Building a Conceptual Math Lesson

Let's explore the essential components of a well-designed math lesson! Recently, I received a question on TikTok asking about the structure of my math lessons. While many educators feel confident in planning reading lessons, the process can be a bit more uncertain when it comes to math. Drawing upon research on learning trajectories (learningtrajectories.org !) and how children develop mathematical understanding, I've identified key elements that should be incorporated into each math lesson:

1. Practice with numeracy/number

2. High cognitive problem solving

3. Review

4. Content

So, let’s break down each part and what it might include.

1. Practice with numeracy/number

   This could include counting, subitizing/representing, or comparing. This should be a quick activity like a counting around game, looking at a quick dot image (and sharing!) or a mystery number line game. Read more about my quick math warm up ideas here. This should be 5-7 minutes.

2. High cognitive problem solving

   This could include a problem of the day (check out my series on Tik tok! or a resource by clicking here) or a number talk where students are sharing and adopting strategies for solving. This would be 10-15 minutes.

3. Review

   This one should be the least shocking. Even though I believe in helping students understand concepts, it’s still good to review concepts. Make sure you are asking deep probing questions, using more open-ended tasks or questions, and allowing students to do a lot of deep thinking. This review should be quick, though, less than 10 minutes.

4. Content

   This is when you look at and practice the current concept you are wanting students to understand. Again, this isn’t so much about drilling and practicing, but about giving them opportunities to use the skill and dive into the concept. This would be the time you do some practice together, asking deep probing questions, and then incorporate centers/stations or independent practice time.
   It’s important to note here that I don’t usually adopt the “I do-we do-you do” method for math time. Instead, bank on student's inate connective/math thinking and incorporate “You try-we do-I connect”. Let students try solving something with the concept, let them help each other, and then use your role to make connections, teach the representation or math words for what they’re doing, or ask questions to get them closer to understanding.

   The time for this will depend on how your math block looks. I would do no more than 15 minutes of whole group and then break into stations and meet my small groups for deeper understanding. If you want to know more about my math stations, click here.

Let’s do an example using 3rd grade and multiplicative thinking as our current concept.

1. Counting game - I’d play a round where they are practicing counting large numbers (start at 997 and go up) and then a round with skip counting.

2. Quick dot image using groups - display the image on the screen for only 5-6 seconds. Ask students how they could figure out the total without having to count all! Annotate their thinking on the screen as they share the groups their mind creates.

3. Problem of the day: There are bikes and trikes for sale in the shop. If there are 23 wheels, how many bikes and trikes are there? - give students time to think in groups, share their thinking and give them vocabulary (multiplication, groups, times, divide, etc.)

4. Quick review - pull up 2 questions from previous content (probably addition) and have students turn and talk

5. Practice multiplication representation by using a four square map (fact in the middle, 1 square of array, 1 square of repeated addition, 1 square of number line, 1 square of groups).

6. Stations! Practice making groups at teacher table with manipulatives.

I hope that helps give you an idea for a well rounded lesson time that incorporates numeracy, deep thinking, and content.

Happy Math-ing!