Overview & Rationale

When you bring students together for a whole class discussion following the exploration, the main teaching of the lesson occurs. This is the time when you help students to connect the mathematical thinking and work they did to the mathematical ideas underpinning your learning goal. This phase of the lesson should still be student centered – you don’t just tell students how their work connects to the learning goal, and you don’t want this time to be a generic “show- and-tell.” Instead, you purposefully select which students will share and what they will share. You sequence the mathematical work intentionally as you ask questions that support students to make connections across solution paths/strategies and to the central mathematical ideas in the learning goal.

1. Select 3-5 mathematical ideas that you will ask students to share.

Review your learning goal and the anticipated solution paths/strategies or misconceptions and think about which mathematical ideas you will ask students to share. Even if you only have 3 solution paths, you might have more than three mathematical ideas that you want students to share. For example, solution paths could involve more than one mathematical idea, so you might decide to break up these ideas. Or, you might decide it would be beneficial for the class to consider some incorrect solutions because these are often great learning opportunities. You’ll also want to think about what you might consider as you choose who will present.

2. Sequence the selected mathematical ideas intentionally.

In order to steer instruction towards a mathematical point (in this case, your learning goals), you need to develop and maintain a mathematical storyline – a deliberate progression of mathematical ideas – throughout your summary. This means that you need to sequence mathematical ideas in such a way that the mathematical story is coherent and has a plot – in other words, something “happens.” This plot will be different depending on your goals, but you should always aim to present a plot that makes the mathematical ideas accessible to every student. Several options for sequencing towards a coherent mathematical storyline are discussed at the beginning of CHAPTER 5 in Five Practices book.

3. Plan for connections

Another important piece of maintaining a coherent mathematical storyline is making connections – connecting the mathematical ideas students share to each other and connecting them to the central mathematical ideas of the learning goal. These connections are essential for making something “happen” and without them, your summary becomes a “show-and-tell.” Think about how you can ask questions to make sure the mathematics is openly addressed and to help students make the connections as they build from what they know. Plan some specific questions that you can ask for each mathematical idea that students share to facilitate connections across solutions/strategies and to the learning goal. Connecting is discussed at the end of CHAPTER 5 in the 5 Practices book, and the sample lesson plan in APPENDIX B may also be helpful.