Ms. Bearse's Site

We had an interesting problem today (3.5 #3).  It involved two inline skaters holding on to a rope.  One skater pulled the rope, hand over hand.  We were given the force that they pulled with, and the distance they were separated, and the mass of each skater, and had to figure out the time it would take them to meet.

After looking at free body diagrams there was still some confusion about what would happen, so we modeled the situation.

We had two classmates on rollerblades pull on a ruler (no rope here today) and noticed that they both moved towards each other.  We knew now that they would meet in the middle.

Here’s the math that we did to show how we figured out the time it would take.  We needed our kinematice equations from last unit to help us out.

It is satisfying to be able to solve tricky problems.

Today we explored visual patterns again, and worked on connecting the pattern growth to an algebraic model.

When given the same term 3 we tried to make different possible patterns.

We made 3 of them, then explored the algebra that gets us from term number to the number of tiles.

We then colour coded the constant term (what stays the same in the pattern, aka term 0) and related that to the constant in the equation

We tried many different patterns, some were linear, some were not.  It was a good challenge to make the pattern rule and test it out by building more terms, or by making tables and charts, or using algebra.

In grade 10 we worked on similar things today.  We showed all the different ways to visualize patterns and create algebraic expressions from the visualization.

Here’s an example:

We looked at figure 3 in many different ways.

It’s neat to see how no matter the way you visualize it, and no matter the expression you create, it simplifies to the same thing in the end.

We are factoring a lot these days!

Today we took over all the walls to practice in groups.

No homework tonight, get a good sleep before the literacy test tomorrow grade 10s!

Today we started graphing our bean growth.  We know that they will continue to grow over the next few weeks so we will leave some space to add more points to our graph.

We made sure that the axes have reasonable scales

And that we graphed our beans wih a legend so we can make sense of the results.

We had to figure out how to account for weekends, when we didn’t record data.  We can always interpolate later using our trend line.

The beans in the dark are looking long and spindly. They aren’t growing as fast as they were.  We will graph all the growth next week and see what the trends look like.

We are working on factoring algebraic expressions.  Today we visualized this by makingg rectangles out of algebra tiles.

The area inside the rectangle is the trinomial x^2+7x+12 and the factors are the length and width of the rectangle (x+3)(x+4).  This is the only combination of length and width that work for this polynomial.  We also noticed that there is a pattern.  3+4=7 (the middle coefficient of the polynomial) and 3×4=12, the constant term.

Things were a bit different today!  We had a bit of a search for our quiz questions.  They were all hidden in eggs around the room.

Each colour of egg had a different question.

After we solved that question we hid it again for our classmates to findEdit
We are working hard to understand how to add and polynomials and what exponents mean.  We represent them visually, in expanded form, or with algebra tiles to help us work with them.

It’s important to practice how to use calculators to evaluate expressions with exponents.

Today in physics class we are listening to a presentation about what engineers do and what problems engineers can solve.

Today we worked on our math review using a “speed dating” set up.  Partners sit across the table from each other and both solve the question in front of them.  Once both get the question, one side of the table stands up and shuffles one position to their left.  They will be sitting wih a new person and working on a new question.  They will have an expert sitting in front of them who ensures their expertise gets passed along.  After 5 minutes the “experts” will shift one space to their left and have a new partner and a new question.  

This method of review is good because everyone is working in a team, and gains knowledge and confidence working together.  Caution is needed to make sure that each question should take about the same amount of time to solve.

Today we looked at our beans.  There had been a tiny bit of growth when we checked them on Friday, but now hings are looking very exciting for some groups!

We planted them in small containers.

And put them in the sun or in the drawer

We are looking forward to measuring some progress soon!