What Does a Subtraction Sequence Look Like in Prep/One? - Reflections from Phase 2
What Does a Subtraction Sequence Look Like in Prep/One? - Reflections from Phase 2
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I sit here writing this article feeling super excited about the learning happening in our Prep/One classrooms. I have chosen to focus on one classroom for the purpose of showing a sequence of lessons around subtraction using our new framework with ‘relentless consistency’. I have enjoyed the Phase 2 role of observing, assisting with planning and ideas and being a sounding board for Lou (it is definitely easier to watch and help than run the lesson myself!)
I would like to thank Lou for her work and celebrate the success we’ve had with her students, both from an academic perspective and creating a culture of deep thinkers.
Please find below the series of prompts that Lou used and some observations we had during the activities.
We labelled this the ‘explore phase’, students were using known strategies such as tens facts, known facts and manipulating counters and materials.
The story shell was amazing! The students were hooked and wanted to explore all the ways to make 10 and were able to relate to the context. Putting the mathematics into a relevant context created excitement and a purpose for the investigation.
Discussion points:
The students were utilising their known ten facts from previous lessons. Some students were systematic in the way they recorded and made tables of possible combinations.
Our wonderings:
Were they understanding the concept of subtraction or just using number facts?
What questions could we ask to gauge the level of understanding when looking at a systematic table approach in prep / one?
What does success look like during the ‘explore phase’ of a new concept in a Prep/ One grade?
Lou cleverly brought the attention back to subtraction through modelling at the end of the lesson when she told them ‘what actually happened’. She told the story again but used a picture to model the chocolates being crossed out and writing the equation.
Session 2 began with the group fishbowling to see ‘Race to Zero’ being played. Lou and I spoke about highlighting the uncertainties around what to do when you are on 91 and you have to move 6 less – how do I move my counter? This was modelled and the class agreed about how it can be confusing at first. Lou also highlighted the need to say the number they land on to their partner. This was particularly important to reinforce number recognition and to help some students who were reversing some of their numbers. eg. 84 they said 48.
Through playing this game and modelling strategies such as using place value to take 10, we realised there was a gap in most of the students knowledge of not understanding place value enough to use this strategy effectively. So then, we tweaked it by using the cards that said ’10 less than’, ‘1 less than’ and ’10 more than’ and ‘1 more than’. This targeted focus worked well and when we went back to playing race to 0 – Students were able to use -10 strategy using place value more effectively.
The power of recapping yesterdays lesson! Lou started this part of the session with recapping the chocolate story. She redrew her chocolate picture and how many she had eaten. Lou wrote the equation, stopped and said ‘I didn’t tell you what this symbol was! Does anybody know?’ The students responded excitedly and were able to explain it.
Discussion points
Did it matter that we didn’t explicitly tell the students what the subtraction symbol was in the first lesson? Did it stop them from exploring the last prompt? Did it help them understand the symbol better in the second session?
With the story, Lou had 10 chocolates, how many did she eat? We implied the second part but didn’t specifically ask, how many were left? We discussed in relation to students using known facts to work out the answers. It wasn’t until we started to record our work that this became something to think about and really interesting to prompt students with. eg. So you had 13 and she ate 4. How many are we taking away? So how many are left?
The progress from the previous work was obvious. They were engaged in exploring and using various methods to work out the answer. The exciting part was the discussion with Lou at the end of the lesson thinking about what the focus should be for the following day. Recapping the last prompt seemed to be a great way to refocus students onto an efficient strategy.
Session 3
This lesson started with a warm-up. Students started with 10 unifix blocks, rolled a dice and took that many away. They used a game board to record the answer by placing a counter on the number. Eg. Rolled a 4. 10 – 4 = 6.
Discussion points
While simple in theory, this game worked really well. Students utilised different strategies such as: using the unifix to subtract, using the game board to count back and some grabbed a number line and preferred to count back by drawing. The best thing was that students were ‘playing the game’ which enabled the teacher to observe, conference and gather evidence.
After playing the game we adapted it to use a 10 sided dice and a game board of 20.
This prompt enabled students to connect with the story and visual what context (giving someone flowers and how many flowers were left in the garden).
Discussion points
It was really interesting to see the students finding it difficult to explain the different parts of the story when looking at the equations or as they were telling us their number stories. Often mixing up the amount of flowers given and how many were left in the garden. This was particularly evident with some of the students who had chosen to use a systematic approach to finding the different possibilities (making a table). They could justify the different ways but found it challenging to relate it in reference to the story.
Lou prompted some of her students to use the subtraction strategies board to show their thinking in new ways. This worked really well because it prompted students to 10’s frames and number lines.
Session 4
The focus of this session was to develop the students ability to tell subtraction stories and explore the different words that mean subtract. The lesson began with a warm up game and launched into Lou developing a story. The prompt was for students to create a story using subtraction. 25 – 5 = 20 was a prompt and some students used this.
The lesson concluded with Lou having the students share their stories and recording the different words that meant subtract or getting less. A lot of the stories seemed to revolve around something eating or chewing on something (pretty funny when they were sharing)
The students created their own story and drew a picture of what was happening. They worked out the answer and hid it under a sticky note. The lesson was really enjoyable and ended with the students going into the other prep/ one rooms and sharing their stories with the students trying to guess what the answer would be.
Reflection of the sequence
The lesson prompts were heavily influenced by the stories that Lou was telling and the students loved it. Although Lou did feel like she was running out of stories! We discussed keeping it simple and just pretending the materials were different things, eg. lollies, or fruits or tyres (shout out to Michael Ymer)
The lesson sequence was predictable and students got the hang of the drill: launch, explore, share and summarise. This allowed us to spend more time conferencing and asking questions rather than giving instructions.
The focus of the lesson was influenced by what we saw the students do. Eg. We noticed that they weren’t making a connection to taking away so Lou built a warm up game around that and the next prompt of subtraction stories.
The emphasis was on building strategies and proving rather than a quick response to equations. Students enjoyed sharing and absolutely loved showing the other students their subtraction stories (so much so that before the teachers were finished chatting about the stories they had moved into the next room and begun sharing with the other class.)
Things we are still developing
The right timing to incorporate the mathematical mindset goals. We both had uncertainties with some students rapidly working out an answer and rushing to show us. Lou and I discussed setting up the ‘depth over speed’ goal to encourage students to show, prove and record their work. The students often wanting to show were quick had an answer that worked but were in the habit of wanting instant feedback and encouragement to keep going. Our dilemma is not to have students sitting and listening for too long (prep/ one). More to come on this one….
Another timing issue…. Lou and I have discussed wanting to utilise the reflection time better. We would like the introduction and explore time to be shorter to gather data before entering the consolidating task. We both found that the warm up almost became the first lesson and the launch the second, without entering the consolidating and reflection stages. This happened mostly because the warm up required some instruction time and we were enjoying the success the students were having. Not a bad thing. Our idea is to make the warm up shorter and to the point. Eg. What number is bigger 31 or 12. Prove it. Conference two students and celebrate a strategy to get the answer. Launch.
Lou had the great idea to use the subtraction anchor poster to introduce new strategies that students hadn’t demonstrated through the explore stage. This was a great link to our idea of building depth (solving it in more than one way) for our students who were quick to get an answer and wanted to check in with the teacher. This enabled the teacher time to conference and check in with other students without interruptions
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