Day 60
I started today with another multiplying two binomials question. Some have become very proficient at these, others are still working through the process. I do believe that the repeated practice is helping.
We worked on trig for the rest of the period. Some students seem to like being able to use calculators instead of the trig tables, but they do have the option of using either. I have noticed a real improvement in stating which sides are opposite, adjacent and hypotenuse. Having worked the ratios before, they had no issues choosing the correct trig ratio which was awesome! It was a fairly quiet period where I circulated and helped out where needed and gave stickers along the way. They like stickers : )
For the last 5 minutes we did the Estimation 180 bacon challenges. A little bit of fun at the end of rather dry period. And now I just remembered that I forgot to do Acts II and III of the Boat on the River. Tomorrow, maybe?
Tuesday, 13 May 2014
Monday, 12 May 2014
Day 59
Day 59
I returned from OAME to find lots of fantastic posters hung in my class, and a few less than fantastic ones. I haven't had time to really look at them yet or address those that need more work, but will soon and will post some pictures too.
Today's plan was to do the Penny Circle activity with Desmos. I had booked the COWs (Computers on Wheels) and a minute or so before the end of the first period of the day I checked the booking system to see which teacher had the COWs first period. And that's when I realized that I was an idiot and had booked them for the wrong period. A mad rush to figure out what to do with my class ensued, including me printing a lot things the wrong way and looking somewhat like I might have lost my mind.
I handed out another mutiplying binomials practice question which they seemed to be doing well now, although I was scrambling to get organized so I didn't do a good job of checking who was struggling today. Next, we moved back to trigonometry and they glued a number of sheets in their comp books. I showed Act I of "Boat on the River" and they came up with some good questions. We talked about the owner of the boat needing to know the angle at which the boat needed to lean in order to safely pass under the bridge as taking down the mast would involve a crane and a lot of money. Then I introduced them to "sine", "cosine" and "tangent" which was really just putting a name to the ratios they have been working with all semester. My version (which I'm sure I stole from someone else) of SOH-CAH-TOA looks like this:
I find that this ties into the ratios a little better.
Getting them to quiet down and get to work was rather like herding cats this morning but we got through the basics. More tomorrow, including Acts II and III.
I returned from OAME to find lots of fantastic posters hung in my class, and a few less than fantastic ones. I haven't had time to really look at them yet or address those that need more work, but will soon and will post some pictures too.
Today's plan was to do the Penny Circle activity with Desmos. I had booked the COWs (Computers on Wheels) and a minute or so before the end of the first period of the day I checked the booking system to see which teacher had the COWs first period. And that's when I realized that I was an idiot and had booked them for the wrong period. A mad rush to figure out what to do with my class ensued, including me printing a lot things the wrong way and looking somewhat like I might have lost my mind.
I handed out another mutiplying binomials practice question which they seemed to be doing well now, although I was scrambling to get organized so I didn't do a good job of checking who was struggling today. Next, we moved back to trigonometry and they glued a number of sheets in their comp books. I showed Act I of "Boat on the River" and they came up with some good questions. We talked about the owner of the boat needing to know the angle at which the boat needed to lean in order to safely pass under the bridge as taking down the mast would involve a crane and a lot of money. Then I introduced them to "sine", "cosine" and "tangent" which was really just putting a name to the ratios they have been working with all semester. My version (which I'm sure I stole from someone else) of SOH-CAH-TOA looks like this:
I find that this ties into the ratios a little better.
Getting them to quiet down and get to work was rather like herding cats this morning but we got through the basics. More tomorrow, including Acts II and III.
Sunday, 11 May 2014
Mother's Day
My mum has always been an incredible person. She was always there for me when I needed her when I was little. She sat with me through my tears when I wouldn't say what was wrong and gave hugs and support when she finally got it out of me. My mother has always been the kindest person. She is giving of herself and her time. She is a physiotherapist and truly cares for the whole person, not just the injured part of them. Her patients have always loved her.
