Ms. Bearse's Site

We are exploring how to evaluate and also how to simplify expressions involving exponents.

We worked on multiplying, dividing, powers of powers and also on some complicated combinations.

We have many ways to express the same answer.

We are doing a lot of work at the blackboards and then consolidating our thinking every so often.

We are taking pictures of our work to record our thinking.

We wrote summary notes for ourselves

and we’ll see how well we’ve built our knowledge in tomorrow’s quiz.

We are exploring what expressions with exponents can look like.  We noticed that exponents of 2 make squares, and exponents of 3 make cubes.

The base of the exponent will be the dimension of the square or cube.  If there is a coefficient and a variable in brackets with the exponent it means the coefficient and the variable together form the base.  Here’s an example of 2 x cubes compared with one cube that has sides of length 2x.

We explored a variety of combinations, with coefficients of 1/2 or 2 or 3

One group even made a representation of (3x)^3

We started to explore how many little cubes (x cubes) there are inside, and look for connections with the algebra and the physical model.  We will continue doing more with this in coming days.

In grade 10 we are working on quadratics.  We looked at visualpatterns.org and modelled some patterns by drawing terms 4 and 5 and 0 to extend the pattern in both directions.

We made tables, and looked at differences (it’s quadratic if the 2nd difference is constant).  We also looked for groups of “n” and squares of “n”.

We notice the constant, and colour it so we can see it’s always there.  It is also in the equation at the end (the term with no variable).

We also made our own patterns from a given expression.

We noticed by the end of the class that the “a” value (the coefficient of the squared term) is HALF of the 2nd difference.  

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.