Ms. Bearse's Site

Today we focussed on solving problems.  Whether our problems are in life, or in math, we have similar strategies!

Gather information

Organize information

Make a plan

Check to see that the plan is working

Ask for help if needed

Check to see that the problem is solved

Our problems we are solving now are based on coordinate geometry.  We can calculate many things (slope, midpoint, length, perpendicular bisectors, medians) and we can do these calculations for various segments (side lengths, or diagonals of shapes).  We need to really be clear about our plan, because we can waste a lot of time if we get off track.

We are classifying triangles, calculating area and perimeter

We are classifying quadrilaterals, and looking at their diagonals
We are working hard in our groups to solve the problems, and to check our work and present our thoughts in an organized way.

Today we developed the formula for calculating the volume of a sphere using a tennis ball and a juice container, some water and a displacement tank.

The important thing to know is that a juice container has the same radius as a tennis ball.  We cut the container so that it is the same height as the tennis ball too.  The height of the cylinder is the same as the diameter of the cylinder, or 2r.

We fill the displacement tank and let it drip until the water is just at the level of the spout.

When the water stops flowing from the spout, we place the empty juice can under the spout and then we submerge the tennis ball, and press it down under the water.  The water displaced by the tennis ball will flow into the juice container.

The water stops flowing, and the container is 2/3 full.

Here comes the math:  the volume of the cylinder is V=(pi)(r)^2(h), but remember h=2r since we cut it.

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

V=(pi)(r)(r)(2)(r)

V=2(pi)(r)^3

Now we know that the sphere’s volume fills 2/3 of the cylinder

Vsphere=(2/3)(2)(pi)(r)^3   And we multiply the (2/3) and the (2)

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

We also started an experiment today!  We are going to see if beans will germinate.  We have several kidney beans and black eyed peas, and have put them in paper towel and in a baggie.  We will check in at the end of the week and see the percentage that germinated.

We also looked at bumping up our portfolio writing.  We have submitted one task already, but have a chance to make it better using the feedback we received.

We looked at some composition samples, and highlighted all evidence in yellow, all reflections in green, and all summaries in orange.  We looked at our rubric, and determined where we could add more supporting details, and improve the writing.

We have another composition to do next week, and we’re feeling more prepared!

In grade 9 today we celebrated pi day by looking at circles, measuring diameter and circumference and making a scatter plot.

We made a line of best fit using desmos.

Next we looked at the surface area of spheres.

We traced oranges to make circles with the same radius as the sphere.  We peeled the orange and filled the circles with the peel.

We filled 4 circles.  Each circle has an area of pi(r)^2, so this explains why the formula for the area of a sphere is 4(pi)(r)^2.

Grade 10s looked at the equation of a circle, and how a circle is defined by the equation x^2+y^2=r^2.

Grade 12s did the tootsie pop experiment.  The initial circumference is measured.

After sucking on the lollypop for a minute, the circumference was measured again

We kept a table of data

And now we are going to make graphs comparing circumference to time, surface area to time, and volume to time.

Happy March Break every one!  Have a happy Pi Day on March 14. (3/14)

Here’s the recipe I used for the butter tarts we ate today.

1 1/2 cups packed brown sugar
2 eggs
1/2 cup butter
2 cups raisins
2 tablespoons heavy cream
30 (2 inch) unbaked tart shells

Preheat oven to 325 degrees F (170 degrees C).

Cream the butter, sugar and eggs well. Add remaining ingredients and mix thoroughly.

Pour batter into tart shells, no more than half full. Bake for 20 – 25 minutes. Watch carefully!!–they’ll burn quickly. 

Divers in flight are pretty close to tangent lines to a parabolic trajectory.

We watched some fast races, all timed to the 100th of a second.  We recorded split times (every lap) of the races for our swimmers so we could compare speeds (distance/time) for the different sections of their race.

We watched divers practice from the platforms, and they we able to rotate and flip so many times as they fell.  I wondered how much water was in the pool, and how heavy that’d be.  I also wondered about how many tiles it would take to cover all the surfaces.

