problem by using a technique like:
3 + 3 + 3 = 9Which is the correct procedure and provides the correct answer.
However, math has been designed to shortcut lengthy process.
With our word problem involving apples, what if there were more boxes? Instead of just 3 boxes we had 6 boxes, how many apples in total now?
Knowing the answer had been achieved previously, a child is likely to resort to the same process, instead of adding 3 sets of 3, they now apply 6 sets of 3:
3 + 3 + 3 + 3 + 3 + 3 = 18
From here it’s important to move to a completely different set of objects, but which uses the same numbers .
The purpose of changing the object, but using the same set of numbers is to emphasise that regardless of what the object is, if there are 3 sets of 3 objects they will always total 9.
Abstract Example
After iterating through a few tangible examples with objects, try to have the child guess what the answer would be if you had 3 bones for each dog and there were 3 dogs in total.
How many bones would there be?
If the child has discerned the pattern with our concrete examples then they should guess correctly. If they don’t, start drawing the bones on a piece of paper and illustrate how to arrive at the answer of 9.
If jumping into the abstract is proving difficult then go back to concrete examples where you are using different objects (coins, stamps, sultanas, etc), but keep asking the same question .
It’s when the child understands 3 sets of 3 equals 9 for all instances that we can progress on.
Expanding the Abstract Concept
Once a child has understood a basic concept of 3 \times 3 = 9 we broaden their understanding by asking what they think 3 sets of 4 apples. It helps if you can maintain a similar order, or the same objects previously taught to help them see a connection with the concept that is being taught.
How many apples do I have if I have 4 apples in each box, and there are 3 boxes?
It’s important to make minimal changes when progressing on a concept in mathematics. Confidence is an important ingredient when learning mathematics and while fireworks may be going off when your child grasps the concept, you still need to be patient.
When making the small incremental change to your problem the child should hopefully discover the same answer when the objects are of the same quantities.
When you feel your child is grasping the concept that you should then ask a question without any props:
How many apples would I have if I have 5 apples in each box, and there are 3 boxes?
Continue increasing one of the numbers, and the child should see they are increasing their answer by a step value, eg. 9… 12… 15… 18.
Write the answers down and as you do so annotate the paper like so:
\def\arraystretch{2}
\begin{array}{c:c}
3 \times 3 = & 9 \newline 4 \times 3 = & 12 \newline 5 \times 3 = & 15 \newline 6 \times 3 = & 18
\end{array}
Ask your child what they think the $\times$ symbol means. Your child could give various answers, but they should be around the definition of sets of .
Once you’ve established what the multiplication symbol looks like, you can then proceed to the times tables.
Learn Times Table Quickly
The best way we have found to teach the times table is to have the child memorise it. Once a child thinks they have memorised their times tables, it’s good to randomly check for understanding.
If through the process the child stumbles on learning a particular times tables there are two approaches you could take to help them learn:
Use Jumps
As we illustrated at the end of the abstract section above, you want your child to be able to see the jumps or steps that are taken with each incremental number.
If your child stumbles to learn say the 7 times table, write on a sheet of paper the times table questions (leave the answers intentionally blank and don’t write all the questions down, you’re just trying to kick start their memory):
\def\arraystretch{2}
\begin{array}{c:c}
1 \times 7 = & ... \newline 2 \times 7 = & ... \newline 3 \times 7 = & ... \newline 4 \times 7 = & ...
\end{array}
As your child progress from the first multiplier they should discern they need to add 7 to the previous answer to get the next answer.
Continue down the page with the remaining questions, and have them complete the rest of the times table for that number.
Return to Concrete
Where possible stay with the abstract aspect of the concept, and where needed return to the concrete. Children love to play with toys and objects, so be mindful they may just want to play with toys rather than doing the work!
Memorising Times Tables
The best way to learn the times table quickly is to find times during the day when your child can be doing the work. We found the best times during the day was when they were in the car travelling to the grocery store or even to school!
We then printed out a times tables PDF, cutting out each individual group and then clipping them together with a little bulldog office clip (paper clips tend to slip off).
Now you have printed out the times table all that is needed is to find opportune moments for your child to learn them.
I have found learning the times table in the car to be one of the best ways to learn times tables as fast as possible, because it’s surprising how much time we spend in the car and all we’re doing is staring out the window listening to the radio! Why not spend that time learning the times table?
