Ms. Bearse's Site

Today we looked at the distance between 2 points. We had an easy time if the segments were horizontal or vertical, but stumbled when we had to calculate the distance of a segment that is diagonal. Pythagorean theorem helped us out!

We also looked at the group of points that are a fixed distance from the origin (0,0). This example is a lot of points that are 5 units from the origin. It makes a circle!

We now know the equation of a circle is x^2+y^2=r^2.

After watering and measuring our plants…

…we looked at correlation in scatter plots again. We started with this image as inspiration.

We wondered if feet matched up with forearm length.

We measured, and put out table of values on desmos.

We noticed the trend was positive, weak, linear and partial.

We got desmos to do a linear regression for us, and then we estimated the forearm length of someone with 15cm feet to be 17cm.

Just for fun we used the equation that desmos gave us, and we calculated it too, using BEDMAS.

Good luck grade 10s as you prepare for your test.

Today we were busy working on chapter review, graphing lines, solving problems, and asking lots of questions to clarify last minute concerns from chapter 1.

We used our desmos graph and added a line of best fit (by typing y=mx+b) and adjusted it with the sliders.

We noticed that “m” changes the slope (steepness) of the line, or makes it positive or negative. We noticed “b” changes the place where the line crosses the vertical axis.

We are practicing lots of our vocabulary as we look at these graphs.

We also got desmos to do a regression for us (to make the best line of best fit). We need to type in y2~mx2+b this time. The ~ tells the program that we want a regression, and the little 2s after the x and y link to the headings of the table of values we used.

We looked at interpolating and extrapolating, and making a rate triangle to approximate “m”.

We have some homework for tonight that uses desmos and analysis of graphs.

Voici le graphique que nous avons fait en utilisant les dimensions horizontales et dimensions verticales de nos télévisions.  Ici c’est le format de desmos.

et ici c’est le format de google sheets.  Avec les deux formats nous pouvons faire les droites/courbes ajustées.

Nous allons pratiquer comment faire interpolation et extrapolation en utilisant les deux graphiques.  Une télévision avec la dimension verticale de 200cm aura une dimension horizontale de ___cm?  Une télévision avec la dimension horizontale de 80po aura une dimension verticale de ____po?

Grade 9s planted their beans today, but first we calculated the percentage that germinated. Some groups had some stinky rotting beans too.

We put them in cups of soil and made sure that the roots were covered.

We gave each bean a name, and labelled them all so we know what type of bean is growing and we can track their growth rate. Some plants are already above the soil!

Our beans are on the windowsill, ready to soak up the sun.

Grade 9s are at the park tomorrow for their fun day.

Grade 10s are working hard on solving systems of equations, and interpreting word problems. We spent some focused quiet work time today, and made good progress.

Grade 9s measured the televisions in their homes last night. We compiled the data today to see if TVs length and width are related.

We looked at lines of best fit for linear graphs, and curves of best fit for non linear graphs. We talked about direct and partial, negative and positive, and strong and weak correlation.

We looked also at what interpolation and extrapolation are, and how to use the line of best fit to estimate values.

Grade 9s are working on solving some challenging problems.

We are asked to prove whether triangle PQR is a right triangle or not.

We looked at calculating missing sides with the pythagorean theorem.

Some of us were thrown off by the potential hypotenuse being the base of the triangle, or by the fact that we were having to prove something instead of solving something.

We needed to use the pythagorean theorem again to show that 10^2+8.2^2=11^2 was not true, so it is not a right angle triangle.

The pythagorean theorem is only true for right triangles, so if the pythagorean theorem doesn’t work, we can assume the triangle is not a right triangle.

We are working on multiplying, and using many strategies to solve problems.

We looked at 6×8 today, which we can break into 5×8 and add that to 1×8, or also by using subtraction find 8×8 and subtract 2×8.

We can also double the 8 and halve the 6 and multiply 3×16 to get 48.

Another way is to halve both the 6 and the 8 and then multiply our resultant by 4 (by 2 twice).

We can decompose the numbers into factors and multiply them in any order.

We can write down 1+1 so many times! Actually, we made it into an array so we could keep track. The array was 6 by 8. We can divide this array up into rectangles with friendly numbers and then add up the rectangles. Here it would be 6×4 and another 6×4 each one is 24 and 24+24 is 48.

Another really neat observation was that when the numbers hat we multiply are different by 2, we can say that the answer will be one less than the middle number’s square.

E.g. since 8-6=2 we know the answer to 6×8 is 7×7-1. We tried it with smaller models, and showed how it works with a visual model.