Ms. Bearse's Site

We are working on representing abstract concepts with concrete manipulatives to build conceptual understanding.  Today we used a concept circle where we can change the “a” (what is in the center of the circle) and we can represent all the other expressions in terms of “a”

We called this tile “1” to do some of our figuring.  We needed to do a bit more thinking when the tile in the center was the rectangular tile, representing “x”.

We saw that the rectangular tile is a variable, and so to show a variable squared we need the big square tile, and a variable cubed can be actually a cube! 

We took a summary note which covers the importance of noticing the brackets and following PEDMAS

Today the school buses are not running due to the snow.  This means our summatives are postponed to MONDAY.  Stay safe.  Schools are open.  Teachers will arrive to school as it is safe for them.  You can come to the school and get extra help, or work in the library, but there are often very few people at school, so classes don’t usually happen on inclement weather days.

We had a good math review session this morning….

We went from this…

To this…

With enough practice we start to see potential pitfalls and traps, and have enough strategies to work through problems, avoiding errors, or at least noticing them and correcting them when they happen.

Grade 9s worked today with algebra tiles.  We learned about what each type of tile means, and what a trinomial, binomial, and monomial are.

We learned how to add polynomials, and even made our own problems to meet criteria, like 2 trinomials that add to make a binomial.

The big key is realizing that a red and blue tile of the same shape will cancel out and make zero.

Les 9e explorent Desmos géométrie.  Nous allons créer les polygones, trouver les points milieux, mésurer les angles et les longueurs, et verifier les conjectures.

Period B:

“Explore” p.395 méthode 2

P.398#1-9

Assemblé pour les classes d’immersion
Period C:

“Explore” p.395 méthode 2

P.398#1-9

“Explore” p.402 and “exemple 1” p.403

P.405#1-6

Les 9e, dans le courriel cette semaine, prenez un moment pour réfléchir à propos de vos habilités d’apprentissage que vous avez demontré depuis septembre.  Voici une grille d’évaluation pour vous guider.

Responsibilité

Organisation

Collaboration

Travail indépendante

Initiative

Régulation de soi même

Donnez vous même un niveau (1-4) avec la justification et aussi créez un but pour chaque un pour le 2e moitié du semestre.

Attachez aussi votre tâche, pour que vos parents puissent le voir.

Grade 10s branched out to work on factoring trinomials with a leading coefficient (a value) that is not 1.

We did it with algebra tiles, which can be very quick, and we also worked on an algorithm to separate the middle term into 2 terms, and then factoring by grouping.

We worked in stations today in grade 9 to solve some angle problems from the past EQAO tests.  We are looking for triangles, quadrilaterals, polygons, interior and exterior angles, supplementary angles, and transversals (sécantes) through parallel lines with corresponding, alternate interior, and opposite angles.

How are these two connected?

We are using algebra tiles to visualize polynomials and factor them (make them into rectangles and the dimensions are the factors), and then relating that to the graph.

Here’s the example we worked through together

We notice that the dimensions of the rectangle are related to the roots (x intercepts/zeros) of the parabola.  We know that the axis of symmetry is at the midpoint of the roots (and we know how to calculate midpoints!) if we sub in the axis of symmetry for x, we can calculate the y value of the vertex.  We see that the constant is the y intercept (ordonnée à l’origine).

To figure out the roots, we look at factored form y=(x+7)(x-2) in order to find where the graph crosses the x axis, we need to make “y” be 0, since on the x axis the y value is always 0.  For the result of a multiplication to be 0, on of the two things multiplied together MUST be 0 too.  We have 2 options, either (x+7) is 0…so x=-7 or (x-2) is 0…so x=2.  Those two values correspond to where the parabola passes the x axis.

We looked at our data today.  We used google sheets because of how easy it is to insert formulae into cells to calculate more things from our data.

We noticed one data point for circumference was really off, graphically it was separated from the others.  We learned the vocabulary for outlier (valeur abbérante)

Our graph showed a weak negative correlation for circumference

The graph with thickness showed a weak positive trend

And there was no real trend visible with the height of the pumpkin.

We explored how to enter a formula in a cell to calculate the radius from the data for circumference, and from that we can calculate volume, area, cross sectional area, and try to find more strong correlations.

We noted that we didn’t have pumpkins that were the same variety, also we didn’t apply the elastics consistently among all groups, which led to more variation.

Safety first!  We exploded pumpkins today using elastic bands.  We made some measurements first, and put our safety glasses on, and started applying elastic bands.

We kept track of how many bands we added, and noticed that the pumpkins started to change shape.

We recorded our progress with our devices as it got close.  We wanted to catch the moment when it exploded.

The following are stills from one of the videos

You can see the moment

It was pretty exciting

At the end, we measured more things, including the wall thickness.

We removed all elastics and bagged up the pumpkins for donation to a farm and also a wildlife sanctuary.  We will be analyzing the data next week to look for trends and correlations.