My mum did not grow up in an ideal situation, but made the most of her life in many respects. But she changed. She did the bravest thing and left my father many years ago now. And it was like she became a new person. This was hard for me as she was no longer the person I had known my whole life. I understood that she was becoming her true self, but it was odd and difficult to feel somewhat like a stranger to her. I have gotten to know her again over time. She lost herself anew in 2005 when she fell and hit her head resulting in a traumatic brain injury. Noah, who was then a baby in my arms, is the only one who saw it happen. Although some memory issues still plague her, she was not about to let any of that keep her down. She continues to work and travel and helps out with my crew often.
Many, many people have said to me that they don't know how I do it. "It" being working full time while raising four little people and two dogs and doing a bunch of other mathy stuff on the side. My standard reply is "I just do." Growing up, my mum always worked and took care of us and the house and was on committees and ... This was my normal. I think I always want to be better at what I do, that I want to do more, because I had such a good role model.
My mum and I do not always agree and definitely have different views on some subjects, but we are connected at our cores. In many ways, I believe she is my biggest fan. And I am hers. All of the goodness in me comes from her. All of it. And as a mother myself, I strive (not always successfully) to be as kind and supportive to my children as she was to my brother and me. I feel very fortunate to have her in my life and that my kids have the most amazing Granny.
Mum - we all love you, but me, most of all. Thank you for everything.
My mum did not grow up in an ideal situation, but made the most of her life in many respects. But she changed. She did the bravest thing and left my father many years ago now. And it was like she became a new person. This was hard for me as she was no longer the person I had known my whole life. I understood that she was becoming her true self, but it was odd and difficult to feel somewhat like a stranger to her. I have gotten to know her again over time. She lost herself anew in 2005 when she fell and hit her head resulting in a traumatic brain injury. Noah, who was then a baby in my arms, is the only one who saw it happen. Although some memory issues still plague her, she was not about to let any of that keep her down. She continues to work and travel and helps out with my crew often.
Many, many people have said to me that they don't know how I do it. "It" being working full time while raising four little people and two dogs and doing a bunch of other mathy stuff on the side. My standard reply is "I just do." Growing up, my mum always worked and took care of us and the house and was on committees and ... This was my normal. I think I always want to be better at what I do, that I want to do more, because I had such a good role model.
My mum and I do not always agree and definitely have different views on some subjects, but we are connected at our cores. In many ways, I believe she is my biggest fan. And I am hers. All of the goodness in me comes from her. All of it. And as a mother myself, I strive (not always successfully) to be as kind and supportive to my children as she was to my brother and me. I feel very fortunate to have her in my life and that my kids have the most amazing Granny.
Mum - we all love you, but me, most of all. Thank you for everything.
Wednesday, 7 May 2014
Days 56, 57 & 58
Day 56
Daily repeated practice of multiplying polynomials seems to be paying off. They will take a break for a couple of days as I will be away. It will be interesting to see how they fare on Monday.
We then went back to our systems of equations. Following up from yesterday, we did this question:
It didn't take long for a student to say that we needed one of the quantities to be the same so we could double the first order. Then they reasoned through finding the price of one latte and the price of one cookie.
]
Here is the next example:
And our solution:
I love how well they can reason through these problems. I cannot believe that I have been teaching for as long as I have without teaching "solving by elimination" this way. Live and learn... Thank you again to Sheri Walker for these brilliant examples.
We then went back to yesterday's question and replaced the words with variables so that they saw how to solve it algebraically by elimination. Some were ready for that, some wanted no part of it. I told them that they need to be able to solve these systems, whether that is with words, pictures or algebra.
For the last 15 minutes, we watched Andrew Stadel's basketball 3-act and they attempted to solve it. Without much success. But we will work on that some more next week.
Days 57 & 58
I will be at the OAME (Ontario Association for Mathematics Education) annual conference in Toronto. My students will be working in randomly chosen pairs on a poster project involving sums of squares (Pythagorean theorem), similar triangles and trigonometry. I expect great things when I return on Monday!
Daily repeated practice of multiplying polynomials seems to be paying off. They will take a break for a couple of days as I will be away. It will be interesting to see how they fare on Monday.
We then went back to our systems of equations. Following up from yesterday, we did this question:
It didn't take long for a student to say that we needed one of the quantities to be the same so we could double the first order. Then they reasoned through finding the price of one latte and the price of one cookie.
