Introduction to Substitution

We are starting substitution in MPM2D. We used a visual task to start.

4 acrobats and 5 grandmothers are tied in a tug of war.

A dog is now tied with 2 grandmothers and an acrobat.

we need to figure out which side will win the final round.

We worked in random groups up at the boards to make sense of the situations, and represent our thinking and our logic. I enjoy this problem as it allows multiple approaches, and there is usually at least one group that will “discover” the algebraic approach of substitution.

we had groups work on representing their data and organizing it in tables, and creating equations.

one group decided to say that 1 grandmother was the base unit of strength, and that an acrobat was 1.25 times the grandmother’s strength since 5 grandmothers=4 acrobats. They determined that a dog was 3.25 times the strength of a grandmother, then decided that the side with the dog would win.

this group decided that since 4x=5y that they could relate this to 20=20 so x would be 5 and y would be 4. They then calculated that the dog would be 14, and then they substituted values to decide that the side with the dog would win.

Here is what one group did, substituting the value of (1a+2g) in place of d, and then using that to solve.

We will be using substitution a lot moving forward. It was good to have such enthusiastic participation on day 1.