Hello Grade 12s,

Here’s the code for your desmos activity today.  Make good notes! 

Période C: Mercredi

Bonjour les 10e: Dans vos groupes, notez les choses que vous REMARQUEZ et les QUESTIONS que vous avez/que vous voulez répondre.

ACT 2: Vous allez faire le travail!

Quelle information voulez-vous savoir?

Faites les estimations de ces dimensions dans vos groupes.

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Voici les dimensions:

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Maintenant, déterminez la longueur de la corde que vous avez vue dans la première vidéo.

Act 3: Voici la réponse

Période B: Mardi

Bonjour les 9e: Dans vos groupes, notez les choses que vous REMARQUEZ et les QUESTIONS que vous avez/que vous voulez répondre.

ACT 2: Vous allez faire le travail!

Quelle information voulez-vous savoir?

ACT 3:

Les questions supplémentaires:

1.  Combien de façons pouvons nous trouver pour modifier le cylindre pour DOUBLER le montant de maïs soufflé.  Lequel prend le MOINS de papier de surplus?
2. Pouvons nous utiliser le même montant de papier, et créer un contenant qui contient PLUS de maïs soufflé?
3. Si un théâtre demande 5$ pour le cylindre plus court, combien est-ce qu’ils devraient demander pour l’un qui est plus mince?

Desmos geometry  helps us to visualize and manipulate some interesting geometric properties.  We can create medians (les médianes) and perpendicular bisectors (les médiatrices).  We can also adjust drawings and see if relationships among points and lines change.

From a simple construction, we were able to create a perpendicular bisector (médiatrice)

We also looked at a median for a triangle, and how medians always intersect at the centre of gravity.

In grade 9 we looked at a variety of pyramids and their related prisms (same base and height).  We estimated the number of times the pyramid could be filled with water and emptied into the prism to fill it up.  Guesses ranged from 1.75 times to 3.5 times, with most of the class finally settling around the guess of 2 times.

However minds changed quickly when the pyramid was poured once into the prism.  After that we all agreed that it’d take 3 pyramids to equal the prism volume, or that the pyramid was 1/3 the volume of the prism.

 We set about to build a pyramid with the volume of 300cubic centimeters. We needed to do some calculations, and figure out what dimensions would work.  Many groups figured out dimensions of a prism that has a volume of 900 cubic centimetres to start with.

We then figured out what to cut out of the paper.

Some pyramids were short

Some were tall
And some started to look more like a prism than a pyramid, but the good things about building with old file folders is that you can always start over!

Many groups had to start over, because for many their pyramids were too short.  Many built pyramids hoping for the height to be 9, but instead they measured the height of the sloped triangle sides to be 9, so the entire pyramid height would be smaller than that.

The pythagorean theorem is there, right inside the pyramid.  The height (black) and half of the base (pink) form the legs of the triangle, and the slant height (pink) is the hypotenuse.

h^2+(0.5b)^2=s^2

We had a few good pyramids by the end of class, and we also had a much better understanding of area and volume.

We experimented with squares, plotting area and perimeter against side length

We are making tables of values, visual models, graphs, and looking at the trends we see.

With the squares we noticed that perimeters increase steadily as the side length increases, and so we have a linear relation.  We also made a formula for calculating perimeter and noticed there is no exponent.  We compared the area graph, which is an increasing curve.  We noticed there is an exponent when we calculate area.  We also saw that the perimeter and area are the same if the side length is 4, because there is an intersection on the graph.

Our next experiment was all about hot water.  We boiled a kettle and then poured the hot water into a mug.  We took temperature measurements each minute and put them into a graph.

We made some predictions after the first few minutes…

Some of us drew lines that continued downward all the way to the bottom of the graph (the x axis) which would represent the temperature becoming zero.  Our classroom is ridiculously hot so we know the water can never get to zero!We need to be careful when extrapolating; we should think about what is happening, and what the limitations might be, or what the future values could be.  Each situation is different so we need to consider the details and constraints very carefully.

Great work grade 9s!