![]() Yet now, approaching the content from a much more connected methodology initiated by my work here, I’m questioning the emphasis I put on practising carrying out and describing transformations. ![]() So I felt pretty confident that I knew how to present and work through the topic. I don’t know about you but I’ve spent many years teaching rotations using plenty of practical equipment: large shapes to rotate on the board shapes on a bamboo cane to show how they rotate around a point jigsaw puzzles tracing paper and dynamic geometry packages and I even wrote a chapter on transformations for the CUP GCSE text book. It is further supported by considering the tasks and activities we ask pupils to carry out. Developing coherent learning sequences can be more time efficient and allow for a much greater depth of study. ![]() One reason I am here working at Cambridge Mathematics is I passionately feel that the Framework can support teachers in developing a more coherent, joined-up sense of mathematics, both for themselves and their students. Obviously this has serious consequences for our learners. Secondly, it showed how the nature of our curriculum really does compartmentalise content, potentially leading to disconnected schemes of work. Firstly, it highlighted how little geometry content there is within the KS4 English national curriculum. Recently I spent a wonderful couple of hours with Tom Button from MEI, considering the use of dynamic geometry and KS4 geometry content. Recently I’ve been struck by the number of things I have taught without fully and completely recognising how they are connected, even what I considered relatively ‘simple’ concepts. The image will be half the size of the original shape.Every week I learn something new at work. If the scale factor is 0.5, then simply multiply each of the original coordinates by 0.5. The image will be 3 times larger than the original object. For example, if the original coordinates of △ A B C are A ( 2, 1 ), B ( 5, 1 ) and C ( 3, 6 ), then the coordinates of △ A ′ B ′ C ′ are: A ′ → (2x3, 1,3) or ( 6, 3 ) , If the scale factor is 3 (K=3), then simply multiply each of the original coordinates by 3. To dilate something in the coordinate plane, multiply each coordinate by the scale factor (K). Point A (x,y) → A ′(Kx, Ky) if K is greater than 1 the original object will stretch and if K is less than 1 the original object will shrink. Note: in geometry scale factor is often symbolized using the letter K or ![]() All dilations have a center and a scale factor. The center is the point of reference for the dilation (like the vanishing point in a perspective drawing) and scale factor tells us how much the figure stretches or shrinks. In other words, the dilation is similar, but not the exact same as the original. For example, i n the diagram below, the ordered pair (4,3) is 3 units to the right of the origin and 4 units above the origin.Ī dilation makes a figure larger or smaller, but has the same shape as the original (see figure to the right). The numbers in the ordered pair are separated by a comma, and parentheses are put around them to distinguish them from other points. This is called an " ordered pair" (a pair of numbers in a special order).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |