Ms. Bearse's Site

Solving equations with algebra tiles: we first represent what’s on both sides of the equal sign using algebra tiles. There is an imaginary wall between the sides (where the equal sign is)

We next add 2x to both sides (to create 0x on the right)

Next we simplify (eliminate all zero pairs)

Next we eliminate the constant that’s on the same side as the x term (we place 4 blue squares on each side)

Next we simplify. We know that -x=2 so we can deduce (or divide both sides by the coefficient) that x=-2

What do you notice?  What do you wonder?

What would happen if the red function were the numerator and the blue function were the denominator?  What do you know about the quotient function?

What would happen if the blue function were the numerator and the red function were the denominator?  What do you know about the quotient function?

We had a look at the problem in class today. We realized that we don’t need the numbers on the graph, or the equation even, to get an idea of a rational function’s graph.

We looked for places where the denominator function is zero. That’s where we’d find vertical asymptotes. We looked for where the numerator function is zero, and that’s where the zeros of the rational function will be. We looked at the signs, and relative values of the numerator and denominator and strategically looked to each side of the asymptotes, and at the end behaviours.

some groups had time to look at the rational function of “blue” divided by “red” as well. The function looks very different at the ends. We know that when the degree of the numerator is less than the degree of the denominator, the function will have a horizontal asymptote at 0. Above, the numerator had a degree that was 2 greater than the denominator, which led to a parabolic asymptote.

We’re making connections between equations and graphs of quadratics.

We are able to graph parabolas in factored form. We know how to determine equations from graphs too. It was a tasty parabola! Y=2(x-1)(x-3)

Today in grade 9 we made progress in our equation solving skills.

We are sometimes solving by inspection, and then showing a full verification to prove that our answer is correct.

When we can’t solve by inspection, we need to have a strategy. We are able to maintain the balance if we do the same thing on both sides of the equal sign.

We are showing our steps, simplifying, and then isolating the variable. We are certainly building on our algebra skills!

today is the day we’ve been waiting for! We are graphing the growth of our beans. While we work through how to represent our information we are confronted with a few questions and concerns. Did we measure enough? What did we measure actually? Did each group member measure things in the same way? (i.e. measure from the soil or from the table, measure to the stem, to the highest point, or to the outstretched leaf tip?). Should we have watered our plants a bit more?

Was there a better way to organize our data table? Did we collect all the needed information? Are we sure of the dates we measured the bean height?

There was a lot of scrambling to make sense of our information and put it on a scatter plot with a good legend. We needed to consider all of the days, not just the days we measured our plants. We’re going to examine and compare the growth rate of kidney beans and black eyed peas.

Some teams graphed each individual bean plant, and others averaged the growth of all kidney beans on a given day. We then had to consider what to do with beans that died. Do we include them in our average? Exclude them completely?

Some groups used colour to distinguish plants, others used symbols too. When we see black and white with no distinction, we can see an overall trend, but it might be overwhelming as well.

What started as an easy task to “make a graph” turned into a class full of reflection about what variables mean, what data is important, how to measure and decide on a common procedure in a group, the importance of collecting data frequently, and thinking early about how our data will be used in the end, so we can make a good plan.

Today was full of productive struggle!

Today we joined with another grade 9 class to do a fraction/decimal/percent activitywe were given different cards, each with a representation, and asked to notice, wonder, and decide how we might organize them.we sorted, grouped, found equivalents, and put them all on number lines in approximately the right spot (using our proportional reasoning).we needed some benchmarks between the lines, and used quarters and thirds, to make sure things lines up.

We worked well today, in a much bigger group than normal, and impressed a group of teachers who were observing as part of a PD session. Good job today grade 9s!

In grade 9 we looked at a new puzzle today. They are called solve me mobiles. We are working with logic to determine the values of each of the blocks so that the mobiles hang level.

We are calculating, guessing and checking…

Making diagrams is often helpful to model the problem

If we make an error, the mobile is not level anymore!

one key strategy we started using was to cross out elements that occur on two branches that hang level with each other. By doing so we can determine how many of one shape equal how many of another.

We are having fun (and developing our algebra skills without realizing it!)

Today in grade 10 we looked at a parabola on a graph. We graphed the standard form, and the factored form, and looked for interesting points and how the values in the equation relate to the values on the graph.

Our focus was on x and y intercepts, and the vertex.

We are working on developing new skills with algebra, and remembering how to work with fractions! We have a solid understanding of common denominators, even if they need to be big polynomials!we are able to solve for x here by gathering all terms to one side, and creating a polynomial that equals 0. We know that we can solve the quadratic here by the quadratic formula. We are never quite finished with polynomial functions….they keep showing up!

When doing an algebra quiz….algebear is a good supervisor!