Ask a group of students which subject they find the most challenging, and, often, maths will be one of the responses you hear most.
It could be because of the subject’s binary nature or because maths is built on sequential concepts. Without a proper understanding of the previous lesson, a student will struggle to build upon that knowledge and develop a firm understanding of the problem at hand. So, it’s imperative that our students have a firm grasp of the basics.
Most teachers will no doubt recall endless childhood maths lessons and hours spent memorising their times tables by rote. As we know, regurgitating the answer to a problem is less effective than developing a keen understanding of a set of skills that we can use in different applications to solve a problem and explain our work in doing so. Not to mention that memory isn’t always as reliable as we’d like it to be!
In this article, we’ll examine some key strategies and factors for improving mathematical competency before discussing some useful maths tips and tricks that students can use to speed up their calculations.
How to get faster at maths
When most of us think about improving our mathematical abilities, what we’re actually referring to is improving the efficiency of our mental arithmetic. Calculating basic maths problems accurately is an important foundation for building more complex mathematical problems. Below are some strategies for doing maths faster.
Practice, practice, practice (or practice3)
Like any skill, practice and repetition are the fundamental keys to faster maths. It’s a good idea to periodically revisit the basics throughout your maths lessons, even if it’s just for 10 minutes at the start of every other maths lesson – perhaps through a pop quiz. We suggest producing a set of templates that you can easily update and adapt to allow students to practice their skills freshly and engagingly periodically.
This is where something like ActivInspire’s easy-to-use templates can help you revisit material with a fresh perspective. For early years learners, we recommend replacing digits with concepts or images where you can – three cats plus two dogs, for example, is much easier to visualise, not to mention more engaging, and you can use picture cards to aid understanding.
Developing number sense
The nitty gritty of complex arithmetic problems becomes so much easier once we’ve developed an understanding of numbers and how they relate to one another. Simple maths tricks like estimation, rounding and simplification can help to build that comprehension.
When faced with a complex maths problem, asking students to estimate the answer before working on the problem is always a good idea. This teaches them to think critically and consider numbers rather than follow a process. Rounding numbers is a great way to estimate an answer, and we’ll see later on in this article how rounding can also be used to make solving arithmetic problems more efficient.
Gamification
There’s plenty of research to suggest that learning through play is an effective way to build knowledge. If you’re using an interactive display in your classroom, such as the Promethean ActivPanel, consider introducing interactive games to facilitate your maths lessons. These can be as simple as card matching games, and as complex as virtual escape rooms. With the Promethean App Store, you can download your favourite game apps to introduce a fun element to the classroom.
Speed training
If you want to help your students build speed and efficiency when solving maths problems, then it’s essential to introduce an element of urgency to the activity. The ActivPanel Timer app is an ideal way to do this. Set a timer and clarify to students that they don’t need to get the exact answer. The objective is to get as close as possible, enabling them to practice their estimation and rounding skills and allowing you to finally fulfil that fantasy of becoming a Countdown host!
Maths tips – how to do maths faster
There are lots of mental maths tricks that students can use to improve their understanding of numbers and get faster at maths. Below are a few of our favourites that you can add to arithmetic lessons.
Maths tricks for addition
Left to Right
When working with a pen and paper, we often teach students to solve sums by adding the digits together from right to left and carrying any additional digits to the next column.
When calculating the sum of two long numbers in our heads, it’s much more efficient to pick a base number and move from left to right. Using 893 and 546 as an example, we’ll choose 893 as our base number and then solve the sum from left to right, as below:
893 + 546
893 + 500 = 1,393
1,393 + 40 = 1,433
1,433 + 6 = 1,439
Simplification
Simplification rounding offers a different method for solving the same sum. We’ll do this by first rounding our numbers to the nearest 10 and adding them together.
So: 893 + 546 becomes 890 + 550.
890 + 550 = 1440
Now, all we need to do is add the remaining digits together, which we can find by subtracting our original numbers from our rounded numbers.
890 – 893 = -3
550 – 546 = 4
So, in this case, the sum of our remaining digits (4 + -3) is 1. This is the difference between the numbers we started with and the rounded numbers that we used for our simplified sum.
