Day 32

Estimation 180! They are totally into this now. I am aware that it is because they consider it fun, not work but they seem to be missing the fact that it is helping improve their number sense. We did day 9 - day 15 today, as some were very easy. Most of the class got day 10 perfect, a lot also got day 11 and day 12 perfect. Day 13 made us wonder who eats Cheese Balls (I have never seen them in Canada), but also allowed me to talk about using serving size to come up with Andrew's answer. Day 14 surprised me as I have taken a lot of strips of staples out over the years. Day 15 made no sense to me. If there are 24 strips of staples in a pack, each containing 210 staples, shouldn't there be 5040 staples in a box?

Then we continued with the spaghettini bridges handout. Some said they didn't know how to interpret their equations. When I asked them what the numbers meant they told me (correctly) so they seem to understand more than they realize. They did well answering the questions that followed, albeit slowly. Some needed help with the graphing calculators and many had trouble finding the number of spaghettini that would support a given number of pennies. There was an additional handout that provided them with data to analyze and some got through that too.

Tomorrow we move on.

## Monday 31 March 2014

## Friday 28 March 2014

### MFM2P - Day 31 Spaghettini Bridges

Day 31

We started with more Estimation 180 - days 5- 8. We talked a little about really high guesses and really low guesses as the range of guesses was large for day 7. I think it is amazing how close they are getting to the correct answer though. Lots of correct answers for day 5, one correct for day 6, one off by 5 for day 7 and one correct for day 8. They seem to be enjoying this (because of the lollipops and that we "aren't doing math" - huh?).

Next we went through the questions on the back of the Spaghetti Bridges handout. Making sense of the equation and working with some algebra.

Then they made spaghettini bridges - working in groups of four but collecting data in pairs to speed up the process. There was much spaghettini on the floor so the broom I bought for my classroom came in handy again. As this was the second round of this activity, they worked well, got good data, were able to create their scatter plots and come up with equations for the line of best fit much more independently. A good way to end the week.

We started with more Estimation 180 - days 5- 8. We talked a little about really high guesses and really low guesses as the range of guesses was large for day 7. I think it is amazing how close they are getting to the correct answer though. Lots of correct answers for day 5, one correct for day 6, one off by 5 for day 7 and one correct for day 8. They seem to be enjoying this (because of the lollipops and that we "aren't doing math" - huh?).

Next we went through the questions on the back of the Spaghetti Bridges handout. Making sense of the equation and working with some algebra.

Then they made spaghettini bridges - working in groups of four but collecting data in pairs to speed up the process. There was much spaghettini on the floor so the broom I bought for my classroom came in handy again. As this was the second round of this activity, they worked well, got good data, were able to create their scatter plots and come up with equations for the line of best fit much more independently. A good way to end the week.

## Wednesday 26 March 2014

### MFM2P - Day 30

Day 30

Tomorrow, all the grade 10s will be taking the Literacy Test. Today, we did a "dry run" to make sure they the students knew which room to go to and they got to listen to a script and ask questions about logistics. This was all happening at 10:20 so trying to keep my students focused on math from 9:30 until 10:20 was quite a challenge.

We started the class with some Estimation 180. We had done Day 1 a while back so we looked at Mr. Stadel's height again before continuing with Day 2 where we have to estimate Mrs. Stadel's height given that she is standing next to Andrew. This time all of my students came up with a guess, and they were all reasonable guesses. One even got it right and earned a lollipop! We worked through converting the height from feet and inches to centimeters. Then we did Day 3 which is estimating Mr. Stadel's son's height. The guesses were okay, although some were really small, but one was perfect (another lollipop). I asked if they wanted to do another one and they did (I think the lollipops may have been a factor) so we looked at Day 4 Mr. Stadel and the Lampost:

If my students didn't already think I was nuts (about math) then they do now. I told them how great this picture was and that we would be using it as practice for similar triangles. They didn't seem to share my enthusiasm... hmmmm... Anyway, we did our estimation and two students got within 1 inch of the correct answer so they both got lollipops. I will be continuing with Estimation 180. (Someone yell at me if I don't blog that I've done more!)

They worked on the spaghetti bridge handout from yesterday and all got equations (linear regression) but most had a hard time interpreting those equations. We took it up and this is what it looked like:

Some may have started the questions on the back of the sheet, but not many. It was like someone kept yelling "Squirrel!" today!

