Let's get magical (3-digit addition and subtraction)
Stage 3 – A thinking mathematically context for practise focussed on developing flexible strategies and reasoning to support student thinking.
Syllabus outcomes and content descriptors from Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2021
You will need:
- pencils or markers
- your mathematics workbook.
Watch the Let's get magical video (3:16).
Alright, welcome back mathematicians! Today we're going to use our amazing mathematical skills to help us look magical! And to help me today, I'm joined by Barbara and Ayesha.
Now before we get started, I'm going use maths today to predict what I think you're going to respond to, when I ask you a series of questions.
And so, what I'm going to do is write those down ...with what I think your answer is going to be on my sticky note and show everybody so they can see it.
[Michelle writes 1089 on a sticky note and shows it to the viewers.]
And now I'm going to ask you a few questions.
So, the first thing I need you to do is to select a 3-digit number where each of the digits is smaller than the one before and so, for example, we might choose 976.
Or you might choose 531.
Over to you to pick a number.
Can I choose 532?
Alright, so 532.
[Michelle writes 532 on the large piece of paper.]
Then, record another number now be reversing those digits.
So that would mean it is 235.
[On the right of the first digit, Ayesha reverses the number and writes 235.]
And then I'd like you to subtract 235 from 532.
So, we're doing 532 minus 235. Is that right?
[Ayesha creates a second row and writes 532 minus 235.]
OK, so the first thing I would do is I would do 532 and I would take away 200 and that leaves me with 332. So now I still need to subtract 35, but what I'll do is I'll subtract 32 first.
[The number 332 is written down in a new row.]
Because 332 takeaway 32 leaves me with 300.
[The number 300 is written down in a new row.]
And I'm nearly done, but I still need to take away 3. And 300 takeaway 3 is equivalent to 297.
[The number 297 is written down in a new row.]
Great, so now you've got a new 3-digit number: 297.
Can you reverse the digits in 297 to make a new 3-digit number?
[Ayesha writes down the number 792 in a new row.]
Great! And then can you join those 2 three-digit numbers together please.
That's going to be 792 and we're going to join those together...so from 792 I'm going to add 297.
[Ayesha writes down 792 in a new row. Underneath she writes 792 plus 297.]
OK, So, what do I do? Because I can see that 792 is quite close to 800.
It is very close!
I will just add 8 first as that will get me to 800.
[Ayesha writes the number 800 in a new row.]
And now I need to add the rest of it, but I've already added part of it, which was the 8.
So now I'm going to add another 289. And if I add 800 plus 289 that is 1089.
Which is exactly what I predicted!
[Michelle places down the sticky note from the beginning of the video with the number 1089 on it.]
Now, you know what you should be asking....
How did you do that?
How did you do that?
Is it magic?
Over to you, mathematicians!
[End of transcript]
- Choose a 3-digit number where each digit is smaller than the previous one (but they don’t have to be in order. For example, 982 or 531).
- Then, reverse the digits and subtract the second number from the first one. So, if I had chosen 531, I would now work out 531 – 135. The answer is 396. (If you get 99, record your answer as 099).
- Next, reverse your new number. For example, from 396 I can make 639.
- Finally, add these last two numbers together. For example, 396 + 639.
- Here comes the magic...
- The answer is 1089!
- Try another starting number and test it out again...is the final answer still 1089?
- Explore what happens if you use the same process, starting with a 2-digit number or a 4-digit number...
- What do you notice about the final answer?
- Why do you think this might be happening?
Share your work with your class on your digital platform. You may like to:
- share your discoveries
- write comments
- share pictures of your work
- comment on the work of others.