Snapshots of Math from Today

Today I was in a few classes, and captured some learning and fun to share. In 2P the class was starting their work with visual patterning and linear and quadratic relationships. This is something that they have seen in grade 9, but sometimes forget bits and pieces, so it’s a great refresher before doing more work with linear systems or quadratic models.

using patterns from visualpatterns.org we ask students to draw figure 4 in the pattern, and then to extend it back to draw figure 0. We look for how the figures are changing, and if it’s changing by the same amount each time. We make a table of values, where we count objects, and look for patterns in the table (first and second difference leap out here), and then we add the points to a graph, where we again can see the rate and the y intercept (which is always the same as figure 0). The next step is to push past thinking additively, and just (in this case) adding 2 and then another 2 and then another 2. The best way that I have found to do this is to ask about what figure 10 would be like. How many times would we have added 2? To get to figure 10 we’d have added 2 10 times, and since we started with 1, we’d have to add the 1. We could then jump to figure 100, and determine that there’d be 201 stars there, since we had to add 2 100 times (which is 2×100) then add 1.

Students came up to help consolidate the work at the main board after working through a few different patterns. It was exciting to hear the words that they remembered from grade 9, and how the skills have stayed with them over the summer. Prior knowledge is now activated, and they’re ready to work with some quadratic patterns!

In MTH1W we’re working on our multiplication data collection, and strategies. We’re going to make scatterplots or our data once we’ve done this for 10 days.

we missed our “vennsday” task yesterday because we were outside for grade 9 play day, so we did another belated vennsday activity.

we had an interesting time filling in the sections, and saw some patterns emerge. In the circle that had all the multiples of 8 the numbers were all even. In the circle with multiples of 5 the numbers ended in 5 or 0. In the central section all of the numbers ended in 0 since they had to be a multiple of 5 that is even.

After this, while we were at the boards, we explored the perimeter and area of the figures in this pattern.

Students were prompted to continue to figure 4 and 5 if they were done, and then try the perimeter of figure 100, and figure 1000. The goal was to remember what area is, and how to calculate perimeter, but also to start thinking of patterning, and relationships while we’re at it. To quote the students they said that they were “cooking”.

Connections were made between the perimeter always being 4 times the bottom side length, and then that the bottom side length is always one more than the figure number, so using those pieces of information students could calculate the perimeter of any figure number I gave them. It’s great to see them develop the confidence to work through a new problem, and communicate their thinking, and be really excited to discover the patterns.

My 2D class started working on factoring and expanding today using tiles. We spent a lot of time building rectangles with tiles, and determining the dimensions and the areas. Long sides are named x, and short sides are named 1. Long sides touch long sides, and short sides touch short sides. We have to be careful about colours of tiles, remembering that (-)(-)=(+) and (+)(-)=(-).

Sometimes the questions gave the picture of the rectangle, and we had to determine dimensions and area. Other times we were given the area and we had to build the rectangle and determine the dimensions, and other times we were given the dimensions and we had to build the rectangle and determine the area.

There were some tricky cases where we needed to introduce some zero pairs to complete our rectangles. We’re starting to notice some patterns emerging which we will continue to explore tomorrow. It was a busy day with a lot of positive mathematical energy!