Subtraction Slip
This task focuses on the calculation
62 - 58
What do you notice about this calculation?
How would you work out the answer?
In the video below, you'll see someone calculating 62-58, but she makes a mistake.
Watch it all the way through. You may like to watch it more than once.
What is the mistake? How could she put it right?
Did you use the same method as the girl in the video? Why or why not?
Can you give an example of a subtraction calculation which you would solve using the method in the video, if you did not use it to solve 62-58?
What do you notice about the numbers involved?
What might the - sign tell you?
Where did the girl in the video make a slip-up?
What should she have done instead?
Well done to everyone who spotted the deliberate mistake on the video. As you may have noticed, the subtraction method needed more than one step, so you had to carefully watch the whole clip to see what went wrong towards the end of the calculation.
Krishna, from the CS Academy in India, explained what happened in the video clip:
She took away 50 and she was correct. Then she told us that she will subtract 8 but she subtracted 4 from 12.
Jasmine, from Meavy Church of England Primary, also spotted the mistake as well as suggesting a way to make the calculation correct:
I did a number line and the mistake was that 12 - 8 is not 8 , it equals 4. If you had 12 sweets and you took away 8, there would be 4 sweets left. So the answer would be 4. If you had 16 sweets and took away 8, it would equal 8.
Thank you both.
Aria, from St Michael's School, in Japan, sent in this number line showing the correct working out and answer:
As many of you realised, there's several ways that you can work out 62 - 58. In the video, we saw a number line being used to try to find the answer. Krishna suggested a different way to calculate 62 - 58. See if you can follow this method too:
STEP ONE
62 - 2 = 60
STEP TWO
60 - 2 - 58
STEP THREE
2 + 2 = 4
So 62 - 58 = 4
Krishna preferred this counting backwards approach than using a number line:
The reason I changed the method was that it takes three easy steps to find out how much greater 62 is than 58.
Do you agree with Krishna?
Aria shared this different method:
58 + 2 + 2 = 62
So 62 - 58 = 4
It has fewer steps so you are less likely to get mixed up and make a mistake.
What do you notice about Aria's and Krishna's methods? What's the same about them? What's different?
As we saw in the video clip, it's very easy to make a mistake when we calculate. If you checked your answer to 62 - 58, how did you do it? I wonder if you could have checked it another way too?
Why do this problem?
This task is designed to encourage learners to think carefully about their choice of calculation method. Research shows that once introduced to a formal algorithm, within a year pupils tend to rely on it for all calculations, rather than selecting a method appropriate for the numbers involved, which is more likely to give a correct answer.
Read more about the benefits of having a flexible approach to calculation in our Let's Get Flexible! article.
Possible approach
Write up the calculation 62-58 on the board and give everyone a minute on their own to consider what they notice, emphasising that you're not interested in the answer yet. Then suggest that learners talk in pairs about their observations before bringing everyone together to share ideas. Try not to endorse contributions yourself, instead jot them all down on the board and encourage everyone in the class to ask questions or comment. You may find that some mention individual digits, some consider the meaning of the operation and some think about the size of the numbers involved. Some may give opinions about how difficult or not the calculation might be.
Next, give learners more time to talk in their pairs about how they would go about finding the answer. Make sure that all learners have access to any resources that they need, whether physical manipulatives and/or paper and pencils, or mini whiteboards and pens.
Rather than discussing the answer at this point, explain that you are going to show them a video of someone working on this subtraction calculation. Warn the class that the girl in the video makes a mistake and their job is to look out for it. Ask everyone to try to watch in silence as you play the video once all the way through. Give them a few minutes to talk in their pairs, and then play the video again so they can reflect on their conversation as they watch a second time. Then allow a little more time for the class to rehearse how they would put the mistake right.
Invite a pair to come to the board to talk through the mistake and how they would correct it. Again, try not to be the one to make judgements, instead ask the whole group what they think about the pair's suggestions. In this way, you can build up a whole group 'correction' and agree on the answer.
Ask whether any pairs used the same method as the girl in the video when they tried this calculation at the start of the lesson. What other methods did pairs use? Encourage the class to share their different ways of working so that you have a range to discuss. Allow at least five minutes to talk about the advantages and disadvantages of each method in this context. The fact that the numbers in this calculation are very close to each other means that a mental strategy might be more efficient for many pupils, for example counting up (perhaps accompanied by jottings). It is important to acknowledge, though, that what is the most efficient method for most may not be the most efficient method for all. The crucial idea here is that learners realise they have a choice.
Key questions
What do you notice about the numbers involved?
Tell me about the calculation.
Where did the girl in the video make a slip-up?
What should she have done instead?
Possible support
Being able to watch a video of someone else solving the question, and there being a mistake, takes the pressure off those learners who might become anxious about being given a calculation to solve correctly.
Possible extension
You could ask learners to create a calculation that they think particularly lends itself to being solved using each of the methods that the class discusses. Can they explain to someone else why they have 'matched' that particular calculation to that particular method?