MPM1D1 - Day 18 Optimizing Area & Perimeter

For a warm-up today I had students, individually, do the following:

Once everyone had a figure I had them share with the rest of their group and discuss their thinking. Then I gave them another one to consider on their own. 

This one seemed to be a little more challenging for some. I did see lots of squares and a couple of circles. Students had a good sense that these fit the description but they had a hard time explaining why they thought it worked.

As we were finishing up, one of the students said "Next you're going to get us to draw a figure that has the same area and perimeter. Aren't you?". I actually hadn't considered that as an option, but since he brought it up, I thought it would be a great idea. Most students thought it was easy and they drew a square. I asked a few to show some dimensions so we could compare the perimeter and the area. Many of them just wrote down a length and a width at random. We discussed, as a class, the shapes and dimensions they chose. Their answers were mostly squares that were 1x1, 2x2, 3x3 and 4x4. I drew a 1x1 and asked about the area and perimeter. Students quickly began changing their minds. We realized that a 4x4 would work. I asked if there were any others. Some suggested multiples of 4, then did a calculation to see if it would work. One student suggested 40x40 only to realize that the area and perimeter differed by a factor of 10. One girl pointed out that the areas were getting bigger faster than the perimeters so there couldn't be any more squares that had equal areas and perimeters. Wow! This would have been a good time to pull out Desmos and graph the perimeter vs. side length and area vs. side length to compare the graphs. Unfortunately, I didn't.

Next, we moved onto using a certain number of toothpicks to create all possible rectangles, using all of the toothpicks (we used pieces of straws rather than toothpicks). I gave each group eight straws and I asked them to keep track of the length, width, perimeter and area of each rectangle.

 They repeated the process with twelve and sixteen straws. Then they were asked to look back at their tables to see what they noticed. They needed a push in the right direction but it didn't take too long before they were able to find what I was hoping for. Hopefully this portion gets easier for them as they do it more.

We moved onto minimizing perimeter given a certain area. I gave out linking cubes and asked them to do the same sort of thing using 9, 16 and 25 cubes. The instructions I gave can be found here.

Some groups finished and were ready for the homework a couple of minutes before the bell. Others got far enough that they could finish up at home. Here's a link to the homework I gave. I feel like I stole this from someone. If it was you let me know so I can give you credit.

MPM1D1 - Day 17 Finishing Up Staircase Activity

We started with a few proportions questions as a warm-up. I've noticed that many students are able to solve these questions but they lack structure in their presentation and in explaining their solutions.
I posted these problems on the board and had groups solving the problems at the boards.

I told them to focus on making sure their solution was easy to follow for someone who happened to stop by to read their work. Most students had no trouble doing the work so I had them work on their presentation a bit. We talked as a group about part/part relationships vs. part/whole relationships. We summarized ratios and proportions in their notes and they tried some examples on their own.

We revisited yesterday's work on Staircase and Steepness. Only two students completed the work I assigned for homework. One was able to find a ratio for the base divided by the height that worked. We talked about how the order that his method gave might seem backwards to what would be intuitive. The other student who found a solution went home and taught himself (with the help of the internet) how to use trigonometry to find and angle in a triangle given two sides. I was blown away.

Eventually we settled on the base over the height as a good measure of the steepness. We called it slope. I went back to the suggestion by a student yesterday to put the line on a grid. We looked at how to find the slope then the class worked on practicing solving proportions and calculating slopes.

MPM1D1 - Day 16 Introduction to Slope

We started the day with this Which One Doesn't Belong.

The conversations led to a review of some of the terminology that we've covered (quadrants, origin, axes, etc.). One student chose the lower left because it looked different. I asked what he meant. Eventually, he motioned with his hand indicating that it wasn't as steep. Another student helped him find the word steep. We talked about how the other three looked as though they were the same steepness. This led to some discussion about parallel lines and steepness.

My goal today was to introduce the idea of slope. I used Fawn Nguyen's Staircase and Steepness activity. I've used this activity before (with a grade nine applied class I believe) and I seem to remember it working out alright. Today, that was not the case. Students were able to do the first part just fine. They were even keen to measure things. Most opted for a protractor. Those that didn't weren't sure what to measure. After a while I asked how they could come up with a number for the steepness without using a protractor. I threw up Fawn's image so that we were all using the same terminology.

