As a new year begins, planning and programming are often the focus for classroom teachers. It’s a time to try new things, adapt what has worked before, and think about what makes a great lesson. For mathematics, as with any subject area, flexibility is the key. Catherine Attard (@attard_c) provided some good advice regarding lesson planning and structure in her blog:

“… most importantly, know what you are teaching, provide opportunities for all students to achieve success, and be enthusiastic and passionate about mathematics!”

Attard, 2017. *A recipe for success: Critical ingredients for a successful mathematics lesson*

I regularly get asked *What does a good maths lesson look like?* In fact, this was exactly what I worked with a school on last week. In a primary school there is usually a number of staff changes at the beginning of the year. New teachers arrive, some teachers switch stages, and others are returning to classroom teaching from support or other roles. Whatever the situation, it’s good to discuss as a grade or stage if there are aspects of the lesson structure that should be consistent across the school. Consistency in teaching builds a school’s learning culture and supports transition for students from year to year.

This blog is focusing on lesson structure. When I first started teaching, we ‘borrowed’ the modelled, guided, independent (MGI) lesson model from English. There are elements of my lesson that still involve say modelling, but sometimes MGI results in *I do, you do, we do* where teachers explain how to do it, then students copy and repeat. In mathematics particularly, investigation and exploration are essential for student learning where they come to their own understanding (a-ha moments) that require me, as the teacher, to hold back – to not explain. This is where a model like L*aunch, Explore, Summarise* is useful.

@sharynlivy leads @CatholicEdParra teachers through the power of launch-explore-summarise, productive struggle and wait time. @NumeracyNow @AnnDownton @surfmaths @MonashUni #EMC3 pic.twitter.com/9GbR0dPvaq

— Kathryn Salkeld (@SalkeldKathryn) March 28, 2019

“… the traditional lesson structure of teacher explanations followed by student practice and correction of answers is inadequate. The alternate structure of launch-explore-summarise (see Lappan et al. 2006) is more likely to facilitate the conversion of tasks with potential for Doing Mathematics into lessons.”

*Supporting teachers in structuring mathematics lessons involving challenging tasks*, by Sullivan et al. (page 125)

The quote above by Peter Sullivan is one I’ve used in a previous blog where I briefly mentioned the Launch, Explore, Summarise (LES) model of lesson. The National Council of Teachers of Mathematics (NCTM) explain the LES model in this document. Or you can read this excerpt for more information. We use the LES model with our pre-service teachers at Sydney University and I use it regularly when I conduct demonstration lessons. I like that the terms are action words, it tells me what the purpose of each section of the lesson is (more so than introduction, body and conclusion). Below I have listed some ideas and resources to support teachers in using the LES model in your mathematics classroom.

### Launch

The launch is the first 7 – 10 minutes of the lesson. This is where you want to hook students into the concept and get them ready – engaging their brains in mental mathematics, visual representations, and making the link with what’s come before (prior knowledge). I find that this is where I spend a lot of planning time, I use my content clusters to identify the focus concept. It is important that whatever you do, it links to the concept (not just the topic) of the lesson sequence. Here are some ideas for launch tasks:

- Number talks
- Noticing and Wondering images (see our resources)
- Open Middle
- Which One Doesn’t Belong (wobd)
- Esti-Mysteries
- MathStratChat
- Picture books (list of maths books or these ones)
- Concept videos (like Numberphile)
- Use talk moves (throughout the lesson but here especially)

It's time for #MathStratChat!

— Pam Harris (@pwharris) January 23, 2020

Rules: tweet your favorite, clever solution or be inspired to find an equally clever strategy.

Like, RT so more can see!#MTBoS #ITeachMath #MathIsFigureOutAble #MSMathChat #ElemMathChat #HSMathChat #T3Learns #MathChat pic.twitter.com/dBZGaXqmW6

### Explore

The explore phase is where student venture more deeply into the concept introduced in the launch. It could be organised as a whole class, small groups, pairs, ability or mixed grouping or as individuals. Give yourself, and your students, time to explore and play with the mathematics, make mistakes, try ideas and strategies, make predictions and solve problems. During this time you can stop if needed to re-clarify a concept (explicit teaching) or highlight a useful or efficient strategy being used (fishbowl). Here are some ideas and strategies to use during this section:

My grade 4s showed deep thinking during our 'magic lollipop tree' task - which gives one lollipop on the first day, two on the second, etc. Some used counters to show their thinking, others began exploring a formula for triangular numbers. #iTeachMath #challengingtasks #mtbos pic.twitter.com/vHp3QcL5C7

— Toby Russo (@tobyrusso) April 3, 2019

- Challenging tasks
- Nrich investigations (I have mapped these to the AC)
- Open-ended tasks (tasks by Peter Sullivan)
- Parallel tasks (this video by Marian Small is excellent)
- Week of Inspirational Math(s) tasks
- Games and activities at point of need (DENS)
- Math menus

### Summarise

During the summarise phase is where connections are made. This is not just the last 5 minutes of the lesson and a quick exit ticket (although these are great!). This is where the main teaching occurs, not at the beginning of the lesson. It is at this point that your pre-planning of the types of questions to ask to probe for understanding come into effect. Links are made for students between prior knowledge and new knowledge, students share and critique their strategies and notice similarities with others’ work. Students provide reasons for their thinking and justify their solutions. The teacher’s role is to observe if students got the ‘big idea’ or if there is more teaching that needs to follow. It’s a time to notice any misconceptions or highlight students’ generalisations. Some strategies include:

- Intentional Talk strategies (eg compare and connect)
- Productive mathematics discussions (5 practices)
- Talk moves are extremely valuable
- Exit tickets, twitter (sharing) walls, gallery walks feedback session

In 1S today we thought about what we know and trust and used that to investigate how many 5s in 100. Bead strings and pegs really helped us with our thinking. This is our summary of learning. #trialling #practice #usingwhatweknow pic.twitter.com/bqnkv3cpBh

— Karen Sor (@KarenSor23) November 13, 2019

There is lots of planning that goes into the making of a mathematics lesson. Much of the important work happens well before the lesson or sequence of lessons takes place. Any activity or game or problem you want to try with your students, do it yourself first. Lesson rehearsal is an important part of planning in the teaching and learning cycle. I try to think about my lessons in two aspects – what the students are saying and doing, and what the teacher is saying and doing. I also need to think about what possible responses – both correct and incorrect, my students might produce. I use these possible responses to frame up the questions I plan to ask or prompts or probing questions I may need to use. The LES model still needs to be seen as flexible. You may find your students deep in the explore phase at the end of a lesson time, that’s ok, just keep going from there the next day (you may just need a very short launch to restart the concept). You may go through two cycles of LES during one lesson – it all depends on your students.

#### References

Similar to the LES model is the Three Act Math by Dan Meyer

Graham Fletcher (@gfletchy) also has some example Three Act tasks

More information and questions to think about during the LES model

Lesson ideas for investigations https://www.mathalicious.com/