Every child in my spiral of inquiry this term, I also taught last year when they were year 4's. Because of this, I already had a good understanding of what they know and can do, and I didn't need to spend weeks getting to know this. (Hence the starting a full learning load in week 2!)
I knew that these students get stumped when they are dealing with numbers in the 100's, and had never dealt with anything in the 1000's before. This showed me that they had some gaps missing in their place value knowledge.
On Tuesday and Wednesday, I used popsicle sticks with my whole class so I could judge their place value concepts. I would say 'show me 23', and the response I was hoping for, was 2 lots of 10 popsicle sticks, tied together with rubber bands, and 3 popsicle sticks by themselves. However, I got everything but that. Even my year 6 students didn't do this. They counted out 23 and showed me them scrunched up in one hand, or made the shape of the letter 23 with the popsicle sticks as their pen (if that makes sense?). Some remembered that they were supposed to tie something together, so they tied the 2 lots of 10, together, in one big pile, and left the 3 ones by themselves. I modelled what I wanted them to show me, and explained why. Some of them just couldn't understand why I said only bundles of 10 were allowed to have a rubber band around them. There was definitely a gap in the students knowledge of exchanging numbers (i.e. ten one's is the same as one ten). We started to process through this bundles and rubber bands business, when I tripped them up again. Instead of 'show me X number', I asked them to 'show me X number, then add/minus X number'. These questions were designed to force students to exchange - opening up 1 lot of 10 to take out some ones, adding ones then exchanging them for a 10, etc.
What I liked about how I ran this activity was that after a few of this new type of question, I then asked students to buddy up. The pair, together, would do the 'show me X number' part. Then, student A from each pair would come to me and I would whisper the 'add/minus X number' part, which they then had to go back and EXPLAIN to student B - not tell them. For example, if the question was 128+13, they were not allowed to say 'plus 13', they would say 'add 3 ones, then change 10 ones for 1 ten', explaining the process step by step. This showed me a deeper level of understanding then just 'show me X number', because I could judge student A's understanding of the process of exchanging, and student B's understanding of mathematical language, at the same time.
Of course we swapped, did a bunch of varying questions that all were showing the same thing although they kids didn't realise that lol.
It was a great way for me to judge the whole classes understanding of place value (and maths language) at the same time.
On Thursday and Friday, I introduced place value counters I made. I made these on Wednesday, because I knew there was no way I could use popsicle sticks to show place value into the 100's and 1000's, I literally just don't have enough - and can you imagine the mess??
The kids LOVED them straight away.
I did the same thing to begin with - 'show me X number'. Instantly I found misconceptions about their place value knowledge.
It was a great first week of maths - I learnt A LOT about my whole classes place value knowledge, and was able to introduce big numbers, and new concepts such as the place holder zero, and demonstrate old concepts, such as exchanging 10x1 (etc), thanks to the materials I was using.
For my spiral of inquiry group, I think they responded really well to using materials every single day, (rather than as a sometimes thing), a few even asking to do more because it was fun. Although I do not think they will remember everything from this week going into next week, using the materials will help them remember quicker, have a deeper understanding of it, and contribute towards a positive attitude and growth mindset in maths (oh yeah, I can do maths! I am smart!). I will keep using materials as part of my maths inquiry and documenting the outcomes on my blog.