Ms. Bearse's Site

We are working on problem solving, and showing complete, well communicated solutions. Today we had 6 groups set up each with a question on a chart paper.  We worked on whiteboards as a group to solve the problem, and communicated out answer fully on the chart paper with the marker colour we were given.  

We then brought our marker with us as we rotated to the next station, and we used it to add to the solution that was presented, or to highlight good parts of their answer.

We are working on making a list of things that are present in well communicated and well justified answers.

We explored some of the patterns at Visualpatterns.org and worked on extending the 3 terms by creating term 4,5 and jumping to fimd term 10.  We also worked backwards to term 0.  We made pictures and tables and graphs to determine if the growth patterns were linear or non linear.  Some of us worked on making equations for the growth we see in the patterns.

Some patterns were pretty tricky.

We had to look carefully to see how the pattern was growing.  Some grew in multiple places.

We looked for what didnt grow.  We coloured the constant bits blue.

We then looked for what was growing, and how.

We made an equation that was C=(n)(n+1)(2)+3 since each rectangle was going to have the dimensions of n by n+1 and there were always two rectangles, and the constant was 3 which had to be added on at the end.

This was pretty advanced for grade 9!  We did a good job today!

Grade 9 eqao is June 6/7 in class.  Grade 9 exam is June 22 at 8:30am

Grade 10 exam is June 22nd at noon

Today we looked at solving the cake cutting problem that was yesterday’s homework.

We showed how ro cut the cake into the most possible pieces

We showed our data in a chart and looked for patterns

We extended the trend

We graphed it

We came up with an equation using trial and error

Y=(x^2+x+2)/2

Y=0.5x^2+0.5x+1

Then we looked at how desmos.com can help us model the data graphically and also with an equation.

Finally we ate cake

Yummmmm

Here’s a triangle.  A B and C are internal angles.  D E and F are external angles.  Here is a nice visual proof of some of the theory we’re working on.

The external angles, have a sum of 360 degrees.  Here’s proof.

When we put them all together, they match up perfectly, completing the full circle, which is 360 degrees.

Also, when we put the interior angles together, they make a straight line.  They are supplementary.  They add up to 180 degrees.

Here is an expression: 1x^2+6x-3

We are going to write it in vertex form by completing the square.  To make a square, we take the x term and split it in half.  Half of the x goes vertically and half horizontally.

We notice that we could complete the square with 9 little red squares.  Since we don’t have any, we need to add some zero pairs.

With 9 additional blue and red squares added, we can complete the square.

We now have a square: (x+3)^2 and also 12 blue square tiles.  The expression can now be expressed as (x+3)^2-12.