Ensure Academic Growth
Being a kid is not easy. There’s so much on their to-do list and a lot less time to execute it all. They have to remember the timings of their favorite show and try to like the greens in their lunch. They also have to be a little bit careful while making mischiefs so that the pranks are funny enough to make someone laugh but not stupid enough to land them in their room grounded for a week.
These are the things that pretty much tickle our brains when we see kids these days. We don’t think about what pre or post-crisis analysis they do of their surroundings before coming up with some pranks. We applaud their memory power when we see them recite some dialogs from their favorite shows. We don’t judge their observation powers and skills when we see them mimic an animal. But then, why do we become critical and concerned when it comes to their academic mastery?
The part where we want them to learn and grow academically is where we should be the most accommodating of our kid’s understanding. It is where we should encourage them to follow their instincts and hunches and to change their perspective. We should help them to solve problems their own way – by being smart and hitting the bullseye instead of shooting arrows in the dark.
We stress upon practicing math because it makes our kids critical of the world around them and is important for their academic journey. But are we making sure that they “practice” it and not “learn” it?
It’s true that concepts like addition and subtraction can be done on fingers but what about multiplication and division? Are they also easy enough to ingrain in a kid’s mind? Or do we need a more cumulative and witty approach to teach our kids that it is not as difficult as it seems?
Read on to successfully answer the above questions and help your kids love the ins and outs of multiplication.
Table of Contents:
- Multiplication: Addition’s Goofy Friend
- Multiplication Chart
- Times Tables
Multiplication: Addition’s Goofy Friend
Kids don’t really put much thought into learning addition. They see a problem saying 2 + 1, they imagine two objects, conjure one more of the same type, count them all, and brava; 2 + 1 = 3.
But it is difficult for them to imagine objects in their thoughts when they see an expression that has a cross instead of the plus sign,
2 ✕ 3,
So what happens now?
Making multiplication fun!
We learned multiplication through a traditional, more conventional, and boring approach called rote memorization. We would just memorize facts of 2, answer the question and move on, thinking that we fully understand the concept. But this became a problem when we would go into higher grades, where multiplication was just not an independent problem to solve.
In higher grades, multiplication concepts get connected to division concepts. And division gets inter-linked with fractions which are connected to decimals. There’s an all-ruling dynasty of concepts where kids cannot avoid multiplication because it has its own applications like estimating, evaluating amounts of money, order of operations, calculating distances, and even elapsed time problems.
So how do we make multiplication more approachable to kids and not just a saga of rote learning?
The answer lies in how we teach it at an elementary level. A simple term called “Groups” and an easy approach called “Repeated Addition” – is a great place to start!
How to start teaching multiplication: A visual approach – Groups
It’s important to introduce the concept of multiplication to kids the right way. The transition from addition to multiplication can be made easier with the help of “Groups”.
To put it dramatically, using Groups is like sugarcoating multiplication as this approach helps kids find it easy and not be afraid of it.
The above image can easily be described as “5 groups of 2 airplanes each”.
And how do you find the total number of airplanes? By adding “2”, five times i.e.,
2 + 2 + 2 + 2 + 2 and that is 10.
To help your kids become proficient at making repeated addition expressions; you can try this game on SplashLearn!
Repeated Addition to Multiplication Expressions
Once your little learners have aced up their knowledge of writing repeated addition sentences, the next step is to teach them about multiplication expressions. Let’s consider this example:
4 groups of 5 turtles
Repeated Addition Sentence:
5 + 5 + 5 + 5
Now, once your kid gets tired of writing addition expressions, you can introduce to them an easy way to write these expressions in a shorter and concise manner. It won’t be difficult to let your kid observe that we have just written the number “5”, four times. Therefore, we can also write this as
4 times 5
And this becomes the multiplication expression;
4 ✕ 5,
But this step becomes crucial as this is where we subconsciously end up making a mistake. We start teaching them how to solve these expressions and forget about the fact that this step also needs to be practiced more.
Support is the key
Before starting with skip counting, it’s imperative to bring a sense of familiarity with multiplication expressions.
Kids should be able to find out the product without knowing the multiplication rules. We can do this by encouraging the learners to relate expressions to story situations by giving them a random multiplication expression and asking them to build a situation as to what would have resulted in this expression.
Allow their creativity to be a part of their learning experience. When all of this is done and your kids have stopped drawing their multiplication symbols like the letter “X” of the alphabet (yes, there is a difference), you will know that they are ready!
Try this game and let your kid become an expert at turning repeated addition expressions into multiplication expressions before we move on to teaching them how to solve these expressions.
Multiplication Strategies 101:
Multiplying using Fingers
Yes, you read that right!
We usually just add using fingers because it seems pretty easy and straightforward, but we can also multiply using fingers.
Let’s try to solve this expression,
4 ✕ 5
This strategy seems to make it easy to find the answer to a multiplication expression with smaller numbers.
