We want students to look for the perpendicular measurements, which in the case of a rhombus, are the diagonals. Question 5 is aimed at getting students to see which dimensions on the original shape make up the “base” and the “height” of the new rectangle. Later in question 6, they will see that if no sides are parallel, the path to making a rectangle is not as clear cut because congruent angles are not guaranteed. It is important for students to make use of the parallel lines of the bases to identify the congruent corresponding angles. Are there other methods?Ī key question to ask students as you monitor groups is why the triangular piece of the parallelogram, for example, fits perfectly onto the side of the parallelogram. Though students may use different dimensions to determine the “base” and “height”, their final area will be the same. Below we’ve shown some different ways to rearrange a trapezoid into a rectangle. There are multiple ways students can go about doing this, and seeing the different strategies always proves to be very interesting to students. Using the constraint that they can only make 2 cuts, we ask students to turn a parallelogram, trapezoid, and rhombus into a rectangle and apply the rectangle area formula of base x height. Since there are two per page, we recommend printing two copies of the whole document for each group so students have four copies of each shape. Then students start investigating other shapes.Įach group will need several copies of each shape. For rectangles and squares this is easy, but what if we don’t have full squares? Students investigate this first on a coordinate grid where they may combine partially shaded boxes to make full boxes or take off the triangular part and arrange it on the other side to make a rectangle. First, we remind students that finding an area is nothing more than determining, by counting, or some other strategy, how many unit squares make up an object. Now that students have made important observations about the diagonals of several quadrilaterals, we’re ready to apply these properties to finding their areas. Day 19: Random Sample and Random Assignment.Day 18: Observational Studies and Experiments.Day 13: Probability using Tree Diagrams.Day 12: Probability using Two-Way Tables.Day 6: Scatterplots and Line of Best Fit.Day 3: Measures of Spread for Quantitative Data.Day 2: Measures of Center for Quantitative Data.Day 4: Surface Area of Pyramids and Cones.Day 2: Surface Area and Volume of Prisms and Cylinders.Day 1: Introducing Volume with Prisms and Cylinders.Day 9: Area and Circumference of a Circle.Day 6: Inscribed Angles and Quadrilaterals.Day 5: Perpendicular Bisectors of Chords.Day 1: Coordinate Connection: Equation of a Circle.Day 4: Using Trig Ratios to Solve for Missing Sides.Unit 7: Special Right Triangles & Trigonometry.Day 7: Area and Perimeter of Similar Figures.Day 6: Proportional Segments between Parallel Lines.Day 2: Coordinate Connection: Dilations on the Plane.Day 1: Dilations, Scale Factor, and Similarity.Day 9: Regular Polygons and their Areas.Day 8: Polygon Interior and Exterior Angle Sums.Day 4: Coordinate Connection: Quadrilaterals on the Plane.Day 3: Properties of Special Parallelograms. ![]() Day 2: Proving Parallelogram Properties.Unit 5: Quadrilaterals and Other Polygons.Day 12: More Triangle Congruence Shortcuts.Day 11: More Triangle Congruence Shortcuts.Day 9: Establishing Congruent Parts in Triangles.Day 5: Right Triangles & Pythagorean Theorem.Day 4: Angle Side Relationships in Triangles.Day 3: Proving the Exterior Angle Conjecture.Day 9: Coordinate Connection: Transformations of Equations.Day 8: Coordinate Connection: Parallel vs.Day 7: Coordinate Connection: Parallel vs. ![]()
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