Some students measured the slant. I asked them whether adding a step would change the steepness? The answer was no. Would it change the measure of the slant? They went back to work. Other students wanted to find the base times height. We talked about that being the area and how we could increase or decrease the area by adding or subtracting steps but not change the steepness.

One student suggested putting the steps on a graph like we did for the warm-up. I was liking where this was headed but when I asked how he would determine which was steeper for those that were close he couldn't come up with anything. He was so close.

Many students were starting to pack it in feeling defeated (I wonder if the heat was getting to them). I stepped in and suggested that they look at a bunch of ratios to see if that would help. I told them to divvy up the ratios and complete a table with the ratios for each staircase. This was their homework.

At the end of class I handed back the assessment from yesterday. There were no overall marks on the page. I gave each question a level and students were looking at each question to see where they went wrong. I was hoping to go over a couple of troubling spots but ran out of time. Have I mentioned that it would be great if this class were fifteen minutes longer? We'll do it tomorrow.

MPM1D1 - Day 15 Desmos Intro & First Assessment

We started the class by revisiting Hula Hoop Relay. I had a set of Chromebooks and we made our way to Desmos. This would be our first use of Desmos. We had a few password hiccups and a couple of network issues but they were fairly easily sorted out.

I demonstrated how to create a table, adjust the scale and find the equation of the line of best fit. I used a group's set of data to demonstrate. As it turns out the slope and y-intercept had the same absolute value. What an unfortunate and potentially confusing coincidence. The potential was there to dive into expanding and factoring binomials, but it wouldn't serve the purpose for today's lesson so I let it go. We talked about how we could find how long it would take for 43 people to do the challenge. We discussed how we could use the graph to extrapolate and how we could use the equation. It was a nice link between the graph, the equation and what was really going on. We did it both ways and some students seemed surprised that everything matched up.

As a result of our Desmos introduction I felt as though some students would be able to do it on their own while many would need a little more practice. There will be plenty of opportunity for more practice.

We put the computers away and did the mid-cycle assessment (using the term mid very loosely). A couple of students seemed really worried about how they were going to do. I told them to do their best as it would give them a sense of what they needed to work on for the test at the end of the cycle. This is our first real assessment and I intend for it to be formative. I'm hoping it will provide students with some feedback on what they need to work on. It will also give me a chance to see if there is any particular topic that we need to revisit.

MPM1D1 - Days 13 & 14

I'm away for the next couple of days but here's the plan.

Day 13
Have students estimate the height of Mr. Stadel's son. They will guess a number that is too low, too high and an actual guess. They will see the answer and calculate their percent error.

Once they are done the estimation they will move on to Smart Car Smash. They will take up the fractions mastery test that we did  the day before then do another one. If they finish before the bell they will start reviewing for their first assessment next week.

Day 14
They will warm up with this Would You Rather Problem.

After the warm up they will review for next week's test.

MPM1D1 - Day 12 Hula Hoop Relay

We started with a number talk. I asked students find as many ways as possible to figure out 12 times 18 without a calculator. There was lots of good thinking and most students were able to come up with the answer. They seem hung up on the answer rather than the process. I'm more interested in the process. We saw a few different solutions and I showed a couple more. I need to work at getting students to not stop once they get the answer. I don't think anyone tried to find the answer more than one way.

It's been such a gorgeous week weather wise that it's been hard to work inside. When I saw this tweet from @MrHoggsClass I figured this would be a great excuse to get outside.

Hula hoop relay today in #MPM1D. How long would it take for 28 students? For the whole school? @scdsbmath pic.twitter.com/cv1OCWNoIh

— Mr. Hogg (@MrHoggsClass) September 15, 2017

Today was the day to try it. I had students work in groups of 5. I showed this video and gave them this handout and a hula hoop and we headed out to the front of the school. I had forgotten that when you mention to grade nine students that you're heading outside, they tend not to listen after that. As a result three quarters of them were missing either something to write with or the page to write on. I should have mentioned it more than once. Next time.

