Based on the results from yesterday's test my students need more practice with exponents. When they arrived I put them in groups and sent them up to the boards and I fired exponent questions at them. They worked while I walked around and questioned what they were doing. There was lots of great talk in some groups. A couple of groups had a hard time focusing.
After about 20 minutes of practice, we resumed work on Pumpkin Time-Bomb. When I gave this activity I purposefully gave them the entire spreadsheet of data. I wanted them to be able sift, sort and think about what data was useful. It was a bit of a frustrating experience but clearly they need more practice making sense of large data sets. They also need way more practice with spreadsheets. I told them that they should copy the relevant data to a spreadsheet so that they could clean it up. A few students asked what a spreadsheet was. Eeeek!
They worked their way through the activity. Many students finished their analysis as the bell went, a couple stayed to finish after the bell and the rest will have to get it done on their own time.
Showing posts with label exponents. Show all posts
Showing posts with label exponents. Show all posts
Thursday, November 9, 2017
Monday, October 30, 2017
MPM1D1 - Day 37 Exponents & Equations of Lines
With Halloween approaching I thought today would be a good day to look at a candy corn estimate. As a side note, I'm not sure that Canadian teens are as fond of candy corn as American teens are. It seems that every year half of my class says that they hate this stuff. Perhaps a more formal study will be necessary.
My students had a three day weekend so I thought I should remind them of some of the exponent work we did last Thursday. We quickly recapped some of the rules and went through some of the challenging homework questions. We also spent some time talking about what it means to have a fraction raised to an exponent. The overwhelming majority of my students wanted to convert the fraction to a decimal then use their calculators. I pushed them to stay with the fractions and write the power as a multiplication statement. Most were able to do that, but again wanted to convert to a decimal and multiply. We got to the point where we had an answer as a fraction, but I think we need to work a little more with fractions so that students are as comfortable working with fractions as they are with decimals.
I also gave this problem:
I figured students would be able to come up with an answer but I asked them to also come up with an answer that involved using exponents. There were some great discussion, and arguments, around the room.
Next, we moved onto writing equations of lines. We've done this before, but there was always a context. I wanted to move away from the context to make this a little more abstract. The goal was to find the equation of a line given two points. We reviewed what the equation of a line looks like and how to find slope. Then we talked about how we could use a point, along with the slope, to find the y-intercept. We worked through an example and then I let them try it. Here's the handout we started with.They didn't have much time so we'll continue with this tomorrow.
My students had a three day weekend so I thought I should remind them of some of the exponent work we did last Thursday. We quickly recapped some of the rules and went through some of the challenging homework questions. We also spent some time talking about what it means to have a fraction raised to an exponent. The overwhelming majority of my students wanted to convert the fraction to a decimal then use their calculators. I pushed them to stay with the fractions and write the power as a multiplication statement. Most were able to do that, but again wanted to convert to a decimal and multiply. We got to the point where we had an answer as a fraction, but I think we need to work a little more with fractions so that students are as comfortable working with fractions as they are with decimals.
I also gave this problem:
I figured students would be able to come up with an answer but I asked them to also come up with an answer that involved using exponents. There were some great discussion, and arguments, around the room.
Next, we moved onto writing equations of lines. We've done this before, but there was always a context. I wanted to move away from the context to make this a little more abstract. The goal was to find the equation of a line given two points. We reviewed what the equation of a line looks like and how to find slope. Then we talked about how we could use a point, along with the slope, to find the y-intercept. We worked through an example and then I let them try it. Here's the handout we started with.They didn't have much time so we'll continue with this tomorrow.
Thursday, October 26, 2017
MPM1D1 - Day 36 Surface Area, Exponents & Compound Interest
We did the extensions to the Big Nickel today (interior angles, exterior angles, cost to resurface, etc.). This provided some great review on topics already covered to date. It was interesting to watch them struggle with surface area. Right away they jumped to their formula sheets and started looking at formulas for triangular prisms. The trouble was that many of them couldn't make sense of the variables on the page. Now to be fair we haven't done any work with surface area. I stopped the class and asked what surface area means. They knew exactly what it was. I asked them to show me which parts of the nickel we had to find the area of. They nailed it, so I set them to work to find the area of all the pieces. No formula required. I can't believe I thought we'd get the entire task done in a day.
Once we finished with the nickel it was time to head into exponents. I threw this question up on the board and asked them to come up with an answer individually.
It was great to see where everyone was starting from. One student said "This is easy! I just have to multiply 3 by 3 by 3..." and off he went. Others used the exponent button but got caught up on the order of operations. Many students found the value of the numerator, then found the value of the denominator, wrote both of them down then did the division. A handful of students were able to use the exponent laws to quickly realize that the entire expression was equal to 1. After getting all of the errors corrected a student who knew the rules wanted to share, so she told us how to do it. It was such any easy transition into what is often a boring list of rules.
As we discussed the rules one boy asked why we needed exponents. He understood that the rules were helpful in evaluating the expression above but wondered when in his life would he ever come across exponents. This sidetracked me as we discussed one of my favourite mathematical topics: compound interest.
I'm always surprised that students aren't aware that they are paid interest by their banks. In any case we talked about compound interest and how if you set aside money every month for the majority of your live you can become quite wealthy. When I was in high school my classes received these types of lessons from Bob Gunter. I had Bob as a teacher for four out of seven math courses. To me these lessons were the most memorable parts of any course. It was clearly something he was passionate about and he was able to share and spread that passion to his students. So Monday (tomorrow is a professional activity day) we'll look at some financial scenarios (at least a little bit).
I handed out some exponents practice and bid the class a happy and productive weekend.
Once we finished with the nickel it was time to head into exponents. I threw this question up on the board and asked them to come up with an answer individually.
It was great to see where everyone was starting from. One student said "This is easy! I just have to multiply 3 by 3 by 3..." and off he went. Others used the exponent button but got caught up on the order of operations. Many students found the value of the numerator, then found the value of the denominator, wrote both of them down then did the division. A handful of students were able to use the exponent laws to quickly realize that the entire expression was equal to 1. After getting all of the errors corrected a student who knew the rules wanted to share, so she told us how to do it. It was such any easy transition into what is often a boring list of rules.
As we discussed the rules one boy asked why we needed exponents. He understood that the rules were helpful in evaluating the expression above but wondered when in his life would he ever come across exponents. This sidetracked me as we discussed one of my favourite mathematical topics: compound interest.
I'm always surprised that students aren't aware that they are paid interest by their banks. In any case we talked about compound interest and how if you set aside money every month for the majority of your live you can become quite wealthy. When I was in high school my classes received these types of lessons from Bob Gunter. I had Bob as a teacher for four out of seven math courses. To me these lessons were the most memorable parts of any course. It was clearly something he was passionate about and he was able to share and spread that passion to his students. So Monday (tomorrow is a professional activity day) we'll look at some financial scenarios (at least a little bit).
I handed out some exponents practice and bid the class a happy and productive weekend.
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