Skip to 0 minutes and 14 secondsAMY: 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?

Skip to 0 minutes and 40 secondsSTUDENT: You, um--

Skip to 0 minutes and 44 secondsAMY: What did I do with the bottom number?

Skip to 0 minutes and 46 secondsSTUDENT: You move the bottom number. So you did the line in the middle and now [INAUDIBLE]..

Skip to 0 minutes and 52 secondsAMY: So-- OK-- I put a line down the middle, and what did that do?

Skip to 0 minutes and 57 secondsSTUDENT: Um, it made--

Skip to 1 minute and 0 secondsAMY: It made two. But if I'm finding a quarter?

Skip to 1 minute and 3 secondsSTUDENT: It made it three.

Skip to 1 minute and 6 secondsAMY: So I put three lines down. Yes. So how many sections did I have?

Skip to 1 minute and 10 secondsSTUDENT: Four.

Skip to 1 minute and 10 secondsAMY: And then what did I do?

Skip to 1 minute and 11 secondsSTUDENT: [INAUDIBLE]

Skip to 1 minute and 14 secondsAMY: What? I put them all in one section?

Skip to 1 minute and 16 secondsSTUDENT: No, one in each. Like one three, one four, one to five--

Skip to 1 minute and 20 secondsAMY: Until I got to what number?

Skip to 1 minute and 21 secondsSTUDENT: Eight.

Skip to 1 minute and 23 secondsAMY: Well done.

Skip to 1 minute and 30 secondsGEORGE: 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.

Skip to 2 minutes and 1 secondI'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.

Skip to 2 minutes and 38 secondsSo 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.

Skip to 2 minutes and 50 secondsSTUDENT: The first one is incorrect.

Skip to 2 minutes and 50 secondsSTUDENT: No,

Skip to 2 minutes and 51 secondsSTUDENT: The second one is correct.

Skip to 2 minutes and 53 secondsSTUDENT: No, the middle one.

Skip to 2 minutes and 54 secondsSTUDENT: And they are the two and

Skip to 2 minutes and 56 secondsSTUDENT: Not.

Skip to 2 minutes and 57 secondsSTUDENT: Not correct.

Skip to 2 minutes and 58 secondsSTUDENT: Because you think of eight as zero.

Skip to 3 minutes and 0 secondsSTUDENT: Yes.

Skip to 3 minutes and 0 secondsSTUDENT: Minus one is seven, too

Skip to 3 minutes and 2 secondsSTUDENT: And that one in the middle

Skip to 3 minutes and 6 secondsSTUDENT: You've got to subtract four, five.

Skip to 3 minutes and 7 secondsSTUDENT: Yes. And he's done it right, because he's done

Skip to 3 minutes and 11 secondsSTUDENT: 14 subtract 5 is 9,

Skip to 3 minutes and 13 secondsSTUDENT: 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.

Skip to 3 minutes and 25 secondsSTUDENT: And seven then subtracts from the four.

Skip to 3 minutes and 33 secondsAMY: 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?

Skip to 4 minutes and 10 secondsSTUDENT: Because they're the same.

Skip to 4 minutes and 12 secondsAMY: They're the same where?

Skip to 4 minutes and 17 secondsSTUDENT: On the shape.

Skip to 4 minutes and 18 secondsAMY: The shape's the same? Violet, do you have any ideas? What were you saying in your pairs?

Skip to 4 minutes and 26 secondsSTUDENT: We were saying that we split the circle in the middle. And then after that, we worked out that both sides were equal.

Skip to 4 minutes and 40 secondsAMY: 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.

Skip to 4 minutes and 56 secondsGEORGE: --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?

Skip to 5 minutes and 33 secondsSTUDENT: Three take away one.

Skip to 5 minutes and 34 secondsGEORGE: 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?

Skip to 5 minutes and 46 secondsSTUDENT: Four minus two.

Skip to 5 minutes and 46 secondsGeorge: Four minus two. So what would that be? Because this is the tens column.

Skip to 5 minutes and 50 secondsSTUDENT: 40 take away 20.

Skip to 5 minutes and 51 secondsGEORGE: Right. 40 and 20. Good. And in the hundreds column, what could we go for?

Skip to 5 minutes and 58 secondsSTUDENT: Four minus one.

Skip to 6 minutes and 1 secondGEORGE: Or, what does it mean in the hundreds--

Skip to 6 minutes and 3 secondsSTUDENT: Four minus one.

Skip to 6 minutes and 3 secondsGEORGE: 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.

Classroom examples: representing success (primary)

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.

Comment

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  • How do these activities help the children understand what makes a good quality answer? Post your thoughts below, and compare to other comments.

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This video is from the free online course:

Planning for Learning: Formative Assessment

National STEM Learning Centre