Five pages that build the area formulas from the rectangle. Page 1 draws right triangles on a grid inside their rectangles: the rectangle is b × h, and the shaded triangle is half of it. A table makes the pattern clear, and students write the formula A = 1/2 × b × h and explain why it works. Page 2 estimates first, rounding each side to the nearest ten (a 12 ft by 9 ft triangle is about 1/2 × 10 × 10 = 50 square feet), then finds the exact area, 54 square feet. Then the triangles have all three sides labeled, so students must use the two sides that meet at the right angle, even on a triangle standing on its longest side. Page 3 cuts a triangle off a parallelogram and moves it to make a rectangle with the same base and height, finds areas on a grid, then the area and perimeter of labeled parallelograms. Page 4 joins two copies of a triangle into a parallelogram, so any triangle is half of b × h; the grid and the labeled triangles include ones whose height falls outside the triangle. Page 5 splits trapezoids into a rectangle and triangles and adds the parts, then six story problems ask for an area, a perimeter or a missing height, and students write the units.
Cut a paper rectangle along its diagonal and lay the two right triangles on top of each other: they match, so each is half. Do the same with a parallelogram: cut along the height and slide the triangle to the other end. Before page 4, have students trace a triangle, cut out two copies, and make a parallelogram from them. On page 5, ask why one answer is in square feet and another only in feet.
Look for triangles and parallelograms at home: a slice of sandwich cut corner to corner, a kite, a roof. Ask your child which line is the height and how they know it meets the base at a right angle.
This pack supports the following Common Core State Standards for Mathematics:
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
A 5-page area pack for 5th grade. See on a grid that a right triangle is half of a rectangle, fill in a table, and write the formula A = 1/2 × b × h. Estimate the area of right triangles by rounding the sides, then find the exact area in square units, even when all three sides are labeled. Cut a triangle off a parallelogram to make a rectangle (A = b × h), find the area of any triangle from its base and dashed height, split trapezoids into a rectangle and triangles, and solve area and perimeter story problems with the right units. Every page comes in color and in black and white. Answer keys included.
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