Eventually they collected and recorded how long it took their group to complete the relay and then the determined how long it would take for our class and the school to do the relay. Some of them asked if we were going to try it as a class. They were really excited. We will try it but not until everyone is finished. Once they were done that I wanted them to see how long it would take for 1 person, 2 people...5 people. They were to fill in the table then create a scatter plot.

I was hoping to head back to the classroom and show them how to get an equation for the line of best fit using Desmos, but we didn't get to it today. A number of students weren't going to finish in class. We'll have a look at it again later.

We headed back into the classroom to do a mastery test on fractions before the bell went.

MPM1D1 - Day 11 Fractions

We started with this visual pattern:

I asked them to find three rules for the pattern: the number of squares, the perimeter and the area. All groups were very quick to find the rate, most using a table and looking at the first differences even though we haven't talked about them yet. Most groups determined that they needed to multiply the rate by the step number but the answer was off so they adjusted, adding the appropriate amount. I love how much of this they're figuring out on their own.

For groups that finished early I asked them how things would change if we said that each square was 2 unit by 2 units. Their first reaction was that they just needed to double their previous answer. I asked them to prove it to me and they soon discovered that the area of the new pattern was actually four times the area of the original. Such great thinking by a great group of students.

The other day one of my students asked why the rule for dividing fractions worked. I was so happy to hear this. We didn't have time to get into that day so we had a look today.

I started with this visual, then moved into looking at dividing with a common denominator.

Clearly the picture above wasn't going to cut it so we split things up a little differently.

From here it was easy to see that the green would fit into the red once (the green rectangles would fit over 8 of the red) leaving one rectangle. So we would need 1 out the 8 green ones. The solution then was that the green fit into the red once plus an eighth. I think many students appreciated the visual nature of this approach. However, when I asked them to try it some of them just wanted to use 'the rule'. We talked a little about how you could do this without drawing a picture. You could find a common denominator then divide the numerators by each other and do the same for the denominators. I love this approach.

Next we talked about adding and subtracting fractions, again starting visually, then becoming more abstract. We were running out of time so I had to forgo doing a problem today. I gave them the last 8 minutes to practice operations with fractions.

One of the students asked today if we were going to be doing any textbook work this year. Since we don't have any books for this course my reply was no. He seemed happy, which seemed odd given that the homework I give is the kind of work you find in a textbook. The boy sitting beside him was the boy that approached me last week saying he wasn't sure what was going on. He said that he really liked all the group work, problem solving and working at the board.

It seems that my daily routine in this class, generally, consists of a warm up, a problem and some skill work. I really like the balance but it's tight to fit it all in everyday. It would be perfect if our classes were 20 minutes longer!

MPM1D1 - Day 10 Finishing Up The Giant Toonie

The warm-up for today was this Would You Rather problem:

I had students work in groups but at their desks rather than the whiteboards since their work from Friday was still up on the board. It was much harder to see what was going on when students were seated compared to what they would do at the board.

One student said he'd prefer the 40' pool because it was longer. He seemed happy to stop their so I asked if he could find out how much water in the pools. Some groups converted the feet to yards, others the yards to feet. One student wanted to use the formula for surface area but fortunately his group convinced him that he was calculating the wrong thing. All the groups had some good success with this problem.

We then went on to find out how many toonies would fit in the giant toonie. This problem had multiple steps to it and many students struggled with those steps. This reinforced the importance of being organized and methodical. All groups were able to find the volume of the actual coin, after asking for a formula. Determining the volume of the giant coin proved to be a challenge. They had a hard time figuring out that they needed to find the scale factor, then use the scale factor to find the thickness of  the giant toonie. There were a few unit conversion errors but all of the groups knew that they needed to divide the volume of the big coin by the volume of the little coin. Of course this assumes that the coin can be packed in (melted down?) without any space for air.

This was a fun problem to watch groups struggle through. They really had to think about what the problem was asking and come up with a plan. Some students were quite frustrated by it, but hopefully this process will get easier for them as we do it more often.

Once we were done we did a quick not on calculating area and perimeter and I gave them some questions to practice.

MPM1D1 - Day 9 Fractions and Measurement

I came across this problem last night so I thought I try it in class since we had been discussing fractions.

