thinking about equivalence in grades 5 & 6

Posted on: November 20th, 2014 by jnovakowski

Last week during my visit to Gillian Ewart’s grades 5 and 6 class, we played around with the big idea of equivalence. The focus of our time together was coming to an understanding that the = symbol is a sign of equivalence or balance.

I began by reading the first few pages of the picture book One is a Snail, Ten is a Crab, pausing a few times to check in with students to see if they were “getting it”.



I wrote the equation 9 = 2D + 1 on the whiteboard, intentionally choosing the order in which I presented the equation. I asked students to talk to a partner about what I had written. They shared their thinking and they realized the D was for dog (D is 4 legs) and that the +1 was the “constant” of the snail, as expressed in the book. I asked if there was another way I could have made 9 and they shared that a S + 1 would also work (S is the eight legs of a spider).

As a whole class we played around a bit with the idea of the balance scale and balancing both sides of the equation. So I added another dog to the right side and asked what I need to do to the left side to keep the equation balanced….D + 9 = 3D +1.

I asked the students to create an equation and add different animals or amounts to keep it balanced. A student asked, “Do we have to write the equations like that? (pointing to the whiteboard) Backwards?” which led to a great discussion about equations and trying to really get at what the = sign means. Some of the students continued to refer to “5″ in the example below as “the answer” which as teachers, gives us great information about the myth-busting we can work on together.



The students engaged in the balancing equations work in a range of ways. Some students got very creative and complex with their equations on their whiteboards, others modelled their equations with materials, some students were able to think about the big idea using less complex equations and with the support of an adult and others used patterns in their equations to build and extend.

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As students created equations, they took photos with the iPads to document their experiences. I did a quick demonstration of the PicCollage app and asked students to combine some of their photographs with a statement of learning for our time together. This is a great assessment check-in as a teacher and helps students to focus on big ideas in mathematics and providing evidence of their learning.




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