Frustrated
Have you ever been frustrated by a friend who answers the day’s tricky maths question in their head before you’ve even had a chance to get your pencil to paper? If you want to be that quick off the draw then you need to be confident and secure in a few maths basics first. You’ll soon boost your mental maths skills.
First Steps
Know your times tables. Really know them. Learning them as a sequence (2, 4, 6, 8, 10…) is useful but knowing them as facts (1×2=2, 2×2=4, 3×2=6…) is better and recalling facts in any order is best. Hit The Button is great for upskilling your tables. My top Hit The Button score is 37 mixed times tables facts in 1 minute. Can you beat me?
Know your place value. This is teacher talk for thinking about the thousands, hundreds, tens, ones (and tenths, hundredths if you’re Year 5+). Understand how you can easily multiply and divide numbers by 10, 100 and 1,000.
Understand all the ways to make 10 from 2 and 3 numbers. You might have heard these called number bonds. Once you know ways to make 10, find and learn all the ways to make 20. Then step up to all the ways to make 100 and all the hundreds numbers to make 1,000.
Know, understand and play with ‘inverse’ operations: addition is inverse to subtraction, multiplication is inverse to division.
Get these facts secure and you’ll already be well on the journey to boost your mental maths.
You can download our free maths resource pack to get you started.
Growing Skills
Now you have the basics under your belt, you’re ready to follow and practise these tips to speed up your mental maths for addition and subtraction:
Number Bonds
Look for number bonds. You spent ages learning them so now is the time to use that knowledge! Pick one of these calculations and spot the number bonds you could use to help you add.
14 + 26
320 + 684
1931 + 8107
Did you spot them all?
In the first calculation, 14 + 26 you can use the ones to make ten. Then you just have to add the tens together (along with the new ten that you made from 4 + 6).
In the second calculation, 320 + 684 you probably spotted 20 + 80 as a bond for 100. If you looked really closely, you might have spotted that you could also use 32 + 68, as this makes 100. Of course, in our calculation we have to think about place value too. These digits really represent 320 and 680, but what if, for the moment, in our heads, we called them 32 tens and 68 tens. When we added them we’d have 100 tens. If you practised your place value a lot then you’ll be ahead of me and already be shouting at the screen that 100 tens is 1,000. I love your enthusiasm!
We can use the same trick for the third calculation, 1931 + 8107. Let’s concentrate on the thousands and hundreds numbers for a sec. We’ve got 19 hundreds and 81 hundreds and that makes 100 hundreds. One hundred hundreds? Write it down. Does it look like 10,000?
If it does, give yourself a huge pat on the back, but not before we go back and add those tens and ones on too. Remember, we had 1931 + 8107, so we will need to work out 31 add 7 then add it to the 10,000 we already have, so 10,038. And just like that, we’re using place value to add up to five digits in our head.
Near Multiples
Another trick I like to use for mental addition and subtraction, and this is a real wowzer, is to use a near multiple to help me add.
Let’s imagine we have an addition problem… like…
3247 + 506 =
We can use a near multiple to help us add this mentally. 506 is just a little more than 500. It’s 6 more, in fact. We can make this addition easier then, by adding 500…
3247 + 500 = 3747…
Then adding the 6 that we haven’t included yet.
3747 + 6 = 3753
Near multiples don’t always have to be bigger than the amount that you add. Here’s another example where the near multiple is smaller…
3247 + 498
In this case, we’d still add on 500 because 498 is pretty close to 500. In fact, it’s just two less. Let’s go ahead and add 500 then…
3247 + 500 = 3747
But we’ll need to remember that we added two too many. So let’s take 2 away from our answer…
3747 – 2 = 3745
And there you have it, we are calculating 3747 + 498 in our heads without the need for pencils and paper.
Think In Chunks
Whenever life gets a little hard I like to think in chunks. Smaller problems are easier to deal with and I get a chance to tell myself ‘really well done’ for each little success. So let’s apply this life skill to mental maths too.
Imagine we have a subtraction this time (just because I want to switch up the skillset, although you can apply any of these methods to addition or subtraction just as easily). Here’s our calculation…
48,795 – 6,384 =
Is anyone else thinking, “Eeeeeeek!”? Hold that Eeeeeeek. Let’s see if we still need it after we’ve chunked this problem down.
We’ll start by partitioning the number we’re subtracting. This will help us chunk…
6,384 =
6000
300
80
4
So let’s subtract in chunks. We’ll find it’s only one digit changing for each chunk we subtract.
48,795 – 6,000 = 42,795
42,795 – 300 = 42,495
42,495 – 80 = 42,415
42,415 – 4 = 42,411
We’re all out of chunks. Did you remember to tell yourself ‘really well done’ at each calculation? I’m glad about that, because we’ve just calculated…
48,795 – 6,384 = 42,411
I have many more tricks like this and I’ll be writing some soon that will help you tackle tricky multiplications and divisions. In the meantime, keep learning those times tables and number bonds and when you come across an addition or subtraction problem, pause for a second to see if number bonds, near multiples or chunking can help you.
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