Area of Parallelograms and Triangles - Lesson Plan [Show Teaching Plan Only][Show All]

Teaching Plan

This eModule is split into five sections and a quiz, each with multiple activities.

Area of Parallelograms and Triangles (50 minutes)

Area of Parallelograms

The objectives of this lesson is for students to construct the formula for the area of a paralellogram.

1. (1 activity) Students create parallelograms by distorting a rectangle. Students explain the relationship between the area of parallelograms and rectangles.
2. (1 activity) Students are presented the definition of base and height of parallelograms. They are then guided through the process of comparing height and base with length and width.
3. (1 activity) Students are presented with an animation of the geometric relationship of paralellograms and rectangles. Students then predict the formula for area of a paralellogram based on the formula for area of rectangles.
4. (1 activity) Students are presented with examples to calculate of area.

Area of Triangles

The objectives of this lesson is for students to construct the formula for the area of a paralellogram.

1. (1 activity) Students create triangles by cutting a rectangle and distorting the resulting right triangle. Students explain the relationship between the area of triangles with the same base and height.
2. (1 activity) Students are presented the definition of base and height of triangles. They are then guided through the process of comparing height and base with length and width.
3. (1 activity) Students are presented with an animation of the geometric relationship of triangles and rectangles. Students then predict the formula for area of a triangle based on the formula for area of rectangles.
4. (1 activity) Students are presented with examples to find area of triangles.

Measuring Area: Addition Method

The objective of the second lesson is to teach students the addition method for finding the area of shapes with diagonals and to give them practice with the method.

1. (2 activities) Students find areas of figures by comparing them to triangles and rectangles.
2. (1 activity) Students explain how to find the area of a shape that has diagonal edges Students find the area of the shape.
3. (1 activity) Students are presented with the algorithm for splitting a shape into rectangles and triangles and then adding the areas of all the pieces together.
4. (7 activities, 2 online) Students practice finding the area of shapes using the addition method.
5. (1 activity) Students are asked to describe how they would find the area of a shape containing an obtuse triangle.

Measuring the Area of Shapes with Diagonals: Subtraction Method

The objective of the second lesson is to teach students the addition method of finding the area of shapes with diagonals and give them practice with the method.

1. (1 activity) Students are presented with the algorithm for splitting a figure into rectangles and triangles and subtracting away the areas not included in the figure.
2. (4 activities) Students practice finding the area of shapes using the subtraction method.
3. (1 activity) Students are asked to describe how they would find the area of a more complicated irregular figure.

Creating Shapes of a Given Area

The objective of the third lesson is to have students create shapes of a given area.

1. (5 activities) Students create shapes with diagonals of a given perimeter.
2. (2 activities) Students create a figure with a given area and number of sides. Students explain the process they used

Quiz

1. As the need arises, review concepts and processes with the class before having students complete the quiz.
2. (7 activities, 5 online) Students find areas of shapes and construct figures of a given area.

Assessment

Each section has its own online assessment.

Credits

Correlation to Standards

Correlation to Utah Standards

• 6.IV.2.e Calculate the areas of triangles, rectangles, and parallelograms using given formulas.
• 7.IV.2.3 Develop formulas for the area of parallelograms (including rectangles and squares) and triangles.
• 7.IV.2.4 Determine perimeters of polygons and circumferences of circles; areas of triangles, parallelograms, and circles; volumes of right rectangular and triangular prisms and cylinders; and surface areas of right rectangular and triangular prisms and cylinders using formulas.
• PreAlg.IV.2.6 Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids.
• PreAlg.IV.2.6 Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas.

Correlation to Maine Standards

• F.3-4.1 Solve and justify solutions to real-life problems involving the measurement of time, length, area, perimeter, weight, temperature, mass, capacity, and volume.
• F.5-8.3 Demonstrate an understanding of length, area, volume, and the corresponding units, square units, and cubic units of measure.
• F.S.2 Derive and use formulas for area, surface area, and volume of many types of figures.

Correlation to North Carolina Standards

• 4.2.01 Develop strategies to determine the area of rectangles and the perimeter of plane figures.
• 4.2.02 Solve problems involving perimeter of plane figures and areas of rectangles.
• 6.2.01 Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.
• 6.2.02 Solve problems involving perimeter/circumference and area of plane figures.

Correlation to Massachussetts Standards

• 2.M.6 Make and use estimates of measurement, including time, volume, weight, and area.
• 4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring.
• 4.M.5 Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.
• 6.M.1 Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate.
• 6.M.4 Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes.
• 8.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.

Correlation to Arizona Standards

• S4.C4.G3.PO 9 Determine the perimeter using a rectangular array.
  
• S4.C4.G3.PO 10 Determine the area using a rectangular array. 
• S4.C4.G4.PO 9 Determine the area of squares and rectangles.
• S4.C4.G5.PO 5 Solve problems involving the perimeter of convex polygons.
  
• S4.C4.G5.PO 6 Determine the area of figures composed of two or more rectangles on a grid.
• S4.C4.G5.PO 7 Solve problems involving the area of simple polygons.
• S4.C4.G6.PO 6 Solve problems involving the perimeter of polygons.
  
• S4.C4.G6.PO 7 Determine the area of triangles.
• S4.C4.G6.PO 9 Solve problems for the areas of parallelograms (includes rectangles).
• S4.C4.G6.PO 10 Identify parallelograms having the same perimeter or area.
• S4.C4.G7.PO 6 Solve problems for the areas of parallelograms, traingles, and circles.
• S4.C4.G7.PO 7 Identify polygons having the same perimeter or area.
• S5.C1.G5.PO 3 Develop an algorithm or formula to calculate areas of simple polygons.