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Classroom examples: representing success (primary)

It is important for teachers supporting children to understand the process and reasoning of how to achieve success, rather than the outcome itself.
13.5
AMY: Right. We’re moving on, now. We’re going to find a quarter of a number. If I told you a quarter of eight is two, how did I get there? What did I do to work out a quarter of eight is two? Tell the person next to you. Emily and Reese– a quarter of eight is two. How did I get there?
39.7
STUDENT: You, um–
43.9
AMY: What did I do with the bottom number?
46.1
STUDENT: You move the bottom number. So you did the line in the middle and now [INAUDIBLE]..
52.4
AMY: So– OK– I put a line down the middle, and what did that do?
56.8
STUDENT: Um, it made–
59.6
AMY: It made two. But if I’m finding a quarter?
63.2
STUDENT: It made it three.
66.1
AMY: So I put three lines down. Yes. So how many sections did I have?
69.6
STUDENT: Four.
70
AMY: And then what did I do?
71.4
STUDENT: [INAUDIBLE]
73.6
AMY: What? I put them all in one section?
75.5
STUDENT: No, one in each. Like one three, one four, one to five–
79.5
AMY: Until I got to what number?
81.2
STUDENT: Eight.
83.2
AMY: Well done.
90.1
GEORGE: I know that you are pretty good at the column math. So I got my dad to have a go at the weekend. He said Mr. Gardner, he didn’t call me Mr. Gardner, obviously, but he said he was better than me at doing subtraction. He had a go at this example. I’m not convinced he’s right, though. With the person next to you, can you have a look to see if he has answered this question correctly? The question was 645 people went to a fair. 234 of them left. How many were still at the fair? And this is what he’s done. He’s used the column method.
121.1
I’m happy that he’s done that and laid it out correctly, but I’m not sure that he’s done the answer correctly. Can you, with your talk partner, chat about if you think he has done it correctly or if he hasn’t and what is the mistake that he’s made. Off you go. What do you think? Are we happy with what he’s done there? 804 subtract 335 is a bit more difficult, because you cannot exchange from the zero. So I said have a go. And he had three attempts at it. And he’s got three different answers, as you can see. OK? Now one of these he’s done correctly, I think, and two of them he’s done incorrectly.
158.3
So again, with your talk partners, you as a three have a look. If it helps you to do it on your whiteboard yourself, go for it. Have a look. Which one is correct? Which are the two that are incorrect? Off you go.
169.5
STUDENT: The first one is incorrect.
170.4
STUDENT: No,
171.1
STUDENT: The second one is correct.
172.5
STUDENT: No, the middle one.
174
STUDENT: And they are the two and
175.8
STUDENT: Not.
176.7
STUDENT: Not correct.
178
STUDENT: Because you think of eight as zero.
179.6
STUDENT: Yes.
180.2
STUDENT: Minus one is seven, too
182.1
STUDENT: And that one in the middle
185.5
STUDENT: You’ve got to subtract four, five.
187.1
STUDENT: Yes. And he’s done it right, because he’s done
190.9
STUDENT: 14 subtract 5 is 9,
193
STUDENT: He’s crossed eight out, put seven, and then put a ten onto the zero. And then he’s crossed it out, put nine, and then he’s added the one to the four.
204.8
STUDENT: And seven then subtracts from the four.
213.3
AMY: Last week, we were finding half. If I told you the blue and the green circle have been halved, how do I know that? So, just with the person next to you, we’re going to have a bit of a time to think. Share your ideas. Why do I know that these have been halved? What is telling me that they’ve been halved? Because you kind of have to think. So how do I know they’ve been halved? Eyes back on me. There was lovely discussion going on down here. Keaton’s group– did you have any ideas? How do I know that these have been halved?
250.3
STUDENT: Because they’re the same.
251.9
AMY: They’re the same where?
256.6
STUDENT: On the shape.
258
AMY: The shape’s the same? Violet, do you have any ideas? What were you saying in your pairs?
265.5
STUDENT: We were saying that we split the circle in the middle. And then after that, we worked out that both sides were equal.
280.1
AMY: Yes! That’s the word I was looking for. They are equal on both sides. I know that these haven’t been halved, because they’re not equal on both sides, are they? Well done.
296
GEORGE: –because it’s asking you to show three different examples of column subtraction that do not need exchanging, and give the answer 322. OK? I’m going to just do one example to model it for you now. And then I want you to have a go. Does that make sense, Jack? So, I’m going to work backwards. What I’m going to do is write my answer– 322– first. OK? Happy? And I’m going to start in the units column, and think– can you give me an example of how I could get the answer two? Matilda. What numbers could I put in the calculation to get the answer two?
332.6
STUDENT: Three take away one.
334.4
GEORGE: Three take away one? OK. So, we know the units column could be three and one. Can you give me a different pair of numbers– Liam, please– that gives the answer 20? Or two tens?
345.5
STUDENT: Four minus two.
346.2
George: Four minus two. So what would that be? Because this is the tens column.
350
STUDENT: 40 take away 20.
351
GEORGE: Right. 40 and 20. Good. And in the hundreds column, what could we go for?
358.2
STUDENT: Four minus one.
360.5
GEORGE: Or, what does it mean in the hundreds–
362.6
STUDENT: Four minus one.
363.4
GEORGE: 400 subtract 100. OK. So I want three examples like that. I think that one, Jack, is a lot easier and I think you’d love to do that. Off you go.
In this video we see Amy and George using a range of different planned approaches to represent success and support their children in being able to understand how to produce good quality work.
  • 0m10s – Here’s the answer, how did I get it? Maths. Year 1 (age 5-6).
  • 1m25s – Hack attacked work. Maths. Year 3 (age 7-8).
  • 3m30s – Comparing and contrasting different answers. Maths. Year 1 (age 5-6).
  • 4m50s – Modelling what a good learner would do. Maths. Year 3 (age 7-8).
What is important for the teachers is supporting children to understand the process and reasoning of how to achieve success, rather than the outcome itself. Although these examples are from primary classrooms it is important to realise that they could be also be applied in any context.

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