P.S: Don’t worry, we’ve got you covered! The next part deals with the strategy to multiply bigger numbers.
Step 1: Hold up as many fingers as the second number, which in this expression is the number 5.
Step 2: Skip count by the first number ( “4” in this case) as many times as the number of fingers you have raised.
And just like that, you have the answer to the given expression.
4 ✕ 5 = 20
Kids become comfortable with the multiplication facts of 2, 3, 4, 5 very easily and we can put this to good use by teaching them the distributive property a.k.a the ultimate multiplication strategy.
Let’s try solving this expression:
3 ✕ 9
Step 1: Write the bigger number as the sum of 5 and another number:
3 ✕ 9 = 3 ✕ (5 + 4)
Step 2: Split this expression as a sum of two smaller expressions, like this:
3 ✕ 9 = (3 ✕ 5) + (3 ✕ 4)
Step 3: Solve these smaller expressions and add the resultants to find the final answer.
3 ✕ 9 = 15 + 12 = 27
3 easy steps and multiplication won’t be a ho-hum affair for our young learners anymore.
Multiplication in everyday life
Multiplication strategies are more like simple rituals that can help kids solve problems. But this still won’t give them an idea of how important it is in the real world.
We can help our budding mathematicians associate multiplication to real-life by asking them to check the next grocery bill or asking them about the number of saplings/flowers in a flower bed the next time they go gardening. Counting amounts of money when they are in a thrift store and it’s a buy or bye situation, multiplication can be their savior in a real sense!
The process to prepare kids for higher grades begins once they have understood what multiplication is. For this purpose, there exists a very useful tool called the Multiplication Chart.
Let’s see how it works.
A basic multiplication chart contains multiplication facts of numbers from 1 to 10 and using a multiplication chart is as easy as making a sandwich. It could be even easier than that.
Let’s try solving this expression using the multiplication chart:
Equation: 7 ✕ 9
Step 1: Locate the row that shows “7” and the column that shows “9”.
Step 2: Look for the box where the row for 7 overlaps with the column for 9.
And so we have the answer to our expression,
7 ✕ 9 = 63
To make things easier, you can find a multiplication chart as a free printable for reference at the end of this blog. We have also included an empty multiplication chart for you to make your own games like multiplication bingo!
Before you ask, multiplication charts do work the opposite way as well. You could look for the column that shows facts of 7 and the row that shows facts of 9 and the answer would still be the same.
This fact is referred to as the commutative property of multiplication i.e.,
7 ✕ 9 = 9 ✕ 7
The principle behind this property is as easy as it can get. It’s merely a play on perspective!
Take a look,
This picture shows 3 groups of 6 balls each, so the multiplication expression for this would be –
3 ✕ 6
But if we were to look at the picture another way,
Now it’s 6 groups of 3 balls each, so the multiplication expression would be –
6 ✕ 3
As the total number of balls is the same in any case, this means that both the above expressions will have the same result.
3 ✕ 6 = 6 ✕ 3
Kids can use this escape hatch when they are stuck on the times’ table of a bigger number and can effortlessly find the answer by recalling the related multiplication fact of a smaller number.
Relevance of Multiplication Charts
Multiplication charts are important because they help students become familiar with the facts of different numbers. So, when our young learners move on to learning their times tables, it would not just be rote memorization. They would instead work up their brains to use commutative properties if they ever get stuck somewhere or they could also use the distributive property to derive a multiplication fact.
Using a multiplication chart is a stepping stone towards learning the process of multi-digit multiplication. As kids progress through different grades, multiplication becomes an essential and basic skill for the complicated aspects of math heading their way.
Thus, it is necessary for kids to be able to build upon what they already know and a multiplication chart can help them get comfortable with it.
Multiplication Charts are scaffolding techniques that can help them learn in a better way. But the true test is when kids start learning their times tables and we’re here to help with that!
Times tables surely take us back to the most anxious days of our childhood. Kids establish a strong foothold in the math world once they accept that the times tables for 7s and 8s are not to be taken lightly.
2s, 5s, and 10s are called the brotherhood of multiplication (or sisterhood) as they never betray. These numbers can help kids remember the other times tables as well.
Patience is the ultimate virtue to practice with little kids. If you show the kids a pattern in something, they readily accept that knowledge because it feels comfortable. Showing them a string of numbers and asking them to etch it in their memory will not help them in the long run.
Learning times tables is not something that can be achieved by just repeating it 3 times a day for 3 days. That sounds more like a medicine prescription than a strategy. Nevertheless, here are some tips to help our learners with their times tables.
Tips for Times Tables Mastery
Times Table of 1
This times table has a really interesting take. Accepting who you are is just what this times table is all about. Whatever number you multiply with 1, the result is the number itself.
Times Table of 2
The number 2 is what we call “Double or Nothing”.
Any number you multiply with 2, will get doubled or will simply get added to itself.
