Graphs: Distance/Time

We have been looking at graphs and spent a lot of time looking at gradient and y-intercept and now we are moving onto distance-time graphs. I thought we could start at looking at some gradients and the connection to speed and next lesson we will look at starting later or at a different distance from home. I would like students to connect back to the work with gradients and y-intercepts.

Gradient

I have been looking at Linear Graphs with year 10 and we started looking at problems that I might plot on a graph. We also looked at the connection and patterns between groups of co-ordinates.

We looked at this problem early on and discussed how we knew which lines were equal in length

We then looked at a grouped of lines we had plotted and looked at the connection between the line and equation that matched it. We noticed all the lines were parallel and increased by the same “step” each time.

We also looked at what happened if the y-intercept was the same but the gradient different.

We looked at some DESMOS activities and then we looked at different problems related to parallel lines

Playing with Tiles

This afternoon, I tipped out the plastic 2.5cm tiles and the larger wooden tiles and got out the plastic trays. I started with the wooden tiles because I wanted to design a pattern to make for a “colour the pattern” task and my daughter played with the plastic tiles. She likes to arrange images in each of the differently sized Numicon trays and then stack the trays and ask me to “open the surprise” Today was no different and once I had unstacked the pile and looked, I saw a nice little pattern. She explained that she did the little tray first and then added a row each time she used a bigger tray.

After a while, she pulled out the scales that we’d discovered earlier in the day (we’d done some tidying of her toys and found the scales) She played with these for a while, adding tiles in each side and watching them tip one way or balance. After she had dumped out both buckets, I put 10 large wooden tiles into one of the buckets. I asked her how many plastic tiles would weigh the same. I gave her the other bucket and she started to fill it. She counted up in twos and said; “I think it’s 20,” before replacing the bucket on the other end of the weighing scale. The balance tipped in the wooden blocks favour, so she said she would add more plastic tiles in. She counted out 30 more and realised it was 50. I pulled out all the wooden tiles, except for one and asked her to take how many tiles she thought would make it balance. She left the bucket on the scale and eventually she was satisfied the two buckets were equal when she had just 5 plastic tiles left. I threw in one more tile and she said; “ah that’s easy! Its 5 more plastic tiles” so I threw in another and she did the same. She then said; “lets do more” she then threw in wooden tiles so there was a total of 25 tiles in. She said; “I can work this out” she counted on her fingers in 5’s and stopped at 125. She then threw 125 plastic tiles into the opposing bucket but it tipped ever so slightly to the plastic tiles. She recounted and it was the correct amount so we discussed the fact that one wooden tile might be a little less than 5 tiles.

Angles in Parallel Lines

After I introduce angles in parallel lines to my class and discuss the correct reasoning. I want to show them lots of different examples and non examples so they are confident in recognising alternate, co-interior, corresponding and opposite angles, whilst still noticing basic angle facts.

After we have spent time doing this I want to look at these questions

Surds

I have been thinking about some further connections between area and surds. I started this thinking a few years back after a discussion with https://twitter.com/Arithmaticks

I wanted to look at some shapes where the lengths were roots

I have also been trying to connect surds and prime factor decomposition. Especially since we’re looking for square number factors that are easily identified once the number is in prime factor form.