Ms. Bearse's Site

Since our projector was not cooperating today I couldn’t say as much as I wanted about these patterns. We were looking at what questions might be interesting to ask, and how we could represent the patterns with algebra. Questions are referring to the patterns ABOVE them. (Patterns are from visualpatterns.org)

Figures 0,1,2,3,4 are shown. We looked at representing each colour with an equation, or modelling the growth of the entire set of circles.

There’s another one to look at. What do the colours represent?

What form of equation would be the most logical for expressing this relationship?

We could look at area and perimeter here. Would they ever be equal? Would the perimeter ever be double the area? Would the area ever be double the perimeter?

What do you notice about this pattern? What do you see in a table of values?

We can look at the area and perimeter here too. 2 different equations. Are they both quadratic? How do you know?

How can you show the growth of the area? Simplify your equation to standard form. Is there a way to visually modify the pattern to match your simplified equation? Can you show this in factored form? Can you modify the pattern to match your factored form equation?

Same questions as above…this looks complex! Is there a way that we can visually simplify things? Rearrange blocks? Does that help us with the creation of an equation?

We have been learning math carols recently, and today we took our show on the road, and sang to several high school classes, office staff, and each of the grade 7/8 classes.

Here are the songs, if you’re interested. We didn’t write them.

Grade 10s explored a leapfrog problem.

Using either this site, or a game board and frogs, we looked at the number of moves it takes to have the frogs swap sides. The frogs can slide one space or hop over another frog and each counts as one move.

We aimed to minimize the number of moves to have the frogs switch sides. We can vary the number of frogs, and then look for patterns. The goal was to be able to say how many moves it would take for any given number of frogs.

We saw a few ways to model the problem. Here’s a neat visual model.

Some used tables and used the equation with desmos to show that the equation was a good fit.

Once we figured out the equation for this situation, we were ready for a new challenge. What happens if there were 2 spaces between frogs at the start? What happens if there are different numbers of frogs on each side? How will this affect our equations?

Grade 9s are working at solving word problems.

we’re looking at the words and seeing what information we can get from the question, and then we are making equations out of the information.

We’re working on communicating clearly with words and symbols.we want our work to be able to be easily understood by others.

We’ve got a test on Tuesday, so we’re working hard to prepare.

Voici un graphique de desmos qui montre les transformations d’une parabole

Today grade 10s looked at how many unique high fives there are in our classroom. We had 32 in the room today, and a unique high five is considered a high fove between 2 people.

With 32 it gets challenging to draw out…

Easier to draw smaller cases

We looked at the table of vales we created from these smaller cases, and found patterns which we extended to our number of 32 people. We also looked for a general case, and from the second differences, calculated “a”, from the table we found the constant, or “c” term, and then calculated the value of “b” in our standard form equation.

We have 3 Owens in our class. The Owens have used themselves to create some algebraic representations.

Here is 3 Owen

And here is Owen^3 (Owen cubed)

Mighty creative!

We’re working really hard to get ready for tomorrow’s test. We’re practicing with tiles, practicing with text books, taking pictures of our work, using google classroom, and making our digital study notes. We’re working together to get last minute questions answered, and to be sure of all of the algebra rules we need.

We all need calculators for tomorrow! We’re ready. We’ll do well tomorrow.

Grade 9s worked “speed dating style” to review algebra concepts today, and solve problems together.

by working in pairs, across the table, we can help each other out, and coach our peers to understand and perfect our algebra skills.

We are having fun too!

Today’s the big day in grade 10! Here’s the derivation of the quadratic formula. It shows how to complete the square for any trinomial, and then, to set y=0 and isolate x to find the roots, as we’ve been practicing lately.

we isolate x by doing opposite operations on both sides.

In the end, we have a beautiful formula (in the box) which we will use a lot. We even learned how to sing this formula to the tune of “pop goes the weasel”.

We use the formula to calculate roots of a quadratic.

We could have done the same thing by factoring

But not all equations are factorable. We can always use the formula!

We also saw what happens when there are no roots

We will be using this a lot to solve problems tomorrow.