I gathered from this that most of the children did not have a solid grasp of hundredths. I decided to invite children to work on the '0-1 ruler' and the Cuisenaire rods one more time, this time with 1 metre being equivalent to 1.
Account #1: Elsie has written 2/50 next to the first mark, then 4/50 next to the third mark (see image below, rubbed out)... I notice this, consider intervening, but choose not to. A while later, she calls me over and says "Something is wrong." I sit down next to her, look at what she has done, and then ask: "How do you know it's wrong?" She points to the half mark, and says "50/50 is not a half, it's not the same as 50/100". I am aware of choices. I feel that some guidance would be useful. I take a red rod (2cm), and place it on the ruler. She says: "How many twos in a hundred? Fifty." I hold up the rod and say "So what's the name of this?" She says: "A fiftieth?" There is a pause. She doesn't write anything. I write: "red = 1/50" somewhere on the sheet, not on the ruler. She exclaims: "Aaah! OK...." rubs out what she has done, and starts filling in the fiftieths correctly:
Account #2: Jack is filling in the decimals from 0 to 0.5, and Minnie is filling in the decimals from 0.5 to 1. Jack is filling them in correctly, and Minnie has written 0.7, 0.01, 0.02, ... (as opposed to 0.7, 0.71, 0.72, ...). I notice this. I pause, aware of choices. I choose to be direct. I point to her mis-take and say: "I don't think that's right.". She looks up, Jack looks up too, and he says "Oh, it should be like this!". He points towards what he has done. She looks, says, "Oh, yes!", and corrects her work.
Account #3: I walk over towards Caleb and Callum. I see they have completed the decimals and hundredths, but seem to have reached an impasse [a judgement based on what?]. I sit by them and try to listen to what they are saying, it's talk about the task, but I can't really make out what they are saying. After a while, I ask: "What are you thinking about?" Caleb replies: "How many there are in the whole thing", and Callum points to the second mark and says, "Wouldn't this be fiftieths? Can we have some rods?" I say "Yes," and leave them to it.
Account #4: Sophie says "I found out that light greens [3cm] don't work.. a hundred divided by three is thirty three remainder one." She has been laying laid light green rods next to her ruler, and is now putting them away. She then says, "I don't think pinks work either, a hundred divided by four is twenty two remainder 1... erm". I react: "Are you sure?" [I react rather than respond. Would she have worked out this was not correct without my comment?]. She says "Hold on...," gets some pink rods [4cm] out of the bag and starts laying them on the ruler:
I feel that her partner, Alexis, has not been as involved [judgement] in this lesson as I would like her to be. I have spoken to her a couple of times about this, and am becoming a bit 'frustrated' with her. I ask: "Do you know what is happening?" She says yes. I start to walk away, but become aware of an alternative. I ask Alexis: "So, what's happening?" She is not sure. I ask Sophie not to answer, and ask Alexis to look at the pink rods laying on the ruler: "How many pink rods are in the whole?" She is counting, "Twenty four, no, twenty five." I hold up a pink rod and ask: "So, what is the pink rod worth?" She says: "A fifth... no, erm........ one twenty-fifth?" I smile, and she starts writing twenty-fifths on the ruler:
They have similar success with the yellow rod:
The pairs completed their rulers in varying degrees of detail. Here's part of a completed ruler:
I decide to invite the children to write as many names as possible for each Cuisenaire rod. It feels to me as though it will be most useful for the children.
Jack and Minnie have no trouble writing decimal and (multiple) fraction names for each rod. They finish quickly and I am a little stuck, pedagogically, as I don't want them to sit there doing nothing, but I want more time for the others. I pause, and then ask: "So what questions do you have?" Jack says: "What questions!?" and Minnie says; "What other names could there be?" Jack says we could find other fraction names by multiplying, and then Minnie exclaims: "Percentages!"
If pairs think they have finished, there are other questions that I can ask them that will extend what they have done while others reach a certain point. I then decide to invite responses as a whole class. This might be because I'd like to find out what they know individually, but also it might be a good way for bringing work together. Conveniently, there are ten children here today, and ten rods. Here are their first responses; notice how they switch between representations:
I then invited children to offer any names that were not already written. Every one of the children offered at least one, and generally much more than one response. Answers were coming thick and fast, I recorded them on the board. There was a high level of focus and excitement. All of the children seemed to be enjoying their new found faculty in representing hundredths as fractions, decimals and percentages. This is how the board looked at the end:
I draw attention to the light green rod, saying that 0.03, 3% and 3/100 are three ways of representing the same number. As I am packing up to leave, Jack says to me: "Ah, now I feel good about myself!"