At 10:20 I headed out to Portable 2 with some of my students (and some from other classes) only to find that they were putting down a new floor in portable 2 and we could not go in. So we stood outside in the cold (it was very cold this morning) while I took attendance and then we went back into the school building as a group. I explained the procedure for tomorrow to them (in the hallway) and read them the script. So tomorrow they will be reading and writing and I will be supervising so there will be no blog post. I would definitely rather be teaching!

Tomorrow, all the grade 10s will be taking the Literacy Test. Today, we did a "dry run" to make sure they the students knew which room to go to and they got to listen to a script and ask questions about logistics. This was all happening at 10:20 so trying to keep my students focused on math from 9:30 until 10:20 was quite a challenge.

We started the class with some Estimation 180. We had done Day 1 a while back so we looked at Mr. Stadel's height again before continuing with Day 2 where we have to estimate Mrs. Stadel's height given that she is standing next to Andrew. This time all of my students came up with a guess, and they were all reasonable guesses. One even got it right and earned a lollipop! We worked through converting the height from feet and inches to centimeters. Then we did Day 3 which is estimating Mr. Stadel's son's height. The guesses were okay, although some were really small, but one was perfect (another lollipop). I asked if they wanted to do another one and they did (I think the lollipops may have been a factor) so we looked at Day 4 Mr. Stadel and the Lampost:

If my students didn't already think I was nuts (about math) then they do now. I told them how great this picture was and that we would be using it as practice for similar triangles. They didn't seem to share my enthusiasm... hmmmm... Anyway, we did our estimation and two students got within 1 inch of the correct answer so they both got lollipops. I will be continuing with Estimation 180. (Someone yell at me if I don't blog that I've done more!)

They worked on the spaghetti bridge handout from yesterday and all got equations (linear regression) but most had a hard time interpreting those equations. We took it up and this is what it looked like:

Some may have started the questions on the back of the sheet, but not many. It was like someone kept yelling "Squirrel!" today!

At 10:20 I headed out to Portable 2 with some of my students (and some from other classes) only to find that they were putting down a new floor in portable 2 and we could not go in. So we stood outside in the cold (it was very cold this morning) while I took attendance and then we went back into the school building as a group. I explained the procedure for tomorrow to them (in the hallway) and read them the script. So tomorrow they will be reading and writing and I will be supervising so there will be no blog post. I would definitely rather be teaching!

## Tuesday 25 March 2014

### MFM2P - Days 26, 27, 28

I got a little behind with my blogging...

Day 26

Test day! They did a great job. It was fantastic to see some of them using the manipulatives (pattern blocks & pennies) during the test. They worked really well - I think knowing that they could have more time the following day took away a lot of anxiety. I had told them that the number one rule was that they were not allowed to leave any question blank and they followed it well. Some needed prompting to get going with a question or two. I wrote in pink pen what prompts I provided and took that into account when I marked the tests.

I got to meet some of my students' parents that afternoon/evening which is always interesting. Nice kids, nice parents, what can I say?

Day 27

Test day, part 2 for them and PD for me. I spent the day with @AlexOverwijk and Sherri Walker planning for the next couple of months of this course. It was a great day for me as we got a lot accomplished.

My students finished up their tests (or started if they were absent the previous day) and then worked on solving systems by graphing equations in

Day 28

This was a crazy day as I had some finishing up their test, some who needed to work on a question from the test as I deemed that they had not done enough, and the rest continuing to work on solving systems by graphing. It was a zoo. I had thought I would do an Estimation 180 question with them but didn't. At times I feel like I am letting myself (and my students down) when I don't follow through with these plans. Sigh...

Day 26

Test day! They did a great job. It was fantastic to see some of them using the manipulatives (pattern blocks & pennies) during the test. They worked really well - I think knowing that they could have more time the following day took away a lot of anxiety. I had told them that the number one rule was that they were not allowed to leave any question blank and they followed it well. Some needed prompting to get going with a question or two. I wrote in pink pen what prompts I provided and took that into account when I marked the tests.

I got to meet some of my students' parents that afternoon/evening which is always interesting. Nice kids, nice parents, what can I say?

Day 27

Test day, part 2 for them and PD for me. I spent the day with @AlexOverwijk and Sherri Walker planning for the next couple of months of this course. It was a great day for me as we got a lot accomplished.

My students finished up their tests (or started if they were absent the previous day) and then worked on solving systems by graphing equations in

*y*= m*x*+ b form.Day 28

This was a crazy day as I had some finishing up their test, some who needed to work on a question from the test as I deemed that they had not done enough, and the rest continuing to work on solving systems by graphing. It was a zoo. I had thought I would do an Estimation 180 question with them but didn't. At times I feel like I am letting myself (and my students down) when I don't follow through with these plans. Sigh...

