Ms. Bearse's Site

If you would like, you can sign up for a weekly problem from the university of Waterloo.  They email the problem on Thursday, along with last week’s solution(s).  There are different grade level problems available.  This is one for grade 9&10.  For more info check it out here.

We started our exploration of pyramids today with a challenge.  It was based off of work done yesterday.  Today’s challenge was to build a pyramid with a volume of 300 cubic centimetres.

We made plans, decided on dimensions that we thought would work…

Cut out pieces….

And taped them together…

Some groups made long tall pyramids,

Others made short flat pyramids

Some of our pyramids ended up shorter than we had planned….

We need to use the pythagorean theorem when we design pyramids like this.  We had figure out what height we wanted the pyramid to be overall, but that is not the same as the height of each individual triangle that makes up the side of the pyramid.  

Some of us were challenged today by the openness of the task, and lack of direct instruction at the start.  No, we have never learned about pyramids, but we have the ability to think, and reason, and try things, and work through a problem even if (at the start) we have no idea how to get to the end.  It’s not always a comfortable feeling, but this struggle is a productive one, and we learn that it’s ok to try, and it’s ok to be pushed out of your comfort zone, because that’s where the most growth can happen.

We have now got a garden established on our window sill.  We looked at the sprouting beans.  Most groups had close to 100% success with germination.

We labelled our plants with the type of bean, and the name of each bean (because that’s pretty important)

We were careful to put the roots down, and the leaves up.

We will be measuring them and graphing the results in the upcoming weeks.

Thanks to all who helped with the clean up!

Grade 9s made a lot of rectangular prisms today.  Each one had a volume of 300 cubic centimetres.

Calculations were made, and shapes were mapped out.

We cut out our nets, and formed the prisms.

There were so many different prisms!  Each one had the same volume….but quite different surface areas.

We classified them from biggest surface area to smallest surface area.

Some groups took this to an extreme….and made very long skinny prisms.

Period C’s prisms were infiltraded by an imposter…..(one of these things is not like the other!)

We talked a bit about how surface area and volume are very important in biology.  We have lungs that maximize surface area….our cells divide when they get too much volume compared to surface area….and worms (much like our long prisms) have a big area compared to volume, and they take advantage of this and breathe through their skin!

Grade 10s are plotting lines, and verifying algebraically that the graphed intersection point is correct.

We graphed using y=mx+b (slope and y intercept) and we also graphed by calculating the x intercept (make y be 0) and the y intercept (make x be 0).

In grade 9 We explored shapes with a perimeter of 20 popsicle sticks.  Some thought outside the box…

And others were more constrained to the box….this group had lots of boxes!

This model was easy to use to show the area.  The first one was less straightforward.

Some groups could show many options!

We tabulated the dimensions of all the possible rectangles using desmos, and used our words to describe the trends.

We also graphed the area of the rectangle, and used length as our independent variable.  It was a different looking graph for sure!  We used our words again to describe it.

We even looked at removing the constraint of having a quadrilateral….and tried to optimize the area again.

We made some octagons, and tried circles too!

Did you know there’s an octagon calculator online?
Good work today grade 9s!



Grade 10s were busy making rectangles today our of the algebra tiles that represent a given trinomial.

Here is x^2+5x+6

And here is the same expression, but arranged to make a rectangle.  The dimensions of the rectangle (length and width) are x+2 and x+3.

We noticed some expressions make squares rather than rectangles.  Here’s x^2+4x+4, which is has dimensions (x+2).  We can call that (x+2)^2

Not all trinomials can be made into a rectangle or square.

We looked at the x coefficient and the constant and the dimensions of the final rectangle, and we discovered a trend.

X^2+5x+6  the dimensions will involve two numbers which have a sum of 5 and also a product of 6.

We know from above that the dimensions are (x+2) and (x+3)….2+3=5 and (2)(3)=6

We will continue to work with these relationships over the course of this term.

Grade 9s had a different kind of quiz today.  We were looking at problem solving, reasonig, justifying, estimation and communication.

We watched a video, and wrote down what we noticed, and wondered about the situation…then made some estimations to determine how many stickies it would take to cover the board.

It was then followed by a little bit of information about the dimensions of a stickie and the dimensions of the board, and we refined our prediction using the new information.

Some of us wanted a closer look…

Some of us got pretty creative when we used our resources

After we had our number of stickies, we needed to design a different board that could be covered by the same number of stickies.

Finally we watched the video conclusion to watch him finish creating the image, and to check our work.

No homework today grade 9s, unless you are still submitting assignments online or working on your email.

Problem solving can be a real struggle.  Struggle is not a comfortable feeling, but it is where a lot of learning can happen.  When we struggle we need to embrace the “not knowing” and explore some ways to figure it out.  We know we have lots of strategies!

Today in grade 10 the problem was all about milk and cream.  Imagine you needed 1000mL of 2% milk for a recipe, and you didn’t have any.  You do have 2L of 1% milk and a carton of whipping cream (35%). Can you possibly create 2% milk?

After discussing the easy solution of “just go to the store”, we dug in a bit more.  

We made equations

We used logic

We wrote what we know, and thought about proportions and fractions

We made other equations (using decimal representations of percents)

One group got pretty close with an estimate (we need more than 900mL of 1%).

Eventually we made 2 equations and practiced substitution and elimination, and verified with desmos.  We’d need 970.6mL of 1% and 29.4mL of whipping cream to make 1L of 2% milk.  

Some classmates wondered when you’d ever need to make 2% milk.  This question can apply to any kind of concentration problem, many you’ll see in chemistry next year.  

This has become a bit of a tradition!  In the fall we plant beans and follow their growth and graph their height over time.  Today we started out.  We put 5 kidney beans and 5 black eyed peas in packets of paper towel, dunked them in water and put them in a baggie.

We put the baggies by the window.  

Some groups are being the “control” and leaving them on the window ledge.  Others have added extra to their experiment.  We have groups depriving their beans of light (their baggies are in a drawer).  We also have groups experimenting with giving love to their beans….they love Jeremy but not Hank.  We’ll see what happens there!
Next week we’ll check to sew what has happened, and then plant them in some soil and start our data collection.

We also took stock of what we’ve been learning so far.  We made a mind map of our concepts that we are working on.

Some of us also got into groups to troubleshoot our technology woes as we all learn how to make portfolios and submit assignments online.

We learned these things:  write your assignment in word or a google doc first, because the mindsonline will “timeout” if you have it open for too long, and when you log back in your work is not there anymore.  

Some phones are not so compatible with brightspace, so we can use school ipads, or maybe have our friends use their device as a “class device” and then we can share.

We also learned that we can be experts and help our classmates and even help our teachers!
Impressive work today grade 9s.