How do I create a lesson sequence? This is a question I get asked a lot, both by pre-service and in-service primary teachers. You may feel you are great at designing single lesson ideas that are related or whole programs, but maybe the flow could be better – more conceptually than topically related. For example, the difference between designing a group of lessons for say addition and subtraction (topic-based), to designing a sequence of lessons for say a concept within that topic such as; understanding that combinations to 10 can be applied as the bridging to ten strategy.
Lesson designing and sequencing is an art, it is the heart of teaching (something that recently has been suggested is better done by others outside the classroom context). It is time consuming yes, but it’s pretty much my favourite part of teaching, bar seeing when students have an ‘a-ha’ moment of discovery! With more than 20 years teaching experience, I am still learning this art form. And, like any art form, you learn by practice, you learn by studying others, and you learn by trial and error. Not every lesson or lesson sequence is going to work, not every lesson or lesson sequence is going to be ‘wow’, not every lesson sequence is going to be the same. But every lesson sequence in mathematics should have two goals – be open enough for change and flexibility, be focused on making connections for students. I’m sure I can think of more goals than these two – but they are at the top of my list.
Open for change and flexibility
I like routine, many students also like routine – this doesn’t mean every mathematics lesson needs to look the same, have the same elements, run for the same length of time or follow the same script. I’ve spoken in a previous blog about the Launch, Explore, Summarise model for individual lesson structure – even this structure is flexible. One the first day I introduce a concept, within the launch phase it might be more connecting to prior knowledge or mind mapping what my students already know and within the explore phase there may be a longer explicit (I prefer the word intentional) teaching to build some ground work. The follow day or days might be quite different, they might have an even shorter launch phase into a problem to solve or activity to investigate. If the students are deep in the investigation, we might stop, have a short summarise phase then start the next day straight into the explore phase again – continuing the investigation activity. Whatever the structure, summarising at the end of each lesson session is paramount.
Being open for change also means my lesson sequence, although planned for, still has some wiggle room based on the students. Having your lessons student-driven doesn’t negate the role of the teacher nor does it mean the students are in the driver’s seat. What it means is that as the teacher I’m not always talking (I’m listening), I’m not always teaching (I’m observing), and I’m not always telling (well, I’m never telling!). Questioning plays a large role in leading great mathematics lessons – these questions can be planned for and should include both enabling and extending prompts to support student understanding and learning. Allow conversations to go where students take you, segues are good, but not too far that they derail your conceptual plan. For example, take my conceptual focus above: understanding that combinations to 10 can be applied as the bridging to ten strategy. When asking students for combinations to make 7, a student may suggest “what about zero and seven?” you may not have expected this response but now is a great time to divert the lesson and explore this concept together. If on the other hand, a students says “what about eight minus one?”. I would say, this is a great relationship to subtraction, let’s write that up on the board so we can explore it another time. You need to know when to reign students in. As the conceptual focus is on using combinations to add, although this student has made a great connection (between addition and subtraction), it doesn’t add to the learning intention for this sequence. It’s ok to come back to student ideas later.
Viewing your lesson sequence as changeable and flexible, also means not getting stuck in 40 minute or one hour lots. A lesson you have planned may go over 2 or three days, “a lesson is never finished” (Charles Lovitt), there is always more to notice, wonder, investigate, and connect. Your conceptual focus like my example: understanding that combinations to 10 can be applied as the bridging to ten strategy, could be your learning intention for 3 days or 3 weeks. When your focus is small, you can dig deeper into the concept and you then know that what you plan will be connected. If I just had a focus on ‘addition’, the lessons might be on anything such as; addition as the inverse of subtraction, addition strategies, addition using place value groupings, addition using a number line, addition patterns in number bonds, addition number sentences, turn around facts (commutative), the list goes on … When we plan lesson sequences based on an overarching concept like addition, it is very hard to see how the lessons connect. But when we dig deeper to the smaller concept, our job of planning becomes easier, more directed by the choice we made for the learning intention. Always think about – what do I want my students to know.
Making connections for students
Now that you’ve started to think deeper about the smaller concepts–what you want your students to know–connections are the next thing to focus on. Mathematical connections to other mathematical concepts, to the students’ own knowledge, understanding, and contexts, and to real life, is similar to the idea of text-to-text, text-to-self, text-to-world from an English perspective (see Math Connections blog). Go slow, don’t rush to the next idea (see my blog on slow teaching). In NSW, apart from in Kindergarten, we have two years that span a stage of learning. There is plenty of time to revisit, revise and refine mathematical concepts. Also remember that we collectively have each students for seven years, mathematical connections build over time, don’t expect students to make every connect in one calendar year.
Here are some of my top tips for making connections in mathematics lesson sequences:
- teach the same lesson using different resources (making connections includes seeing the multiple ways a concept can be represented orally, in written words, in pictures, using diagrams, digitally, symbolically and numerically)
- ask questions that lead students to make the connections (what do you already know that can help you? where else might we use this strategy? does this work all the time? when does it not work? Is that always true? what else could we find out?)
- teach a number concept in conjunction with (or follow by) a measurement, geometry or data concept or another number concept (not always, but often, we apply number concepts when working on other mathematical tasks eg multiplication to find area, ordering numbers to create graphs, using decimals to represent accurate measurements) This idea can go both ways: number teaching then application, or application then number teaching – explicit (intentional) teaching can happen at any point in your sequence or lesson, it doesn’t always need to come first (see Russo & Hopkins, 2017)
- create an ongoing map of mathematical connections on your classroom wall (or on a Jamboard). A bit like a map of the world or train map, draw lines of connection between big ‘mathematical cities’. If you regularly make anchor charts of concepts these can be connected over time to build an illustration of your class’ connections
My advice would be to start small, plan a sequence of 3 or 4 lessons based on a concept within a topic/area of mathematics. I always head first to the syllabus (Australian Curriculum if you are perhaps in other states than NSW) this helps me locate the smaller concepts to expand. I’d make a mind map of the things I think the students might need time to explore or things they might need intentional teaching about to make the connections and understand the concept. Here’s an example based on my concept within addition and subtraction:
Once I have this mind map, I know that the lessons I create for this concept (weather they take 3 days or 3 weeks) will be connected. They are all building on the same, small idea. I can then create further links from this mind map to other areas. For example patterning for the number sentences that show associative and/or commutative properties of addition, or a lesson sequence on applying the bridging strategy to solving problems related to length. Or a sequence on using combinations for subtraction (15 – 7 uses the same knowledge of combinations). I hope these ideas kick-start your thinking about how to ensure your lessons are sequential and build conceptual understanding. Remember to ask yourself, what comes next? where does this knowledge go? where do the students need to use this? why does this learning matter?