### MFM2P - Day 29 Spaghetti Bridges

Day 29

Cycle 1 testing was done so we all moved on to something more fun: spaghetti bridges! I punched two holes in little cups and took out a bag of spaghetti (I have a closet at the back of my room that has all my supplies for all my activities) and my tin of pennies.

Each group of students created a bridge by threading one strand of spaghetti through the holes. One student held the ends of the spaghetti while another gently placed pennies in the cup until the spaghetti broke.

The students were surprised how many pennies it took to break the spaghetti! Once it did, they repeated the experiment with 2 strands of spaghetti, then 3, and so on. The data collection took quite a while. I was so impressed when I heard a group say "We should redo with 3 'cause that number was higher than 4." The data is not perfectly linear by any means, but it was generally increasing.

Next, they had to create a scatter plot by hand, then enter the data in the graphing calculator and perform a linear regression to get the equation of the line of best fit.

We will continue with this tomorrow - there are questions for them to answer before we start over with spaghettinni!

Cycle 1 testing was done so we all moved on to something more fun: spaghetti bridges! I punched two holes in little cups and took out a bag of spaghetti (I have a closet at the back of my room that has all my supplies for all my activities) and my tin of pennies.

Each group of students created a bridge by threading one strand of spaghetti through the holes. One student held the ends of the spaghetti while another gently placed pennies in the cup until the spaghetti broke.

The students were surprised how many pennies it took to break the spaghetti! Once it did, they repeated the experiment with 2 strands of spaghetti, then 3, and so on. The data collection took quite a while. I was so impressed when I heard a group say "We should redo with 3 'cause that number was higher than 4." The data is not perfectly linear by any means, but it was generally increasing.

Next, they had to create a scatter plot by hand, then enter the data in the graphing calculator and perform a linear regression to get the equation of the line of best fit.

We will continue with this tomorrow - there are questions for them to answer before we start over with spaghettinni!

## Wednesday 19 March 2014

### MFM2P - Day 25

Day 25

Today was the second day of review for tomorrow's test. They worked really well. They practiced using graphing calculators to perform quadratic regressions (it would be awesome if the 5E-13x term didn't show up), some used manipulatives to solve systems and they all did a good job interpreting quadratic graphs. They should be well prepared for tomorrow.

Today was the second day of review for tomorrow's test. They worked really well. They practiced using graphing calculators to perform quadratic regressions (it would be awesome if the 5E-13x term didn't show up), some used manipulatives to solve systems and they all did a good job interpreting quadratic graphs. They should be well prepared for tomorrow.

## Tuesday 18 March 2014

### MFM2P - Day 24

Day 24

I had planned on continuing solving systems of linear equations today - I wanted them to do one problem in their comp book and to create one of their own, also in their comp book, then work on some more challenging questions. But Thursday's first big test is looming and worrying me, so I changed plans this morning and created a review package for them during my prep period. It is very similar to the test but I felt this was needed as they haven't seen some of these topics since early February. My intent is to lessen their anxiety levels and to help them feel confident going into Thursday's test. So today they worked on the review questions, getting stuck on trig, having to look in their comp books to remember how to find missing lengths in similar triangles and generally helping each other out. It went well. They, for the most past, knew more than I thought they would and they all know what they struggled with. Tomorrow we will continue this process, including going over how to use graphing calculators to find the equation of a quadratic relation. I think they will be ready for Thursday. I'll let you know how it goes!

I had planned on continuing solving systems of linear equations today - I wanted them to do one problem in their comp book and to create one of their own, also in their comp book, then work on some more challenging questions. But Thursday's first big test is looming and worrying me, so I changed plans this morning and created a review package for them during my prep period. It is very similar to the test but I felt this was needed as they haven't seen some of these topics since early February. My intent is to lessen their anxiety levels and to help them feel confident going into Thursday's test. So today they worked on the review questions, getting stuck on trig, having to look in their comp books to remember how to find missing lengths in similar triangles and generally helping each other out. It went well. They, for the most past, knew more than I thought they would and they all know what they struggled with. Tomorrow we will continue this process, including going over how to use graphing calculators to find the equation of a quadratic relation. I think they will be ready for Thursday. I'll let you know how it goes!

## Monday 17 March 2014

### MFM2P - Day 23

Day 23

After a week off it was back to class at 8 am. Sadly, there was little to no heat in the building so I had my coat on for much of the morning. It was only -26 degrees outside - who would need heat?!? There were actually icicles in the girls' washroom! Thankfully, my classroom warmed up as the morning progressed even if the math/English office is still like an ice hut.

