Ms. Bearse's Site

Today in grade 9 we made circles out of string, measured the circumference, and measured the diameter.

We graphed diameter on the horizontal axis, and circumference on the vertical axis.

We looked at the line of best fit, calculated the slope and looked at the y intercept.

The correlation was strong, direct, linear, and positive. The slope was just more than 3, and we determined that the slope should be pi.

Some minds were blown.

Today in grade 9 we investigated how our field of vision changes as we increase our distance from an object. To do this we used paper tubes, a few meter sticks, graph paper and desmos.com.

Each group of 3 had an observer, a measurer, and a recorder. The observer stands away from the wall and looks at a meter stick taped to the wall. The measurer records the distance to the wall, and also helps the observer determine the size of their field of view. The recorder puts all values in a table.

We created graphs and examined the correlation.

We drew a line of best fit, and calculated the slope and the y intercept.

We compared the equations to those that we got when desmos did a linear regression.

We could then make predictions and answer questions based on the best fit line (on the graph, and with the equation).

We’re getting ready for a summative investigation this Friday.

On the PA day I learned a new trick that Desmos can do.

First of all, you can insert images onto axes, which is cool.

The next thing you can do is to model things seen in the image. For instance, the water fountain creates a parabola. We can play with various expressions until we get one that’s close. Give it a try. Add an expression in factored form y=a(x-r)(x-s). Play with values for a r and s until you make the graph fit.

Another way to approach this task is by regression. You can insert a table of values, and fill the x and y columns with points that would be on the parabola in the picture. Be sure there are at least 3 points in your table.

To get the curve of best fit we use a tool called a regression. You need to be careful of the syntax. Type y1~a(x1-r)(x1-s) the 1s included tell desmos that you are dealing with table of values 1. The ~ tells desmos to make the curve of best fit. A curve will show on your screen, and a legend will appear beneath your expression in the sidebar showing the values for a, r and s.

The same thing works for a line of best fit.

You could just play with y=mx+b until the line you create models he slope of the ramp shown, or you could make a table of values and do a linear regression. Insert a table of values, include at least 2 points, and then insert the following expression Y1~mx1+b and desmos will create the best fit line and equation to match.

This is a powerful feature! Graphs with desmos allow you also to easily interpolate and extrapolate too. Touch or click anywhere on the lines/curves created to get the exact coordinates. Intuitive, eh?

Using the program through the website allows you to sign in with your google account or desmos account, and save your graph. The app wont let you save yet.

Give it a try tonight. See what you can do.

We measured our heights, and the length of our feet.

And made a table of data.

We graphed our data and found the equation for the line of best fit.

We’re getting faster at analyzing the data we are collecting, and we’re getting better at making predictions from graphs and from equations.

When you have data to graph in a scatter plot, it is now possible to get the equation of the best fit line using desmos.com (free software/app). You will see the best fit line with equation on the side bar.

Here’s the data set for the grade 9 math candle investigation. It’s possible to make the equations of the lines of best fit by calculating the slope and y intercept, but it’s also possible to use desmos to help you check your work.

The nitty gritty:
You need to enter your data in a table first. The headers of the columns will be x1 and y1.

To do a regression create an expression and type in y1~mx1+b and the line of best fit will appear. It is a new feature of desmos, and a very useful one too!

Today we had Cmdr. Chris Hadfield come speak at our school.

It was a full house as we gathered in the auditorium to hear his story of being in space, and how he made the choices he did to lead him to such a remarkable career.

(no photos were taken during the presentation…this is the “before” shot)

Here are pictures from the @limestonedsb twitter feed documenting the presentation.

He was joined on stage by Rob Baker of the Tragically Hip as they performed his song “Space Oddity”
Here’s how the @limestonedsb saw it.

For all who have not yet done so, follow him on Facebook and Twitter and see the collection of inspiring photos he took while in space.

Sometimes we want to compare two graphs, but don’t want to spend the time to recopy all the data again. If the axes are scaled in the same way, we can superimpose the two graphs at the window!

We were glad to have our “Engineer in the classroom” again today. We spent the class designing and building popsicle stick bridges and then testing them to destruction.