I teach at a really large school. With 750 students and about 40 teaching staff, it’s hard to collaborate and plan with everyone. At my school, we often meet and plan in grade teams. This is great, and it’s definitely helpful to work as a group, but this week, I realized the benefit of expanding this group.

At lunch time on Tuesday, I was having a conversation with one of our great Grade 3 teachers, Mary Barton. Mary was talking about Grade 3 math, and she mentioned how hard it is to teach the Grade 3 students about balancing equations. The students believe that an equation always has to be written as ___ + ___ = ___. She mentioned that when she showed students an equation that was ___ = ___ + ___ or ___ + ___ = ___ + ___, the students were easily confused. Mary said she knows that this concept is largely developed in Grade 3, but it’s definitely one of the harder ones for students to understand. Just as we were getting ready to go back to class, I said to her, “would it help if we spent more time on this concept in Grades 1 and 2?” Even if the expectations develop more past then, I still need to teach addition and subtraction in Grades 1 and 2, so why not spend a little more time showing the students balanced equations? 

Mary loved the idea, so that afternoon, I did this mini-lesson with the students:

I started by writing 6 + 4 equals _____, and the students told me that the answer was 10. Then I asked them if it was also true to write 10 = 6 + 4. The students looked at it for a minute, and then one student raised his hand to say, “yes.” He explained that 10 = 6 + 4 is the same as 6 + 4 = 10, except that the numbers are reversed. I got the students to think about this for a minute, and then I asked them another way to write this equation. One student came up with 10 = 4 + 6, and one student came up with 4 + 6 = 10.

The students were really getting into this, so I pushed things a little bit more. I asked students one way to make ten. One child gave me 7 + 3. Then the equations kept coming from there. I wrote a long list of all of the ideas. When one student suggested 11 – 1, the students started to see new options, and all of a sudden, their mental math skills were hard at work. After generating 14 different equations, I asked the students what all of these equations had in common. The students quickly replied, “They all equal 10.” I used this as a new starting point. I then wrote if they all equal 10, then is it true that 7 + 3 = 10 + 0? A student explained that it was because both sides equal 10. Then I got students to give me other true statements using our long list of equations.

Students quickly moved forward from here. I had students experimenting with adding and subtracting to total various amounts. As a follow-up to this mini-lesson, students were asked to go back to their desk, get out their journals, and write some of their own balanced equations. They could use tools in the classroom to help them figure out the addition or subtraction statements. I just wanted to see what they could do.

During our math congress, six students shared what they did. Below are videos of them talking through the process:

Yes, I had students circle and write down what they did because I wanted everyone in the class to visually see the process. I also purposely kept this activity open-ended, so that my students could work with equations at their comfort level. This was an introductory lesson, and I thought it was important to first see where the students were at: what do they already know? What do I need to spend more time on? And no, all of the videos aren’t perfect. After the first video where I’m trying to teach, question, and record, I learned to hand off the video camera to a student instead. 🙂 Oh, the power of reflection! 🙂

This activity served its purpose though. It had my students look at addition and subtraction in a new way. It helped them see that there are many different ways to write an equation, and it helped them understand each way too. This was a great introduction to the balanced model! This was also an activity that I would have never done — especially with my Grade 1’s — if it wasn’t for Mary and our conversation.

I think that teachers need to know the strengths and needs of the students as they move to the next grade. I think that we need to use this information to inform our teaching practices. The conversation at lunch on Tuesday reminded me about the power of sharing: we need to know what’s happening in each other’s classrooms.

What are your thoughts on this? How do you “share” with teachers in different grades, and how do they “share” with you? Do you find this to be a beneficial process? Why? I’d love to hear about your experiences!

Aviva