MPM1D1 - Day 17 Finishing Up Staircase Activity

We started with a few proportions questions as a warm-up. I've noticed that many students are able to solve these questions but they lack structure in their presentation and in explaining their solutions.
I posted these problems on the board and had groups solving the problems at the boards.

I told them to focus on making sure their solution was easy to follow for someone who happened to stop by to read their work. Most students had no trouble doing the work so I had them work on their presentation a bit. We talked as a group about part/part relationships vs. part/whole relationships. We summarized ratios and proportions in their notes and they tried some examples on their own.

We revisited yesterday's work on Staircase and Steepness. Only two students completed the work I assigned for homework. One was able to find a ratio for the base divided by the height that worked. We talked about how the order that his method gave might seem backwards to what would be intuitive. The other student who found a solution went home and taught himself (with the help of the internet) how to use trigonometry to find and angle in a triangle given two sides. I was blown away.

Eventually we settled on the base over the height as a good measure of the steepness. We called it slope. I went back to the suggestion by a student yesterday to put the line on a grid. We looked at how to find the slope then the class worked on practicing solving proportions and calculating slopes.

MPM1D1 - Day 8 Fractions and Proportions

We started with this Open Middle Problem:

The idea is to fill the squares using only the digits from 1 to 9, at most one time each. This was fairly easy for the class. Somebody asked if they were allowed to have improper fractions. Some groups drew pictures, while others just worked with the numbers.

Since the students were so quick to solve the first one we moved onto this one:

Some groups started with pictures but realized that it was tough to tell the difference between 4/9 and 5/11 when they were roughly drawn on the board. Most groups eventually came to the conclusion that they needed a good way to compare the fractions. Some discussed common denominators but most decided to convert the fractions to decimals or percents.

We then talked about equivalent fractions, mixed numbers and improper fractions. I mentioned that at some point we'd have to go over performing operations with fractions. Lot of them were keen to do it right then, so we did talk about it.

Next up was Fast Clapper. All but two of my students were pretty excited to be clapping and counting. They found unit rates and solved proportions by considering them equivalent fractions. I was hoping to do Smart Car Smash but we were running out of time. Instead I handed back the mastery test from yesterday (overall the results were quite good) and then I handed out a page on equivalent fractions, mixed numbers, improper fractions and multiplying and dividing integers. We'll redo the master test tomorrow.