Today we started solving systems of linear equations. Only without any equations. Here is the first problem they worked on:

By the way, these are Smarties. Those things Americans call Smarties are called Rockets here.

My students used patterns to represent the Smarties and jujubes and they used square tiles to represent the pennies (we no longer use pennies in Canada). I will definitely source out some pennies as I think they will help students better understand.

I hoped they would jump right in and start modelling the problem with the manipulatives, but they built things and made pretty patterns and didn't really know where to start.

I circulated and got each group going. Here are some examples of their work:

I also encouraged those in the group who were not working with the manipulatives to work through each problem on paper. Here is one example:

It was interesting to me that the student doing this was trying to move pennies from one side onto the other side, which is why I added circles (okay, so they are not really circles) to the solution. It made it clear to the student that the pennies have to stay within the circle.

I think I would have them work in pairs next time. Some were not as engaged as I would have liked, but overall I think it was a good introduction to solving systems. More tomorrow!

After a week off it was back to class at 8 am. Sadly, there was little to no heat in the building so I had my coat on for much of the morning. It was only -26 degrees outside - who would need heat?!? There were actually icicles in the girls' washroom! Thankfully, my classroom warmed up as the morning progressed even if the math/English office is still like an ice hut.

Today we started solving systems of linear equations. Only without any equations. Here is the first problem they worked on:

By the way, these are Smarties. Those things Americans call Smarties are called Rockets here.

My students used patterns to represent the Smarties and jujubes and they used square tiles to represent the pennies (we no longer use pennies in Canada). I will definitely source out some pennies as I think they will help students better understand.

I hoped they would jump right in and start modelling the problem with the manipulatives, but they built things and made pretty patterns and didn't really know where to start.

I circulated and got each group going. Here are some examples of their work:

It was interesting to me that the student doing this was trying to move pennies from one side onto the other side, which is why I added circles (okay, so they are not really circles) to the solution. It made it clear to the student that the pennies have to stay within the circle.

I think I would have them work in pairs next time. Some were not as engaged as I would have liked, but overall I think it was a good introduction to solving systems. More tomorrow!

## Tuesday 4 March 2014

### MFM2P - Day 20, 21, 22

Day 20

We started today by finishing up yesterday's question: how many boxes of Post-it notes would we have to buy to cover the classroom walls? Many students had not gotten past the point of writing down the dimensions (some hadn't even done that - sigh) so we started there. I circulated and helped them get going by walking them through how to find the area of one wall. They had to choose which units to work in - some chose inches, one chose metres, but most worked in centimetres. They made errors along the way, had trouble figuring out what to do about the cabinet at the back of the room, but eventually did some reasonable calculations. I found that holding a piece of paper to represent the wall and a calculator to represent the cabinet helped them see that only the height and width of the cabinet were important for our calculations and that the depth was not relevant. By the time one student got all the way to the answer of 10 boxes (yay!), they were all far enough along that we could take it up. Here is some of that (we did the other 3 walls too):

Phew! That took way longer than anticipated. Next we needed to figure out if those 10 boxes of Post-it notes would fit in the cardboard box with the given dimensions (the box from Amazon I had at home!).

We discussed the fact that we were not talking about area anymore, but volume. They needed the thickness of 1 Post-it note pad, which we approximated as 1 cm. We had already converted the 3" by 3" to cm, so we were ready to calculate the volume:

They then calculated the volume of the given box.

I hope you all are impressed with my amazing artistic talent!

With only 10-ish minutes left, we launched into the next question.

What I wrote was true. Of course when I went to our local store this morning to buy 473 ml containers of chocolate milk, they had 500 ml containers. Argh! Thankfully my colleague, Julia, spotted students in her morning class drinking from 473 ml container (which they must sell in the cafeteria) and grabbed them for me once they were empty. Yay, Julia! So in class we got as far as calculating the height for the 500 ml container. To do this they needed to measure the containers that I had bought - 1 for each group, after which they were allowed to share the chocolate milk : )

This class leaves me both exhausted and exhilarated on a daily basis. I really like them and it is so great to see them gaining confidence and starting to persevere with problem solving.

Day 21 & 22

I will be away so here is the plan. Finish this work... height for 473 ml container then these 2 tasks:

After that they will cut out and glue 4 examples in their comp books; one for each of surface area and volume of rectangular prisms and cylinders.

Next they have a worksheet of word problems that will hopefully help consolidate what we have been working on this week.