]Here is the next example:
And our solution:
We then went back to yesterday's question and replaced the words with variables so that they saw how to solve it algebraically by elimination. Some were ready for that, some wanted no part of it. I told them that they need to be able to solve these systems, whether that is with words, pictures or algebra.
For the last 15 minutes, we watched Andrew Stadel's basketball 3-act and they attempted to solve it. Without much success. But we will work on that some more next week.
Days 57 & 58
I will be at the OAME (Ontario Association for Mathematics Education) annual conference in Toronto. My students will be working in randomly chosen pairs on a poster project involving sums of squares (Pythagorean theorem), similar triangles and trigonometry. I expect great things when I return on Monday!
Tuesday, 6 May 2014
MFM2P - Days 54 & 55
Day 54
We started the class with another exercise in multiplying two binomials. I think the daily practice is helping them improve/solidify their understanding of how to do this. They miss doing Estimation 180 questions though...
Back to Barbie Bungee. Lots of good talk around how to find the distance bungeed when given the height and how to find the height given the number of elastics. Their equations were in terms of x and y so they needed to make the correct associations with their graphs. And do some algebra. There was also some unit conversion going on - most had taken their measurements in cm so they had to convert 4 m into cm to use their equation, but some groups had used inches when they collected data so they had a little more conversion work to do. Overall, it went well but it surprised me how long it took.
Day 55
Another exercise in multiplying two binomials. Most did it perfectly which meant that I could work with the few students who were still struggling.
Next, the Barbie Bungee challenge was on! I stuck with doing it in our classroom as there is really nowhere with a big drop at my school. I stood on a desk and showed them how I would be dropping the Barbies and told them to figure out the height. Thankfully, one student took that task on and wrote 2.94 m on the board (yay! they need to convert again). I gave them 5 minutes to figure out how many elastics they would need to and to get Barbie ready. It took closer to 10 (are slip knots really that difficult?!?) and then we began. The first Barbie jumped and hit her head hard. Boo! The second Barbie jumped and also hit her head hard. Oh no! Barbie #3 hit again! Barbie #4 looked like she would also hit, but her hair just brushed the floor and she was safe. Nice. Barbie #5 was safe by a long way. Barbie #6 wasn't quite ready so Barbie #1 got a second turn with 3 fewer elastics and had a perfectly safe and thrilling time. Barbie #6 was safe also, by a fair margin. It was a lot of fun and the winning group got lollipops. Sadly no pictures as I was the one dropping the Barbies.
We moved on to systems of equations. I gave them another jujubes and Smarties question to solve having taken out the pattern blocks and pennies. See here for more on this. Some students needed the manipulatives, others remembered how to do it without. They all had access to their comp books if they couldn't remember how to solve these types of questions. They all got the correct solution and we moved on to this (created by the awesome Sheri Walker):
(FYI - Tim Horton's is referred to as Timmy's here - they sell coffee and doughnuts, among other things. But it ain't no Starbucks!)
Here is what their solutions looked like:
Lots of reasoning without requiring any algebra since the number of donuts was the same for both days. Things will get a little more complicated tomorrow. I already had one student ask if there was a "better" way of doing these questions. Hopefully that will lead nicely into solving a system by elimination.
We started the class with another exercise in multiplying two binomials. I think the daily practice is helping them improve/solidify their understanding of how to do this. They miss doing Estimation 180 questions though...
Back to Barbie Bungee. Lots of good talk around how to find the distance bungeed when given the height and how to find the height given the number of elastics. Their equations were in terms of x and y so they needed to make the correct associations with their graphs. And do some algebra. There was also some unit conversion going on - most had taken their measurements in cm so they had to convert 4 m into cm to use their equation, but some groups had used inches when they collected data so they had a little more conversion work to do. Overall, it went well but it surprised me how long it took.
Day 55
Another exercise in multiplying two binomials. Most did it perfectly which meant that I could work with the few students who were still struggling.
