Today's lesson started with reviewing all the methods they knew to solve a proportion, which lead to the undoing division method, which lead to fraction busters, which lead to the reason why the original method, cross products, works.
Then they converted a decimal equation to a whole number equation and solved it. A lot of students checked their solution in the whole number equation but I prompted them to check it in the decimal equation to make sure that there work in making an equivalent equation was correct.
Then instead of doing a similiar problem from the book, we looked at this clip from Little Big League:
I pointed out that I like this video clip because it shows that they were not afraid to attempt the problem and that it's okay to be wrong. We analyzed why 15 and 8 hours did not make sense as answers. Then when I asked if 4 hours made sense, there was a mix of yes and no answers from the class. Students pointed out if it took 3 hours for 1 person to paint the house by themselves, it can't take more time, or 4 hours, for them to paint it together.
I asked students if it takes me 3 hours to paint the house, how much of the house could I paint in an hour? They said 1/3. So, I defined x as the time it takes to paint the house together. So, 1/3x + 1/5x=1 The 1 represents the whole job getting done. They then applied what they learned to solve the problem. See the attached photos.
In accelerated students graphed the 3 different types of sequences. They then described the growth. I was impressed that Markos got the quadratic equation of t(n)=(3*n)^2. Zoe pointed out the importance of the parentheses to keep the order of operations correct.
Students compared the graphs to see if they represented the growth of a bank account, which one would they want?