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In Shannon’s math class, they have just begun working in the Geometric Reasoning strand. Her teacher introduced MA.7.GR.1.1. (Apply formulas to find the areas of trapezoids, parallelograms and rhombi) by giving each student grid paper and having them copy figures, beginning with a parallelogram from the board.
Shannon attempted to copy the figures, but inaccurately did so. Additionally, she had difficulty recalling definitions of figures.
The teacher then provided Shannon’s class with a worksheet of six similar problems for them to work out. Note: This is a commonly used worksheet with problems that are simple recall (base times height).
Shannon had difficulty with not only copying the figure but also with applying formulas and repetitively got incorrect answers. She was embarrassed by her difficulties and didn’t want to work with others. The way that Shannon’s teacher was providing instruction was not supporting her understanding.
Guiding Questions
What could allow Shannon to be able to access the instruction?
What could allow Shannon to better apply and transfer knowledge with mathematical concepts?
How could Shannon demonstrate her learning in other ways?
Redesign
Shannon’s teacher now designs instructional activities around cognitive learning processes and the UDL framework to ensure that students have options for accessing and engaging with high-quality math instruction, as well as a variety of ways to demonstrate their learning.
He now provides options for students to access instruction in an effort to decrease difficulty with applying formulas to find the areas of trapezoids, parallelograms and rhombi. For example, he models by co-creating a graphic organizer with images and formulas for trapezoids, parallelograms, and rhombi by using different colors to connect the dimensions of the figures to the variables within the formulas.
He has also created an anchor chart with the math vocabulary that will be needed for the concept.
During instruction he uses concrete and virtual manipulatives. For example, students can explore finding the area of figures using manipulatives (concrete and virtual) to develop conceptual understanding.
Using a virtual Geoboard, he explains that if you cut the parallelogram along its height and move the triangle to the other side of the parallelogram, you now have a triangle. Both the area of a rectangle and area of a parallelogram are base x height.
Shannon’s teacher provides options for students to actively engage with the content in one of the learning centers.
Center 1 ( B1G-M Instructional Task): Trace a parallelogram or a rhombus on a sheet of graph paper. Highlight (or color) each of the sides a different color. Slice your two-dimensional figure vertically from a vertex at a right angle to an opposite side to create a right triangle. Move the sliced-off portion to form a rectangle.
Center 2 (B1G-M Instructional Item): A new park is being built in the shape of a trapezoid. The builders will cover the ground with a solid rubber surface to ensure the children playing have a safe and soft place to land when they jump or fall. How many square yards of rubber will be needed for this park?
Center 3 (Small group with teacher): Teacher provides explicit instructions on finding the areas of trapezoids, parallelograms and rhombi using a graphic organizer.
Finally, he provides a variety of options for demonstrating learning, other than copying figures and determining the area. This decreases the possibility of incorrectly copying the figures. For example, all students had the following options:
Complete a worksheet finding the area of nine two-dimensional figures (three parallelograms, three trapezoids and three rhombi).
Create a representation, using a graphic organizer, of real-world objects (one parallelogram, one trapezoid and one rhombus) and determine their areas.
Complete an interview with the teacher, after creating a cut-out of each of the three two-dimensional figures, explaining how to determine the area.
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