Next, the Barbie Bungee challenge was on! I stuck with doing it in our classroom as there is really nowhere with a big drop at my school. I stood on a desk and showed them how I would be dropping the Barbies and told them to figure out the height. Thankfully, one student took that task on and wrote 2.94 m on the board (yay! they need to convert again). I gave them 5 minutes to figure out how many elastics they would need to and to get Barbie ready. It took closer to 10 (are slip knots really that difficult?!?) and then we began. The first Barbie jumped and hit her head hard. Boo! The second Barbie jumped and also hit her head hard. Oh no! Barbie #3 hit again! Barbie #4 looked like she would also hit, but her hair just brushed the floor and she was safe. Nice. Barbie #5 was safe by a long way. Barbie #6 wasn't quite ready so Barbie #1 got a second turn with 3 fewer elastics and had a perfectly safe and thrilling time. Barbie #6 was safe also, by a fair margin. It was a lot of fun and the winning group got lollipops. Sadly no pictures as I was the one dropping the Barbies.
We moved on to systems of equations. I gave them another jujubes and Smarties question to solve having taken out the pattern blocks and pennies. See here for more on this. Some students needed the manipulatives, others remembered how to do it without. They all had access to their comp books if they couldn't remember how to solve these types of questions. They all got the correct solution and we moved on to this (created by the awesome Sheri Walker):
(FYI - Tim Horton's is referred to as Timmy's here - they sell coffee and doughnuts, among other things. But it ain't no Starbucks!)
Here is what their solutions looked like:
Lots of reasoning without requiring any algebra since the number of donuts was the same for both days. Things will get a little more complicated tomorrow. I already had one student ask if there was a "better" way of doing these questions. Hopefully that will lead nicely into solving a system by elimination.
Friday, 2 May 2014
MFM2P - Day 53
Day 53
We started today with a couple of examples of multiplying binomials for their comp books. There were still some issues but they are improving. We will continue to do an example each day next week at the beginning of class.
Then it was time for Barbie Bungee! I randomly created groups of 3 and each group got 1 Barbie and 7 elastics (note to US folks - that's what we call rubber bands up here). There were metre sticks and measuring tapes available.
They had to complete the following table in their groups.
Next they plotted the points on a grid then used a graphing calculator to perform a linear regression. Some continued on to state the slope and what it means and the y-intercept and what it means. Other groups only just managed to collect the data by the end of class (they will all keep working on Monday). There were elastics flying and much fun was had with the Barbies. It is great to see students enjoying math class.
We started today with a couple of examples of multiplying binomials for their comp books. There were still some issues but they are improving. We will continue to do an example each day next week at the beginning of class.
Then it was time for Barbie Bungee! I randomly created groups of 3 and each group got 1 Barbie and 7 elastics (note to US folks - that's what we call rubber bands up here). There were metre sticks and measuring tapes available.
They had to complete the following table in their groups.
Next they plotted the points on a grid then used a graphing calculator to perform a linear regression. Some continued on to state the slope and what it means and the y-intercept and what it means. Other groups only just managed to collect the data by the end of class (they will all keep working on Monday). There were elastics flying and much fun was had with the Barbies. It is great to see students enjoying math class.
Thursday, 1 May 2014
MFM2P - Day 52
Day 52
Well, yesterday was a bust. Apparently my students can only do math if I am there with them. Sigh. So we did a do-over of yesterday's work and by the end of class they were doing a pretty good job multiplying binomials. Interestingly, my students did not want to use algebra tiles. They liked using the area model boxes. I think I will start alternating between estimations, multiplying binomials and doing quadratics "describe/draw" activities at the beginning of class for a while. I am not sure whether to factor quadratics tomorrow or to wait on that and do Barbie Bungee (now that my Barbies are all "dressed"). We will see what tomorrow morning brings.
And since this is short, here is a picture of a protractor:
Well, yesterday was a bust. Apparently my students can only do math if I am there with them. Sigh. So we did a do-over of yesterday's work and by the end of class they were doing a pretty good job multiplying binomials. Interestingly, my students did not want to use algebra tiles. They liked using the area model boxes. I think I will start alternating between estimations, multiplying binomials and doing quadratics "describe/draw" activities at the beginning of class for a while. I am not sure whether to factor quadratics tomorrow or to wait on that and do Barbie Bungee (now that my Barbies are all "dressed"). We will see what tomorrow morning brings.
And since this is short, here is a picture of a protractor:
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