Consolidate This


Consolidation is by far my biggest struggle when it comes to teaching math.  So when I was offered the chance to take PD on it, I jumped. The session was called: “Landing the Plane: Consolidating Learning in the 4-8 Math Class”.

I think my favourite quote from the session was this one:

 “Teacher practices that promote inquiry can be challenging to implement…” Suurtam, C. Quigley, B. & Lazarus, J. (2015) 

Ya think? It certainly wasn’t the way I was taught and I continually have to reassess how I’m teaching to make sure I’m pushing inquiry…but this session really helped.

We looked at the book The 5 Practices for Orchestrating Productive Mathematics Discussions. It’s a practical guide to planning out a 3 part Lesson that guides you towards better consolidation. “But, what ARE the 5 Practices?” you ask. Well, since you are bursting with excitement, let me tell you. They are…drum roll…


When you have chosen your open ended questions (yes, this is based on a 3 Part Lesson) you need to anticipate how you think students will solve the problems. Write down all the strategies you think they will use and also try to anticipate what problems may arise. What misconceptions or gaps in knowledge may come up. Then you consider how you might guide students with misconceptions or get them to solve the problem in another way. You should also anticipate what to say/do to extend the questions for the students that might solve it very quickly.


Monitoring happens during the lesson. Once you have anticipated what the students might do; you circulate in the class and take notes of which strategies they use and which misconceptions they have. We were given this handout : lesson-planner-5-practices to help prep the lesson. I then made this handout for monitoring the students while they worked: Strategies Observation Sheet . What’s great about this approach is all the rich data you can collect, quickly about the students. It would definitely be good for next steps come report card writing time.


Once you have monitored all the students’ work you will want to select the answers that highlight certain strategies and math thinking. The selection of the students’ strategies is done based on the lesson’s goal for that day. The reason you select is to allow you to show one example and then you can always mentions others who used the same strategy without going through every answer.


Before you present the various student strategies decide on an order. This is where the consolidation piece really starts to come together. You’ll want to introduce the different strategies and thinking in an order that will guide the students to more effective strategies and to the lesson’s goal.


Finally you want to connect all the strategies to each other and to the lesson’s goal. This is where you weave together the students’ strategies showing the connections to each other and the final goal of the lesson. This is also the time to challenge students to expand their repertoire of strategies and mathematical thinking.

Practic 0?

But wait…is something bugging you about the strategies? Like maybe…,”How do we pick the Lesson Goal?” Yeah that was bugging me during the start of the PD too. I kept wondering, “How do we know what the goal is?” Luckily the authors and session trainers had asked that question too. Turns out there’s a “Practice 0”. Yep. Chapter 2 of the book is all about setting goals and picking rich questions. Unfortunately the book doesn’t provide the actually questions save for a few sample lessons that they analyze through the book. This is where Marian Small saved the day.

I’m very fortunate to have an amazing admin who are always ready to share resources. So, when I felt I was ready to try this type of lesson out I went to see them about some resources that had been suggested at the PD session. You see, there are some amazing people who LOVE, I mean, really ADORE math and they have written tons of books on how to do make it more engaging. Marian Small is one of those amazing people and her books are full of low floor high-ceiling questions. Her books can be expensive…but, like I said, I have an awesome admin who happily shared.

Here are some of the books that helped me: (The links do bring you to pages where you could buys them but I’m not getting any money for that…I just like the books)

Great Ways to Differenciate Mathematics Instruction  This book  is a JEM. Not only does it have a bunch of questions sorted by strand and grades but it also has parallel tasks. Parallel tasks are similar questions that allow you to differentiate for your students.

Making Math Meaningful  This mammoth book is packed with excellent examples of open questions and how to teach them. The first few chapters explain why to teach with open questions and also explains Big Ideas and how to find them and guide your lesson with them. Then the book gets broken into the different mathematical concepts with many examples of questions to go with.

Les Questions Ouvertes  This is another by Marian Small book which is chock full of question IN FRENCH! Immersion teachers rejoice!! I was sooo excited when my VP held this one up. I might have drooled. Maybe, just a little. So far, though my school only has the Number Sense and Numeration book…I’m not sure if that is because that is all that is published or simply because my school hasn’t bought the others yet. Still, drool.

Phew! That was a lot to throw at you and my head was certainly spinning with ideas and questions after this session. I’ll post soon with how the lessons are going.




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