This week we finished up proportions in Pre-Algebra and got introduced to percents in Math Skills. Also had several teacher visitors who are applying for the open math position at our school (our other math teacher is moving to Brazil to teach). Oh, and it was tax day in our classroom economy,
We finished up proportions this week with discussing similar figures and how we use proportions to solve them. As a review activity, I gave them a quiz that I used last year. They worked on it together and we went over it. The following was probably the question that sparked the most meaningful conversations:
A bag contains colored marbles. The ratio of red marbles to blue marbles is 1:4. The ratio of blue marbles to yellow marbles is 2:5. What is the ratio of red marbles to yellow marbles?
The test was super short. I wondered how to use the rest of the class period. Do I start on the next unit? Do I spend the first part of the class reviewing? But we already reviewed all last class period. I decided to do the test first, then have them work on their blog reflections that are due Monday. They pick one of the three lessons and write about a prompt that I provide for that lesson. For example, if they wanted to write a reflection about similar figures, they’d reflect on the following prompt:
Give three examples of real-world objects that are similar and explain why they are similar. The ratio of the corresponding sides of two similar triangles is 4:9. The sides of the smaller triangle are 10 cm, 16cm, and 18cm. Find the perimeter of the larger triangle (this one is tough but draw a picture, and take a picture of you work. Include your thought process in your reflection and how you went about figuring this out. I’m more concerned with your mathematical thinking than if you get the exact right answer).
They write the blog and then share a link to it using Google Classroom. I reminded them that the reason we do the blog reflection is to give me an opportunity to assess if they know the ‘whys’ behind the concept, not just what to do.
We did THIS 3-Act problem for the last 30 minutes of class in two of the three Pre-Algebra classes. It went well! The last class didn’t get to it because most of them forgot their calculators and it took them a large part of the class to do the work on the test. I don’t let them use computers or phones obviously, and I didn’t let them share. I wasn’t even so concerned about cheating with the sharing of calculators, I just wanted there to be a natural consequence of not being prepared. Unfortunately, it left part of the class with about 45 minutes where they were just doing math puzzles and Khan Academy since they had everything done. I’ll put a time limit on the test next time and students who don’t finish have to come in during lunch or after school to finish.
Last year, percents were where I had my richest classroom conversations in my 6th grade class. I wrote a post on it that was featured in Dan Meyer’s year end reflection blog. That was exciting! The conversation this year wasn’t bad, but not nearly as rich either. Students do great when talking to each other in pairs but when we do whole group, it’s often crickets. I can call on people and they can share their thoughts but students don’t naturally just ask probing questions or share various methods of doing it as they do more often in my other classes. To be fair, my Pre-Algebra classes that do that best are filled with students who had me last year and are used to this discussion-based method of learning.
I didn’t actually teach them how to convert percents, fractions, and decimals, just tried to ask the right questions in the right order, starting with what they knew and hoping they would make the connections as we discussed them:
- If you get 50% off an item, what does that mean? How do you know?
- If something has grown by 100%, what does that mean? How do you know?
- Write 25% as a fraction and decimal
- Write 4% as a fraction and decimal
- Write 35.8% as a fraction and decimal (lots of aha moments here)
- Write 124% as a fraction and decimal (more of them got this on the first try than anticipated)
I asked them how they felt about me not teaching exactly how to do it but just working through it having them share their thinking. A few of them shared that while that may not be the best method for every concept, they really liked how it went with percents.
I then taught them how to find percents mentally by using benchmarks like 10%, 1%, and 25%. Some of them really grabbed onto that to the point that they didn’t see the need to make a proportion to find the percents. I’ll have to pose better questions that they see a need for proportions when doing it mentally isn’t as feasible.
HIGH FIVE FRIDAY & TAX DAY
Today a girl told me ‘I’m glad you do high-five Friday because I know if I’m ever having a bad Friday, it will get way better because high-five Friday is so fun.’ 🙂
Students paid their $500 classroom economy taxes this week. They got $50 deductions for any auction they donated to (if they kept their receipts). I was going to have them go in and pay it themselves but decided that I’d withdraw it from their online bank accounts. Less like real life, but a lot easier for me.