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In the first lesson, we decided to tackle the concept of equations in a very visual way. Our students have been exposed to cube lines this year, as a way to introduce the number line, and help them to see relationships between numbers. We decided to leverage this model to think about equations.
In the next lesson, we explored equal money amounts. At the beginning of this lesson, students made connections between the cubes lesson and equal amounts, which made it much easier to launch the idea of equal amounts of money. Pairs of students were given a paper bag with an amount of money between $5 and $7, which they needed to represent using different combinations of coins and bills. Using the mathies money app on a screen, we were able to model the different ways to represent equal amounts of money, in order to consolidate our understanding of the problem as a large group (see the image above for an example).
The power of connections across different models, strands and problem types really stood out to us as a result of these two lessons. The idea of equality resonates everywhere in mathematics, and yet it's an idea that seems to stump many students. That leaves me wondering why? How might we make more explicit connections between big ideas (like equivalence) in order to help all students see the idea more clearly?