Skateboarding around Angles is a direct follow-on from Original Lesson 12: Skating through Parallel and Perpendicular Lines. I started by laying down one metre rulers on the floor of the break out area, with children circling around me. I asked what this looked like to them:
“A cross or X” was the dominant answer. To which I replied, “Yes, very good. What else? Think about geography.”
“A compass?”
“Yes, what points are on the compass?” We revised these.
“Good. Now angles work in a similar way to a compass. There are four main points that you just have to remember, but there is a pattern to them, so once you know a few, you can work them all out.”
I placed the 0 down, asking students to ignore the 360 on it for now. I then placed the 90 down.“If 90 is here, what might be here [pointing to the 180]?”So on and so forth, we placed our nine timetables around the compass, adding a zero to each. “Now, if 90 is here, what might be here [pointing to halfway between 90 and 0]?” In this manner, we learnt about what is between each of our key compass point angles.
Next, the fun part. It is critical for this part to have an arrow on the skateboard, indicating where the rider is facing (we used a whiteboard marker). Students volunteered, with no shortage of willing participants, to jump on the skateboard and I would ask them to turn 90 or 180 and so on. Most would alight the board, move it around and then hop back on. Some were skaters and I allowed them to, in a strictly orderly fashion, attempt to move the board around whilst on it. The class picked up, very quickly, that turning 90 does not just involve going where the 90 is on the 'angles compass', but also depends on where you started from. That is, if they did not start from the 0, they were not going to end up on the 90 just because they were turning 90.Then students started to place the board in different positions and the class would estimate the degrees of movement they had performed. Mostly, we started from 0 to decrease the mental computation difficulty, but occasionally we started from 180 or the like.
I brought out the protractors and explained that it must have its horizontal line on top of the horizontal line of the compass, along the 0/360 and 180 line. Plus, the 90 on the protractors must always be on top of the 90 on the angles compass. This is one of the most difficult things for students to master, with the most common query being, "Where do I put the protractor?" Alas, without this, they are doomed to struggle with even the simplest measurement of angles. So, to demonstrate, I cut a big protractor out of paper, with the 90 line and had children volunteer to place it around the circle to try to estimate the angle of the skateboard. This made it much more visual than using a small, regular size protractor and scaffolded the whole group quite successfully.
We then switched to string and a proper protractor. Finally, the last critical teaching point was the numbers on the protractors. Most protractors have two sets of numbers on an inner and outer circle. So, for any angle, students encounter the question of, "Is it 110 or 70?" or the like. I thought hard about how to teach this and came up with this, drawing on the last lesson's learnings: If the angle is more than perpendicular, use the bigger number. If it is smaller than perpendicular, use the smaller number. We modelled this using both the skateboard and string; one student placing either object at a point around the circle, another then measuring and reading out both potential numbers, and a third picking the correct answer. It simplified a fairly annoying concept very well and with more ease than I had anticipated.
At the end of the lesson, two students from both ends of the achievement spectrum of the class approached me, thanking me for teaching them and allowing them to use the skateboards. A fellow teacher was so impressed that she asked me to run the lesson with her class as well, and it worked better the second time with the added arrow (substituting the whiteboard marker) and, of course, with the extra practice. With younger years, I do even more concrete investigations, such as walks around the school taking pictures of lines and angles, then displaying these in a slideshow on the interactive whiteboard and asking questions based on the images.
How do you bring real-world objects of interest into your math lessons?
“A cross or X” was the dominant answer. To which I replied, “Yes, very good. What else? Think about geography.”
“A compass?”
“Yes, what points are on the compass?” We revised these.
“Good. Now angles work in a similar way to a compass. There are four main points that you just have to remember, but there is a pattern to them, so once you know a few, you can work them all out.”
I placed the 0 down, asking students to ignore the 360 on it for now. I then placed the 90 down.“If 90 is here, what might be here [pointing to the 180]?”So on and so forth, we placed our nine timetables around the compass, adding a zero to each. “Now, if 90 is here, what might be here [pointing to halfway between 90 and 0]?” In this manner, we learnt about what is between each of our key compass point angles.
Next, the fun part. It is critical for this part to have an arrow on the skateboard, indicating where the rider is facing (we used a whiteboard marker). Students volunteered, with no shortage of willing participants, to jump on the skateboard and I would ask them to turn 90 or 180 and so on. Most would alight the board, move it around and then hop back on. Some were skaters and I allowed them to, in a strictly orderly fashion, attempt to move the board around whilst on it. The class picked up, very quickly, that turning 90 does not just involve going where the 90 is on the 'angles compass', but also depends on where you started from. That is, if they did not start from the 0, they were not going to end up on the 90 just because they were turning 90.I brought out the protractors and explained that it must have its horizontal line on top of the horizontal line of the compass, along the 0/360 and 180 line. Plus, the 90 on the protractors must always be on top of the 90 on the angles compass. This is one of the most difficult things for students to master, with the most common query being, "Where do I put the protractor?" Alas, without this, they are doomed to struggle with even the simplest measurement of angles. So, to demonstrate, I cut a big protractor out of paper, with the 90 line and had children volunteer to place it around the circle to try to estimate the angle of the skateboard. This made it much more visual than using a small, regular size protractor and scaffolded the whole group quite successfully.
We then switched to string and a proper protractor. Finally, the last critical teaching point was the numbers on the protractors. Most protractors have two sets of numbers on an inner and outer circle. So, for any angle, students encounter the question of, "Is it 110 or 70?" or the like. I thought hard about how to teach this and came up with this, drawing on the last lesson's learnings: If the angle is more than perpendicular, use the bigger number. If it is smaller than perpendicular, use the smaller number. We modelled this using both the skateboard and string; one student placing either object at a point around the circle, another then measuring and reading out both potential numbers, and a third picking the correct answer. It simplified a fairly annoying concept very well and with more ease than I had anticipated.
At the end of the lesson, two students from both ends of the achievement spectrum of the class approached me, thanking me for teaching them and allowing them to use the skateboards. A fellow teacher was so impressed that she asked me to run the lesson with her class as well, and it worked better the second time with the added arrow (substituting the whiteboard marker) and, of course, with the extra practice. With younger years, I do even more concrete investigations, such as walks around the school taking pictures of lines and angles, then displaying these in a slideshow on the interactive whiteboard and asking questions based on the images.
How do you bring real-world objects of interest into your math lessons?
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