Last night I went and bought 8 pounds of Skittles; I had a fun conversation with the cashier.
Algebra looked at the color distribution of the different sized bags of skittles and made some conclusions on the data.
Here’s how things went.
I threw up this picture and asked ’em how many Skittles thy thought were in the package, then their estimated percent breakdown of each color.
After, I put this up and asked if it changed any if their answers.
They saw the number of each color and calculated the percentage of each.
111 Skittles isn’t a great size to make any conclusions, they asked for a larger bag and then made the same estimations.
389 Skittles isn’t really enough to make conclusions either… the data was everywhere.
Then, I pulled out a 2 pound bag of Skittles, broke students into groups of 2 and had them find the frequency of each color.
I put together a quick Excel document and had running totals throughout the day.
The results of each 2 pound bag were different, but when we put them together and looked at a sample size of 4338 some interesting talking points emerge.
I am excited to hear what students have to say/conclude from this data on Monday.
Geometry is wrapping up areas and moving into volumes. One of my favorite activities to foster spacial reasoning is the Seven-Piece Soma Cube. If you have never heard of this… here is a quick run down.
- Have students grab 27 math-link cubes (the ones that attach to each other)
- Challenge them to create all possible combinations of 3 and 4 piece cubes, the catch is at least one inside edge must be formed.
- Eventually, they will get all possible combinations, this takes some time. For my lower students I put up this visual:
- Once they have all seven pieces, they arrange them to create a 3x3x3 cube.
- There are something like 260 possible combinations…
Students worked hard and gave positive reviews to the activity. This sorta activity is a lot of fun.
Algebra is getting into quadratics. They know a bit about vertex and how to determine what direction a parabola will open. To keep momentum after introducing quadratics, I pulled a great acitivty from Dan Meyer’s Blog again.
Last year I spent an entire day on guessing and tracing where the ball would end it. It was a bit of overkill. This year I spent about 20 minutes on it, which was a good amount.
Students came up and traced the path they thought the ball would follow.
I threw the pictures into desmos and fitted a curve to them.
We watched the end of the video.
After a couple, students picked up that the ball followed the same path on the way up as it did on the way down. They are pretty comfortable with quadratics now and finding the max,min,vertex, and axis of symmetry.
“Over two out two from the origin both ways, then go beneath the x-axis, over 5 down 5, then back above the x-axis above 10 and 10 over”
Any ideas what the graph this student was trying to describe looks like?
Algebra is starting quadratics and with that comes a mountain of vocab; upwards, downwards, vertex, maximum, minimum… ect. Instead of having students read/take notes or listen to a lecture on the important of all the vocab I have them do the following:
- Break into pairs
- Each pair needs a single whiteboard, marker, and eraser
- Move desks around so students are facing towards each other; one needs to be looking at the smartboard while the other has their back to it.
- Throw a graph up on the board (Thanks Desmos)
- Without drawing in the air, pointing, listing off ordered pairs or anything like that the student facing the smartboard describes the graph as best they can to their partner (who can’t see it).
- Students struggle.
- Students get it.
- Partners switch positions and repeat.
Some of the best conversations about math happened today. Listen to a student describe to another what an exponential curve looks like for the first time ever was priceless. Students developed strategies and realized which points were critical in their partners success. They also saw the need for some mathematical framework, which was laid in place only after they encountered some tough ones.
Here are a few other graphs I threw up
Can you guess which one the student was trying to describe?
Geometry was great today.
The sequencing in our textbook is funky. Transformations are scattered throughout, about a section in each chapter, then chapter 9 comes along and is all about transformations. I was feeling unmotivated going into the chapter; I had pretty much taught and tested on everything coming into it.
Looking for hope, I dove into the MTBoS and came across a gold mine of resources from Andrew Shauver.
We started off with 3-Act Best Reflection. I cannot go off enough about how valuable this short discussion was. Students quickly picked a letter, then I asked them why they thought that was the best reflection. The conversation had such a natural progression into properties of reflections; congruent image and pre-image/perpendicular bisectors of each pair of points.
After, students worked on Andrew’s Exploration and Practice for reflections.
After about 15 minutes I passed out miras for students to check their sketches. The mira also made their lives a whole lot easier…
Finally students finished with Reflections Practice.
#4 and 5 will be good areas of discussion come tomorrow.
Algebra explored the expansion of (a + b)² today. Across 100 students, none of them were able to correctly expand (x + 3)² coming into the day. We plugged x = 2 into different expansions. Most students had 13, some had 25. Everyone agreed that 25 was spot on, but couldn’t come up with an explanation as to what (x + 3)² expands to and gives 25 out.
We first talked about the area of a square with side length z and how the are is z². I asked ’em what area meant, they told me length times width. I asked ’em what area meant without using an equation… it took bit but we got here.
We folded the paper and labeled like so
We talked about how the new side length is a + b and to find the area of this square take (a + b)²
They found the length of each piece which makes up the area…
This is where they struggled:
The area of the square calculated from the formula is (a + b)²
But the area is also defied by these squares and rectangles added together.
(a + b)² = a² + 2ab + b²
We used this to expand (x + 3)² to x² + 6x + 9, which gave 25 out for x = 2!!
After a couple more examples students had a good hang of things, I saw a good mix of multiplying out and visual representations.
Tomorrow they are exploring (a + b)(a – b)… it should be fun!
Algebra still needed some practice on Properties of Exponents. Yesterday, I passed around answer keys to a worksheet students had. There ended up being a few mistakes on the answer key. Two periods passed without any students picking up on those. To me this says that most students straight up copied off them then called it a day.
So today students experienced speed dating; here is how things went.
- I passed out a note card to each student
- There was one expression on each side, a black one (the problem) and an orange one (the answer).
- On a sheet of paper students simplified the expression in black.
- A couple minutes passed
- They then flipped their note card over and checked their answer (Almost every student actually listened here or didn’t recognize that the answer was on the backside)
- We moved the room around into two long rows of desks, facing one another.
- I set a timer for two minutes, during that time one student held up the side of their note card with black ink and the person across from them simplified, if they were wrong they tried again.
- Timer goes off, repeat 10-15 times
This is the bare bones of the activity. I played it up a lot before hand and told ’em about how they needed to be masters of solving the problem in black ink. They had to own the problem and know it inside and out.
A couple other things I said: “You can’t just give your heart, or answer in this case, away to the person, they need to understand you”
“While they are trying to get to know you, just hold up the problem and smile back, helping them along the way”
“If you didn’t have a good experience with a person that is okay, move on, another may work out better for you”
I also mixed things up a bit by playing a cheesy gong sound that I found on Youtube at the end of each session.
The main reason I liked this activity: Quite a few students struggled with their problem, throughout the period, they were able to see other students struggle with the same problem, but this time help others out in understanding it. Also, students were able to get immediate feedback and self correct. I heard a lot of comments today about how students didn’t get the problems at first but they became easier after practice.
Two of my four algebra classes seemed to really like the activity, while the other half never wanted to do it again. I know for a fact though that 90% of my students walked away from today knowing more about exponent properties.