I have really enjoyed and found all our PD sessions with Jo Knox very valuable and applicable in the classroom. Today, Team 5 have been fortunate enough to observe 2 modelled sessions using a stage E6-6 group and a stage 7 group of students. Our area of need we asked to be addressed was how to deliver a lesson around finding decimal equivalents for fractions (e.g. expressing 1/5, 3/4, 1/3 as a decimal) using decipipes as materials.
There were so many treasures and learning points I took away from our sessions that I've tried to condense it down to 5 main points that I hope you will also find useful.
1. Sharing/Co-constructing the WALT at the end of the lesson
As we observed Jo, we noticed that both times, at the end of the lesson she closed it off by encouraging the students to verbalise (exactly as they've been doing all session) what they have been doing. The first group had some trouble keeping the vocabulary consistent when explaining what they been trying to achieve. But the second group (Stage 7 group) were able to say exactly what they were doing. "We are learning to add decimals by taking some off one number and add it to the other to make whole numbers." I found this quite a good change of practice and as long as I have it clear in my head where I'm wanting the lesson to go, con-constructing the WALT at the end of the lesson is a great way to end off a lesson.
2. Decipipes magic
Every class needs them! They are the perfect tool when dealing with fractions, decimals and place values with numbers less than one. I watched students experimenting with tenths, finding out how many tenths you needed to make one whole. Students also used decipipes to show how a half and and quarter is written as a decimal as the only columns on the place value houses are 1/10, 1/00 and 1/000. Students used tenths decipipes to find a half, then needed the hundredths decipipes when they were trying to show a 1/4. This made it so much easier to record as they could clearly see they had 2 tenths pipes, and 5 hundredths pipes which looks like 0.25 = 1/4.
3. Teaching Model
We all know the teaching model, but at times in our haste to accelerate our students, we can sometimes miss out crucial steps in ensuring students reach that 'new knowledge/strategy' you've been aiming for. I saw these steps clearly happening in Jo's lessons and students left with 'new knowledge' and understanding. Student were given the opportunity to use materials if they needed to, or work out 1.98 + 0.65 using a strategy they knew (imaging).
4. Share/ Model/ Record
I love this method of sharing! While one pair is sharing how they solved a problem, the other pair is modelling it using the materials (in this case the decipipes) and the other pair is recording what they hear (equation format). This way, it ensures everyone in the group is paying attention, participating and forming their own understanding while others are sharing. Below is a short snippet of one group sharing while the group recording is trying to understand what they did and the modelling group is moving decipipes around to show what was shared.
5. Double number line - Equivalent fractions
This was a very effective way to show equivalent fractions as you teach your group. One of the things we've been reminded to work on to expose students to fractions that are greater than 1. This double number line was the perfect way to show 1 and a half is equivalent to 3/2. This is definitely something I will be using more often with my groups.
I have much more to share but I hope this summary can be of some help to others for now. My next steps would be to try these in my lessons and video the session to see how students respond to the learning and whether the learning is embedded for them. This would also be useful watching how patient I am in a normal class setting, with wait time, and trying to encourage student to use the correct mathematical vocabulary when explaining their learning. This should be interesting!
