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We learned that the balance point, or center of gravity of a triangle is the exact point where the medians intersect.  We are good at finding intersection points, and we are still working on medians, so today we gave it all a try.

For some groups we noticed that there certainly were a lot of steps, and without care, it is easy to get lost!  It’s sometimes hard to find errors at the end of a problem.  We worked through the solution checking each step to see if what we calculated was reasonable.  Our method was a graphical one.

At the end of this exercise we learned that there’s a bit of a shortcut to finding the center of gravity of a triangle….we can average the 3 x values and 3 y values of the corner points, and the result will be the same as if we go through the process of finding medians and then substituting.

Grade 9s wrote their first summative in class today.  We had cake to celebrate all that we’d learned.

We also noticed that our beans have a scare crow now! 

We started class today with a close look at what our portfolio task is.  We read through the prompt together and talked about what evidence would be good to include, and what writing is expected.  We talked about the rubric, and reviewed how to submit work online.  

After that we followed up on a formative we did yesterday.  Yesterday we did 3 questions and indicated where we’d like more practice, and what we could maybe help others with.
Today we got into groups to work on our skills.  Some of us wanted to work on communication, others on using the pythagorean theorem, others on using various formulae for surface area and volume.  Each group had at least one “expert” in that category, and we worked through the solutions to yesterday’s questions, and did a bit of work on the model test for chapter 8.

After some time working, we got up at the boards to show what we know.

We worked together and checked our work for a couple complicated area and volume questions that involved the pythagorean theorem.  

Tomorrow is our “celebration of knowledge” (a.k.a. Summative assessment).  We’re ready!

Spheres are good at any point in the year!

We looked today at the amount of empty space that exists in these packages.

Given minimal information (one side length of the prism) we determined the other dimensions of the prism, and the spheres.  We practiced our volume calculations that we derived yesterday, and we subtracted to find the empty space.

The cups on the desk are our signal that we need help.  If there’s a red cup stacked on top it means “urgent help needed”, if there’s a yellow cup it means “we’re running into trouble, we need some help”, and the green cup on top means “smooth sailing, we’re doing well”.

This will hopefully eliminate some loud attempts to get help.  

After some practice with finding the equation of a line that goes through 2 given points we tackled an application of this process.  We determined where the medians were for the triangle, by eye.  We know a median cuts the area in half.  The way we do that is to join up a corner with the midpoint of the opposite side.  We were pretty good at eyeballing the medians.

We noticed medians all intersect together.  We know we can determine intersections by using substitution and elimination.

We got started on a problem involving numbers.

The fire drill interrupted the flow of things, but we found a numerical way to determine the midpoint of a segment.  The next step (which is for homework) is to determine the equation of the line that goes through point A (3,-5) and M(-4.5,2), the midpoint we calculated. 

Grade 10s had a summative today.  We called it a celebration of knowledge, to maybe make it less scary than a test.

We got out our “roche dans la poche” worry stones, and did our best work.

We also had cake, because that makes it feel more festive, maybe…
The first summative is always an interesting experience.  We know that there’s lots of room for growth, and we can always get better at time and stress management.  It is important to also recognize how far we’ve come since September, or even how far we’ve come since last year.

First of all, look at those beans!

And those beans! Wonder what’s different with these ones….

We got to work today in 5 different stations.

For one, we used displacement of water to determine the volume of a sphere.  Juice concentrate containers have the same radius as a tennis ball, so they work nicely.  The container is cut so the height is equal to the diameter.

Water is displaced, and fills the cylinder 2/3 of the way.

The volume of the cylinder is V=(pi)(r^2)(h), but remember h=2r, so the volume is V=(pi)(r^2)(2r) which simplifies to V=2(pi)(r^3)

So the sphere volume is 2/3 of that.

V=(2/3)(2)(pi)(r^3)

V=(4/3)(pi)(r^3)

We also looked at the surface of a sphere.  We drew circles with the same radius as the orange, then peeled the orange and tried to fill up the circles.

We ended up filling 4 circles.  We know the area of a circle is (pi)(r)^2 so the whole sphere is A=4(pi)r^2

We did an activity with the lateral surface of a cone, using a “pacman” made from the centre of a paper plate.  We looked at how slant height is related to the height and the radius using pythagorean theorem (again).

We also explored pyramids in Egypt to determine the area and volume of the great pyramid (in cubits). For this we needed to learn a bit about scientific notation.

We also learned about a pyramid in Mexico in the town of Cobà, which you can climb.  We determined he lengh of “safety rope” that would be needed to run the length of the side.

With 12 minutes per station, we all got to experience every bit, and practice for our upcoming summative.  

Today we got our quizzes back, and had some good conversation about how to approach he questions, and how to interpret the results.

Look at all this!  All from a discussion about how a square’s diagonal is related to its side length.

We also checked in on our beans.

We are recording lots of measurements for the next week or two.

Finally we talked about pyramids and the prisms they are related to (with the same base, and the same height)

We predicted how many pyramids full of water we could dump into the prism.  Many thought it’d be 2.  It turns out to be 3, each time, even when the base is a triangle, or a circle.  Pretty neat stuff!

Hello Grade 9s (specially those who were not here today because of the trip) you will get a blank quiz on Monday to try (or study from), hopefully someone in hour group watered your beans and checked on them.  Here’s the framework for your email home this week. Have a great PA day.

We talked also about the summative.  We will be looking at all the things we’ve worked on. 

Our list so far of things that can be on the summative:

Pythagorean Theorem, area and perimeter of composite shapes, including circular bits.  Maximizing area and minimizing perimeter (a.k.a. Make it more square), maximizing volume and minimizing area (a.k.a. Make it more cube-ish), surface area and volume of square based pyramids, cones and spheres (we’re still working on these solids next week).  If you are looking for things to work on this weekend, the material is in chapter 8, and a little bit of chapter 9.

We are looking for a more creative and less scary/stressful word than a test.  If you think up a good name please let me know.  Some of the good ones so far are “brain workout” or “celebration of knowledge”.