Times Table of 3
Here is the easiest trick to practice the times tables of 3. If you want to multiply a number by 3, multiply it by 2 first and then add the same number to it.
Let’s have a look at this example:
If you want to find 3 ✕ 6, go back to your 2s and check 2 ✕ 6 and add 6 to it.
So – 3 ✕ 6 = (2 ✕ 6 )+ 6 = 12 + 6 = 18
If you want to find 3 ✕ 8, go back to your 2s and check 2 ✕ 8, then add 8 to it.
So – 3 ✕ 8 = (2 ✕ 8) + 8 = 16 + 8 = 24
Times Table of 4
Time for doubling the doubles. There is no easy way out of this one. If you want to multiply a number by 4, double it once, and then double what you get!
Times Table of 5
The second in the beloved brotherhood, this number does not even need a trick, but if your kid still gets stuck with this one. Here is what you can do:
Any number that you want to multiply 5 with, attach 0 at its end and then half it.
If you want to find 5 ✕ 7, attach a 0 at the end of 7,
So now it’s 70. And half of 70 is 35.
So, 5 ✕ 7 = 35
Times Table of 6
This one works like just the table of 3. If you want to find the product of a number with 6, go back to your 5s, multiply that number with 5 and then add the same number.
So, if you want to find 6 ✕ 8, check 5 ✕ 8 and add 8 to it.
So 6 ✕ 8 = (5 ✕ 8 ) + 8 = 40 + 8 = 48.
Times Table of 7
Before kids try to tackle this one, make sure they know their previous tables so this one does not seem that difficult.
Let’s see how we can do this one.
Up until 7 times 6, the trick is to use the commutative property, i.e.
7 ✕ 2 = 2 ✕ 7 = 14
7 ✕ 3 = 3 ✕ 7 = 21
7 ✕ 4 = 4 ✕ 7 = 28
7 ✕ 5 = 5 ✕ 7 = 35
7 ✕ 6 = 6 ✕ 7 = 42
For the remaining numbers, the easiest trick is to remember to keep adding a group of 7.
7 ✕ 7 will be one more group of 7 than 7 ✕ 6,
So 7 ✕ 7 = 42 + 7 = 49
7 ✕ 8 will be one more group of 7 than 7 ✕ 7,
So 7 ✕ 8 = 49 + 7 = 56
And 7 ✕ 9 will be one more group of 7 than 7 ✕ 8
So 7 ✕ 9 = 56 + 7 = 63.
Tada! We have mastered the table of 7 as well.
Times Table of 8
The easiest way to learn the times table of 8 is to use the commutative property for the first few steps and then adding a group of “8” for the remaining multiples, just like in your times table of 7.
For practice on this one, you can download flashcards for the times’ table of 8 attached at the end.
Times Table of 9
An easy way to remember this times table is to use the facts of 10.
To multiply a number with 9, attach a zero at the end of the number and then subtract the same number.
To find 9 ✕ 8,
Attach a 0 at the end of 8 and subtract 8 from this;
That is, 9 ✕ 8 = 80 – 8 = 72
Times Table of 10
The eldest and the easiest, kids can write this times table with their eyes closed and make no mistakes.
Just attach a zero at the end of whatever number you are multiplying with 10 and you have your answer.
10 ✕ 7 = 70,
10 ✕ 10 = 100.
Time to pat yourself on the back!
You now have some proven tricks to help your kids from these harbingers of anxiety!
Before you teach all about multiplication to your fearless learner, we do have some resources that we think will be very useful when your kid begins this new adventure of understanding multiplication and its mysteries.
Resources on Multiplication (Free printables)
For best practice and brushing up on all concepts of Multiplication, try these Multiplication Worksheets by SplashLearn
You can also click on any of the below links to directly download these resources by SplashLearn.
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Q1. How can I memorize faster?
By practicing repeatedly, we can easily build reflex memory responses. For example, memorizing 6 ✕ 7 = 42 can be made easier by practicing the sentence – six sevens are forty-two.
Q2. What are some times table games?
A great times tables game is “guess the expressions”, where the organizer says a number and you write down as many expressions as you can in a limited amount of time. The product of those expressions should be the said number. The person with the most correct answers will win.
Q3. How do you teach multiplication to struggling students?
Use the method of skip counting or using fingers to multiply. Allow the student to practice repeated addition by drawing models of groups or arrays before they start learning their times tables. Learning about the commutative and distributive properties can be an added help.
Q4. Are multiplication charts helpful?
It’s important to make students comfortable with a concept before they start practicing that concept on their own. Multiplication charts can be a good reference tool for practicing facts before starting the times table memorization process.
Q5. What is the easiest way to learn multiplication?
The way we introduce a concept to a student is how they build their foundation of it. Asking the students to calculate double or triple of something can be fun and a good starting point. Then we can gradually introduce the concept of groups or times tables when the students are at ease with the concept.