Some groups were quick to recognize that the fractions on both sides were equivalent, others performed the calculations and didn't really notice anything that was the same. I asked how they could compare the fractions. That was enough to get them to thing about reducing their answers. Some groups chose to scale the smaller numbers up. All the groups seemed to do just fine with the division, which was a bonus.

We moved on to Jon Orr's R2D2. Which didn't take long to solve. It was interesting to see that the half of the class on the west of the room did it one way (divide the width of the bulletin borad by the width of the sticky note to find how many would be needed, do the same for the width then multiply) and the groups on the east of the room all found the area of the board and the area of a sticky and divided them. Perhaps knowledge was moving around the room but not crossing the centre line.

Next up we were going to look Kyle Pearce's Big Nickel. I showed the video and asked how many of them had been to Sudbury and how many had seen the Big Nickel. I was surprised to see that only two of my students had seen the Nickel.  I then asked how many of them had been to Campbellford to see the Giant Toonie. It was about half the class so I decided to proceed with the toonie.

I showed a picture of the toonie. 

They asked some questions such as "How big is it?" and as a class we decided to find out how many real toonies would fit inside. I gave them the following information about the giant toonie and we headed to Wikipedia for details about the actual toonie.

I told them to assume that the giant toonie was built to scale and then set them loose. We haven't talked about measurement so I was keen to see where this would go. One group started by figuring how many toonies would fit across the diameter of the monument, another calculated the circumference of both. One group wanted to work on volume but couldn't remember how to find the volume of a cylinder so we talked about how to find the volume of a prism and I let them sort things out from there. We ran out of time so we'll have to pick up where we left off Monday.

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.

MPM1D1 - Day 7 Mastery Test, Variation & Slope

I've never done three Visual Patterns in one week, but they seemed to tie in nicely with what we were doing this week. A couple of days ago we did this one:

Then yesterday we did this one:

Today we did this one:

All groups found the equation and the number of squares in the forty-third step easily. I wanted to show this one because we talking about direct and partial variation. We talked about how many squares the 0th step would have. We discussed what the graphs of the three patterns would look like (number of squares vs. step number) and connected an initial value of 0 to direct variations. We also talked about what was the same in all four tables and all four graphs. Somebody mentioned that the values in all the tables were going up by the same amount. Almost all groups had created a column for the first differences, even though we've never talked about it. Somebody else realized that the graphs would be going up at the same angle. We took a few minutes to get some information about direct and partial variations along with some information about slope into their notes.

I was happy to get through this when I did. Today was picture day and shortly after I finished about half a dozen students had to leave and get their photos taken.

The rest of the class did a mastery test on integers. Our department uses mastery tests to get at key skills in a course. They are short ten mark quizzes that focus on very specific but important skills. The idea is that we write the mastery test in class. The teacher marks them then hands them back (usually the next day) and go over any trouble spots. We rewrite a similar mastery test which get marked again. After the second attempt students can rewrite as many times as they want (outside of class time) until they get a mark that they are happy with. In this way the assessment is formative until the student decides it should be summative.

We finished up the mastery test and I handed out a set of data and asked them to create a scatter plot. They had to choose which variables were dependent and independent, create a scale, draw a line of best fit and list the characteristics of the graph (discrete/continuous, partial/direct, positive/negative slope).

MPM1D1 - Day 6 More Cup Stacking

I modified the Visual Pattern we did yesterday slightly to see how quickly my students would be able to spot the differences and come up with a solution. Again I asked them to find the forty-third step and a rule/equation to find the number of squares in any step. Here's what we started with:

Most groups started by making a table of values. Those that didn't weren't really sure where to start and so I suggested a table. I was happy to see many groups showing the first differences (though we didn't call them that) in their tables.

 I asked what was the same and what was different compared to yesterday's pattern. It was great hear things like "The constant is different" or "It's going up by the same amount". We talked a little about how these showed up in the equations.

Next we moved onto more cup stacking. The goal for today was to change how we stacked the cups and how that changed the equation and graph. I asked how many cups would be needed (stacked inside one another) to reach R's height. All groups saw that the height of the stack was changing by the lip of the cup for each additional cup. A couple of groups struggled with the initial value. They thought it should be the height of a cup rather than the body of the cup. Every group did manage to come up with an equation but struggled to solve the 2-step equation needed to find the number of cups (not surprising since we have done much equation solving yet).

