Reasoning to Find Area: Lesson 4 Students were introduced to parallel lines …
Reasoning to Find Area: Lesson 4
Students were introduced to parallel lines in grade 4. While the standards do not explicitly state that students must work with parallelograms in grades 3–5, the geometry standards in those grades invite students to learn about and explore quadrilaterals of all kinds. The K–6 Geometry Progression gives examples of the kinds of work that students can do in this domain, including work with parallelograms.
In this lesson, students analyze the defining attributes of parallelograms, observe other properties that follow from that definition, and use reasoning strategies from previous lessons to find the areas of parallelograms.
By decomposing and rearranging parallelograms into rectangles, and by enclosing a parallelogram in a rectangle and then subtracting the area of the extra regions, students begin to see that parallelograms have related rectangles that can be used to find the area.
Throughout the lesson, students encounter various parallelograms that, because of their shape, encourage the use of certain strategies. For example, some can be easily decomposed and rearranged into a rectangle. Others—such as ones that are narrow and stretched out—may encourage students to enclose them in rectangles and subtract the areas of the extra pieces (two right triangles).
After working with a series of parallelograms, students attempt to generalize (informally) the process of finding the area of any parallelogram (MP8).
A web page and interactive applet showing the ways to calculate the …
A web page and interactive applet showing the ways to calculate the area of a parallelogram. The user can drag the vertices of the parallelogram and the other points change automatically to ensure it remains a parallelogram. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area, which is continuously recomputed and displayed. The text on the page gives three different ways to calculate the area with a formula for each. The applet uses one of the methods to compute the area in real time, so it changes as the rhombus is reshaped with the mouse. A companion page is http://www.mathopenref.com/parallelogram.html showing the definition and properties of a parallelogram Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
The attached PDF provides learners with a unique way to find geometric …
The attached PDF provides learners with a unique way to find geometric shapes through pictures. In the case, the search is for Trapezoids and Parallelograms. Use, revise, or be inspired by the ideas and create your own to support your learners.
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