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Dilation Teacher Resources
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Working in pairs, geometry students will construct a dilation and consider the properties associated with the similar figures that are created to verify the properties of dilation. This activity can be done using dot or graph paper and rulers, compasses, and protractors, geoboards, or dynamic geometry software. Extensions can be added by considering dilations affected by different scale factors, or by dilating other figures such as triangles or parallelograms.
Geometric transformations are explored by high schoolers. They will create a set of instructions for plotting coordinates representing an original transformation of a real-world figure. These instructions are shared with middle schoolers, who reproduce the transformation by plotting the given points, then hypothesizing the name of the figure that was transformed. The project is discussed collaboratively through the use of video conferencing.
Several practice exercises suitable for any geometry class working on transformation, symmetry, and tessellation -- especially visual representations of image translation, rotation, and reflection, symmetry, tessellations and tangrams -- can be drawn from this resource. Much of it works with the computer component of Neufeld Learning System's math program, but three center pages could be well used anywhere.
Mathematicians analyze the vertex form of a parabola and find an approximate fit of a model. They explain the quadratic parabola function and its properties by developing quadratic models. They use translation and dilation to change the general parabola. PDF downloads of the lab activity are included.
Middle schoolers construct a three-dimensional model of a city using both similar and congruent figures and geometric transformations. City must have at least ten buildings with each building labeled and may be constructed out of paper or modeling clay. A two-dimensional representation, drawn to scale, must be included as well.
Here is a lesson that starts out with learners creating congruent figures by drawing the exact same polygon as their partner. From here, they have a discussion about why what they drew is an exact copy, followed by other activities that look at different shapes, some with transformations, to determine their congruence.
In this transformations worksheet, 10th graders solve and complete 16 different types of problems. First, they graph the image of the figure using the transformation given. Then, students find the coordinates of the vertices of each figure after the given transformation.
In this transformations worksheet, 10th graders solve and complete 10 various types of problems. First, they draw the graph of a parabola for all values of x in the interval. Then, students graph and state the coordinates of a triangle. They also write an equation for a given image under the composition of translations.
Twelfth graders explore transforming matrices representing figures in the coordinate plane by entering data points of figures such as triangles and quadrilaterals into a matrix. Students dilate, rotate, reflect, and translate the figures by multiplying by translation matrices.
Ninth graders explore the use of transformations to demonstrate geometric properties. They draw, measure, and construct geometric figures with given dimensions. Pupils sketch various transformations of geometric figures. They discuss the common transformations and view those transformations.