Once they were done finding the number of cups needed to get to R's height they went back to their seats and plotted Height vs. Number of Cups. We talked about how the graph was different from the one they made yesterday. This led to a need for some terminology (partial vs. direct variation) so we wrote a note about graphs. The note included dependent vs. independent variables, continuous vs. discrete data, lines of best fit and interpolation vs. extrapolation. I was hoping to get into partial and direct variation and slope but we ran out of time.

I gave some homework on plotting points on the Cartesian Plane and identifying whether variables were dependent or independent.

At the end of class I had a student come to me and tell me that he was feeling lost. He said he was able to follow what his group members were saying but he wasn't sure he'd be able to come up with the numbers on his own. He told me that he did well in math last year but wasn't feeling very confident. We chatted for a bit and he agreed to come in tomorrow at lunch so we can go over a few things. I'm curious to see if his issue is related to skill or confidence.

MPM1D1 - Day 5 Cup Stacking

We did our first visual pattern today. I started with this one:

I told them that the images represent the first three steps in a pattern then asked if they could find the number of squares in the forty third step. I also asked if they could they find a rule or equation to represent the number of squares in any step (the n^th step). Normally I ask for an equation and I think that is often intimidating at first. This time I focused on the rule, which we could then be turned into an equation. They worked at the problem in groups at board. They did a great job. We spent a bit of time talking about what makes an equation.

Then we moved on to Cup Stacking. I held up a styrofoam cup and asked what they noticed and what they wondered. There were some great observations but they were fairly quiet when I asked what they wondered. So I posed the question "How many cups would be needed to make a stack to my height?". This led to a discussion about how the cups were going to be stacked. Normally when I do this activity I tell the class that I want the cups stacked inside of one another. The class really wanted to stack the cups one on top of the other as shown below, so we started there. I figured we could do it both ways and discuss direct vs. partial variations.

Most groups came up with a solution pretty quickly. Once they finished I asked if they could come up with an equation that related the number of cups to the height of the stack. I had a few blank looks and reminded them of the visual pattern we did at the beginning of the class. That was enough to get them going.

We had a bit time left so they created graphs showing the height of a stack of cups vs. the number of cups. Tomorrow we'll see how stacking the cups inside one another compares.

MPM1D1 - Day 4 Order of Operations & Pythagorean Theorem

We had an assembly today so it was a shortened period. I had thought that it might be a good day to try a visual pattern but decided against it.

Instead we started with our first Which One Doesn't Belong. I decided to use the one below only because my students have seen cards a lot this week. They see them every day to determine where they sit and they saw them when we played integer solitaire. I was curious to see if any of them would make a connection back to the game about black being positive and red being negative. It turns out nobody did.

In our discussion yesterday about multiplying and dividing integers, order of operations came up. They all seemed to know the rules so I went over them fairly quickly but we did spend a bit of time talking about exponents. I gave them a few questions to try and then we took them up.

We also went over the Pythagorean Theorem. They knew how to find the length of the hypotenuse from yesterday's work so we worked through an example of finding one of the legs. I gave them some order of operations and Pythagorean Theorem questions for homework.

MPM1D1 - Day 3 Multiplying & Dividing Integer

For the warm up today I decided to get groups of three at the whiteboards explaining and justifying the rules for multiplying and dividing integers. They all knew the rules for multiplying integers but few could explain why they worked. I asked different groups what it means to multiply two positive numbers. They explained. I then asked what it means to multiply a positive by a negative and let them sort that out. Overall, groups did quite well until they got to a negative by a negative. One group described this as being the opposite of a positive times a negative. This would have been a good time to get into the distributive property but I didn't. I was worried about losing too many students. We'll come back to that idea later. We looked at the patterns in the left column on the board below, then the one on the right. It seemed to make sense to them and the idea of looking for patterns will come in handy later.

 We wrote a quick note about multiplying and dividing integers then got back to the work we started yesterday.

All groups were quick to start. Many groups were asking for details about the Pythagorean Theorem. I gave them enough to get started and let them work. Some made mistakes like forgetting to take the square root when finding the hypotenuse but realized that their answer didn't make sense. We talked about the step they missed. It didn't take long for every group to come up with an answer.

