I have created a whole lesson (30 minutes +) on introducing vector multiplication and addition through extending prior learning of translation. The objective is below.
Objective: Understand and use column vectors and explore their additive properties and the effect of multiplying by a scalar.
Included is a lesson plan for a 30 minute lesson however few students completed all work, as this was originally used as an interview lesson where I didn't want to run out of resources and work for the students.
The flip chart is created using ActivInspire for a Promethean board. However I have also attached a PDF version for ease.
Resource you would need are rulers and ABCD multiple choice answer cards to use for AfL at the start of lesson to assess prior learning.
The Concept if that students works in pairs having numbered themselves 1 and 2.
Person 1 follows a vector trail drawing the vectors onto a grid such as a + a + b + a + c
Person 2 simplifies the expression and draw this onto the grid as well. 3a + b + c
They should notice that they both end in the same place.
The teacher then draws on their knowledge of translations to substitute a, b and c for their corresponding column vector. Through multiplying by the coefficients and adding them together you can find the resultant vector without the need to draw it all out on the grid.
There is also a level 2 trail for students to try which is significantly harder. This resultant vector is found in the same way as above but it's nice also to show that it is also a multiple of one of the original vectors anyway. Showing how vectors can be parallel.
This lesson is very interactive and the students I have carried this out with enjoyed the lesson.
Objective: Understand and use column vectors and explore their additive properties and the effect of multiplying by a scalar.
Included is a lesson plan for a 30 minute lesson however few students completed all work, as this was originally used as an interview lesson where I didn't want to run out of resources and work for the students.
The flip chart is created using ActivInspire for a Promethean board. However I have also attached a PDF version for ease.
Resource you would need are rulers and ABCD multiple choice answer cards to use for AfL at the start of lesson to assess prior learning.
The Concept if that students works in pairs having numbered themselves 1 and 2.
Person 1 follows a vector trail drawing the vectors onto a grid such as a + a + b + a + c
Person 2 simplifies the expression and draw this onto the grid as well. 3a + b + c
They should notice that they both end in the same place.
The teacher then draws on their knowledge of translations to substitute a, b and c for their corresponding column vector. Through multiplying by the coefficients and adding them together you can find the resultant vector without the need to draw it all out on the grid.
There is also a level 2 trail for students to try which is significantly harder. This resultant vector is found in the same way as above but it's nice also to show that it is also a multiple of one of the original vectors anyway. Showing how vectors can be parallel.
This lesson is very interactive and the students I have carried this out with enjoyed the lesson.
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