To get this practice started, simply, do the following:
- Print out the above template
- Cut it so that you have 12 pieces
- Bind them all together using a sturdy bulldog clip to clamp it all together
- Hand it to your child and ask them to start reading out aloud what they see in front of them. Just focus on one sheet at a time. For example have them recite their 1 times table: “ 1 times 1 is 1. 2 times 1 is 2. 3 times 3 is 3…” etc.
- After they’ve finished reading out aloud what they see, get them to do it again.
- As you begin repeating for the third or fourth time for say, the 1 times tables, ask if they could repeat the 1 times table without looking at the sheets. (The 1 times table would certainly be the second easiest times table to complete, 0 times table being the easiest!).
By doing this exercise in the car you will be quite surprised at how quickly your child will be able to get through the entire times table. Some children, such as our eldest, took a little longer than what we thought, but our second child (at the age of 4) completed the entire times table in no more than 3 weeks!
One other tip when undertaking this task with having your child learn their times table in the car is that you might want to go in an order that gives them confidence as they progress. By reflecting on how well they’re doing by getting through the work, it helps to provide impetus in continuing and getting through the task.
Here’s an order that worked quite well for us:
1 \times, 10 \times, 2 \times, 3 \times, 5 \times, 9 \times, 11 \times, 4 \times, 6 \times, 8 \times, 7 \times, 12 \times
Of course, we cannot forget doing the 0 times table, feel free to throw this one in by teasing them that this is the hardest one of them all!
What Do You Mean “Learning Multiplication is Hard”?
As you can see, learning multiplication isn’t that hard. What tends to happen when learning this concept is that we get too bogged down in trying to explain either why we multiply, or what the concept of multiplication is. Sure, it’s great to know this stuff, be as we don’t have a lot of time we need to spend our limited time on learning how to multiply.
If we have the time we can certainly see where it’s applied, why we use it and what multiplication is all about, but let’s not waste time. Children can grow to appreciate math when they have the confidence in getting the work done quickly and easily.
How to Ask Multiplication Questions
Now your child has begun to memorise their multiplication tables it is time to check their ability by having them do some worksheets by themselves.
The free worksheets below are of the following types:
- Vertical styled questions
- Horizontal styled questions
- Questions using numbers ranging from 0-5
- Questions using numbers ranging from 0-12
The reason for the change in question format (horizontal and vertical) is to test their true multiplication skills and flexibility with tackling multiplication problems.
We don’t want our child being too familiar with a layout when it comes to a multiplication question. They need to be able to know that a horizontal or vertical styled question needs the same concept applied.
Therefore, your child needs to know that the same question 5 \times 4 can be structured like that, or like this:
5 \ \times 4
The reason for breaking up the worksheets with two different ranges of numbers asked is so that you can start once they’ve completed the first 5 digits and zero.
One of the worst things regular math worksheets do is that they usually have a great big heading at the top of the page that already contextualises the work that the students will be doing on this sheet, for example, emblazoned at the top for these worksheets would be the words:
This similarly occurs within a regular math class too: a teacher at the beginning of the class will tell the children,
“Today boys and girls, we will be learning basic multiplication and doing single digit multiplication, here are your worksheets”
Math Teacher at a school somewhere every day
The students know they are in math class, and if the purpose of performing an informal test was to check their ability you should give them a worksheet without any prompting or form of context at all!
Therefore, be very mindful when printing these worksheets out that they are context free for a reason. After printing these worksheets out have your child sit down, and do them. Don’t prompt them for at least the first 5 minutes. Let them try to figure out that the questions are not addition, nor subtraction, it’s just plain multiplication.
Certainly if they struggle in the first couple of goes help guide them, but after when you feel they can identify and answer appropriately you shouldn’t need to prompt them any further.
Math Multiplication Worksheets
(Please note no answer sheets are provided)
Conclusion
When teaching your child the concept of multiplication start with concrete tangible examples. As your child begins to understand the concept of multiplication through examples, slowly test understanding without the assistance of tangible learning aids.
As your child gains confidence in the concept of multiplication, assist your child by trying to commit to memory the times table. Find avenues throughout the day when you can easily recite a times’ table, such as in the car on the way to the grocery store, or even to school.
Learning multiplication isn’t a difficult task, but one which will require patience when starting and time to master – just like anything else.
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