MPM1D1 - Day 65 Solving Equations With Fractions

We started with this Which One Doesn't Belong:

It was great to hear all of the terminology that came out of the discussions.

After the warm-up we moved into solving equations with fractions up at the board in groups. I didn't give any instructions. I gave some equations for groups to solve and they did a great job.

Here are the questions they worked on:

I was amazed at how well the groups worked. They required little to no assistance from me. They were able to apply what they had learned about solving equations without fractions and things worked out great. It was also great to see the stronger students really working with those that struggled to bring them along. I feel that we've really developed a community of learners in the class and I'm really happy about that. One of the groups consisted of two students who pretty much refused to work with each other at the beginning of the semester. Today they worked as though they were good buddies.

Once the groups were done I brought the class together and asked what was different about the equations today. Many students said that these equations were more difficult. When I asked why they were more difficult the response was because of the fractions. We then talked about how we could eliminate the fractions by multiplying both sides of the equation by a common denominator. We did a couple so they could see how it was done then they did the first part of this handout.

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.