All we need to do now is subtract 1 from the sum of our rounded numbers:
1440 – 1 = 1,439
Let’s try that again with 657 and 239:
660 + 240 = 900
660 – 657 = 3
240 – 239 = 1
3 + 1 = 4
900 – 4 = 896
Maths tricks for subtraction
Complements
Complements are a simple maths trick you can use when subtracting a two-digit number from 100. We’ll always subtract the first digit from 9, and the second digit from 10, putting them together to get our answer. Let’s use 100 – 27 as an example:
100 – 27
9 – 2 = 7
10 – 7 = 3
73
We can use a combination of rounding and complements when subtracting larger numbers from each other. In this instance, let’s use 836 and 278. We’ll solve the first part of the equation by rounding the second number to the nearest hundred above it:
836 – 300 = 536
Now, we need to find the complement of 78:
9 – 7 = 2
10 – 8 = 2
22
Now that we know our complement is 22, we can add that to the sum we’ve already completed using rounding:
536 + 22 = 558
Multiples of 10
We all know that subtracting round numbers is much easier, and this trick is predicated on that. All we need to do is round up to the nearest 10 – and we’ll always round up rather than down. Let’s use an example of 358 – 82.
First, we’ll round the 82 up to 90 and calculate the difference, which is 8. We’ll then add that to our first number, so 358 becomes 366.
Now, all we need to do is subtract 90 from 366. The answer is 266.
Let’s try again with 542 – 83.
83 becomes 90 with a difference of 7.
542 + 7 = 549
549 – 90 = 459
Maths tricks for multiplication
Quick Fives
This trick works when multiplying any number by five. All you need to do is halve the number you’re multiplying it by and add a zero. Let’s try 5 x 500.
500 ÷ 2 = 250 plus an additional zero = 2,500
It works almost the same for odd numbers but instead of adding a zero, just remove the decimal point. In this instance, we’ll use 5 x 37 as our example.
37 ÷ 2 = 18.5 and remove the decimal = 185
9 on Your Fingers
This is an easy maths trick you can use when multiplying any number by 9. All you need is 10 fingers.
Using 9 x 5 as an example, we’ll place both hands in front of us facing outwards and count from left to right, folding down the fifth finger as this corresponds to the number that we’re multiplying 9 by. You should have folded down the thumb on your left hand. Now simply count the remaining fingers on either side of that thumb. You should have four to the left and five to the right – so our answer is 45.
Let’s try again with 9 x 7. You should have folded down your index finger on your right hand, leaving six fingers to the left and three to the right. So, our answer is 63.
The 11 Separation Rule
This rule works for multiplying two-digit numbers by 11. Let’s use 63 x 11 as an example.
First, we separate the two digits and then add them together, so 6 + 3 = 9.
Now we take that number and add it between our original two digits, giving us our answer of 693.
This works for all two-digit numbers, but there’s an additional step we need to take when the sum of our two numbers is greater than 9. Let’s use 78 as an example.
7 + 8 = 15
First, we take the second digit of our answer and place it between the two numbers to make 758. Now, all we need to do is carry the one from 15 and add it to the first digit of our answer, making 858.
Maths tricks for division
Dividing by 5
This simple maths trick is great for dividing large numbers by five, and there are just two simple steps; multiply by two and add a decimal point in front of the final digit of the result.
Need to divide 3,975 by 5?
3,975 x 2 = 7,950 plus the decimal point = 795.0 (or 795).
Let’s try again with 2,433:
2,433 x 2 = 4,866 plus the decimal point = 486.6
Is It Divisible by 3?
This is a great game for getting children engaged with maths as it allows them to impress their friends and families by solving a seemingly complex problem. To find out whether a number is divisible by 3, all we need to do is add its digits together and see if the result can be divided by 3. If yes, the original number can be as well!
Let’s use the seemingly impossible example of 3,129,432.
3+1+2+9+4+3+2 = 24
We know that 24 is divisible by 3 (24 ÷ 3 = 8).
Therefore, 3,129,432 is divisible by 3.
Find out how you can improve your students’ maths skills
To find out how you can utilise the features of Promethean’s products to further enhance your Maths lessons and improve your students’ mental arithmetic skills, book a demo of the Promethean ActivPanel today.
Before you do that, we’d like to leave you with our favourite maths tip and an easy way to remember the first seven digits of pi. Just memorise the phrase “How I wish I could calculate pi” and count up the number of letters in each word: 3.141592.
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