Then it's March break, so I will get a break from blogging. I will be back on March 17th! Thanks for reading.

## Monday 3 March 2014

### MFM2P - Day 19 Filing Cabinet

Day 19

Today was File Cabinet day! That is Andrew Stadel's (@mr_stadel) fantastic File Cabinet 3-act - his blog post with links to the videos is here.

This is the first time this year that these grade 10 applied students have done any surface area/volume calculations.

Here is the set up:

In the video we see Andrew placing numbered Post-it notes on the filing cabinet - 12 for the first row, and up to 24 for the second row, then the video stops. So, how many to cover the filing cabinet? I asked them what they needed to know to answer this.

Student: "The dimensions of the filing cabinet."

Me: "Great. What else?"

Another student: "The size of the sticky note."

Me: "Okay - anything else?"

They thought they were good to go so I gave them the handout. Their first job was to estimate how many Post-it notes it would take. The guesses ranged from 200 to 6000! As I circulated and talked to them about their estimates and what the first step in calculating the number of Post-it notes would be, many asked an additional question: "Is he covering all the sides?" or "Is he covering the top?" or "Is he covering the bottom?". Many also revised their guesses based on my answer. Good. I found it really helpful to take a box in which I store pencils around the room with me for these discussions.

Many students said that they didn't have enough information to calculate the area of the top of the filing cabinet. It became clear to them that they could when we looked at the length, width and height of the box. They did great work. Some groups had several different answers so I got them to compare and figure out which was correct. Every group did this and chose the right answer and made corrections to errors in the other solutions. (Yay!) Every group agreed on the same answer so we played the Act 3 video and, well, I don't want to ruin it for you, so go ahead and calculate it yourself and see how you do : )

I was surprised that they did not have any trouble understanding that they needed to divide the total surface area by the area of one Post-it note. That was intuitive to them.

Next, we extended:

There were questions.

"All the walls? What about the windows?"

"Do we cover the blackboards?"

"What about the cabinet at the back?"

I suggested that the problem would be simpler if we did cover everything (hypothetically - we are not crazy like Andrew Stadel!), but that we should take into account the weird jogs in the walls and the cabinet at the back.

Some students were reluctant to get up and start measuring, but with a little encouragement, we got all the walls measured. They were not interested in agreeing on units so some used imperial and others metric.

They were busy calculating the surface area of the walls when the bell rang. To be continued tomorrow...

Today was File Cabinet day! That is Andrew Stadel's (@mr_stadel) fantastic File Cabinet 3-act - his blog post with links to the videos is here.

This is the first time this year that these grade 10 applied students have done any surface area/volume calculations.

Here is the set up:

In the video we see Andrew placing numbered Post-it notes on the filing cabinet - 12 for the first row, and up to 24 for the second row, then the video stops. So, how many to cover the filing cabinet? I asked them what they needed to know to answer this.

Student: "The dimensions of the filing cabinet."

Me: "Great. What else?"

Another student: "The size of the sticky note."

Me: "Okay - anything else?"

They thought they were good to go so I gave them the handout. Their first job was to estimate how many Post-it notes it would take. The guesses ranged from 200 to 6000! As I circulated and talked to them about their estimates and what the first step in calculating the number of Post-it notes would be, many asked an additional question: "Is he covering all the sides?" or "Is he covering the top?" or "Is he covering the bottom?". Many also revised their guesses based on my answer. Good. I found it really helpful to take a box in which I store pencils around the room with me for these discussions.

Many students said that they didn't have enough information to calculate the area of the top of the filing cabinet. It became clear to them that they could when we looked at the length, width and height of the box. They did great work. Some groups had several different answers so I got them to compare and figure out which was correct. Every group did this and chose the right answer and made corrections to errors in the other solutions. (Yay!) Every group agreed on the same answer so we played the Act 3 video and, well, I don't want to ruin it for you, so go ahead and calculate it yourself and see how you do : )

I was surprised that they did not have any trouble understanding that they needed to divide the total surface area by the area of one Post-it note. That was intuitive to them.

Next, we extended:

There were questions.

"All the walls? What about the windows?"

"Do we cover the blackboards?"

"What about the cabinet at the back?"

I suggested that the problem would be simpler if we did cover everything (hypothetically - we are not crazy like Andrew Stadel!), but that we should take into account the weird jogs in the walls and the cabinet at the back.

Some students were reluctant to get up and start measuring, but with a little encouragement, we got all the walls measured. They were not interested in agreeing on units so some used imperial and others metric.

They were busy calculating the surface area of the walls when the bell rang. To be continued tomorrow...

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