There were some great discussions, lots of reasoning and a sense of accomplishment at the end. We ran out of time for me to show the answer but most groups felt confident in their work. I'll show Act 3 tomorrow.

I gave them a page of multiplying and dividing integers as homework.

MPM1D1 - Day 2 Integer Solitaire & Corner to Corner

Today we started with Integer Solitaire. The idea is that students work in pairs (I know, it's not very solitary but it allows me to hear the thinking that's going on). As a pair they draw 18 cards from a deck of cards and try to use fourteen of them to fill in the grid below so that each equation is true. The black cards are positive and the red cards are negative.

Some groups struggled with getting starting but once they got going most were doing great. The nice thing about this activity is that there's a ton of trial and error, which means a ton of practice with adding and subtracting integers.

At one point I overheard "A negative and a negative make a positive." This seemed like a good time to discuss what adding a negative and subtracting a negative would mean. The student who made the comment realized his error as soon as I stopped the class but I thought others would benefit from the conversation so we continued on. Some groups were quicker than others so they got to play again.

After a bit of practice we moved on to Corner to Corner. We watched the video and I asked what they noticed and what they wondered. There was a good response for the noticing. Not so much for the wondering. We'll work on it.

When I start with problem solving I like to use a problem solving framework. I really like Robert Kaplinsky's layout so I handed it out and we started filling it in together.We'll do it together the first couple of times, then they can do it on their own and eventually, hopefully, they won't need the framework anymore.  Once they had all the information they needed  I put them into random groups of 3 and sent them to the board to work.

It was interesting to watch. We aren't working on any particular unit now so I saw some interesting approaches. Some groups calculated volume, others talked about finding surface area. I asked a few questions about whether volume or surface area would be helpful. I asked them to remind me what they were looking for then let them try to sort things out.

 Some groups recognized that there were right triangles involved and made reference to the Pythagorean Theorem. I heard "I don't remember the Py...whatever theorem."

We were quickly running out of time so I handed out a page with some homework questions for adding and subtracting integers and the bell went.

Tomorrow we'll get back in our groups and continue trying to find the length of the string.

MPM1D1 - Day 1

This year I decided to change things up for the first day. I decided to skip all the regular first day stuff and dive right into the math. We can do the first day stuff some other day (I guess that doesn't make it first day stuff anymore though). I wanted my grade nine students to be doing math and enjoying themselves rather than being bored of listening to me.

We started with some Estimation 180. I had students guess a number that was too low, another that was too high and, finally, an actual guess. I like starting with this because everyone can pick a number. It's very low risk. I was pleasantly surprised at the too low and too high guesses. Nobody gave number that were crazy low or high. I gave students time to come up with their guesses. I took a bunch and wrote them on the board, which was a great way to get students participating. Once the list was on the board I went to move on when a student asked what the answer was. We had a look, then figured out what their percent errors were. They were all quite close.

After the estimating we moved onto a number talk. I asked students to figure out what 25*8 was without using a calculator. As I said it to the class it occurred to me that this was an easy one to relate to money so perhaps it would be too easy. Oh well. Next time I'll refer to my notes rather than working from memory. I had originally intended to ask 25*12. In any case, we had a few different methods that were shared. Nobody used an area model so I went over it and a couple of other methods. This was another fairly simple task that helped students build confidence.

Once we finished the number talk we moved onto Skyscrapers.

The idea is that you must have a tower of each height (1,2,3 and 4) in each row and each column and the numbers along the outside indicate the number of tower you can see from that location. It's very Sudoku like. I've seen a lot of people use this activity in the past, but I wasn't sure about it. It wasn't until I was at a session where teachers tried the activity that I realized what a great first day activity this could be. It involved problem solving, collaboration, attempting and failing then reattempting and lots of communication.

I was hoping to get to some integer addition and subtraction today as well, but I guess that will have to wait until tomorrow.

I had a great day and I hope my students did as well. I hope they had fun, felt comfortable and enjoyed themselves. We covered a fair bit of ground: estimation, percent, multiplication and problem solving.

I need to remind my self to take more pictures!