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Discovering the Area Formula for Triangles

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Discovering the Area Formula for Triangles

Grade Levels

6th Grade, 7th Grade, 8th Grade

Course, Subject

Related Academic Standards
CC.2.2.HS.C.1 CC.2.2.HS.C.1
Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.3.7.A.3 CC.2.3.7.A.3
Intentionally Blank
CC.2.3.HS.A.3 CC.2.3.HS.A.3
Verify and apply geometric theorems as they relate to geometric figures.
CC.2.3.HS.A.9 CC.2.3.HS.A.9
Extend the concept of similarity to determine arc lengths and areas of sectors of circles.
CC.2.3.HS.A.12 CC.2.3.HS.A.12
Explain volume formulas and use them to solve problems.
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  • Big Ideas
    Measures can be estimated by using known referents.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
    Objects can be transformed in an infinite number of ways. Transformations can be described and analyzed mathematically.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.
    Some geometric relationships can be described and explored as functional relationships.
    Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
    Spatial reasoning and visualization are ways to orient thinking about the physical world.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
  • Concepts
    2- and 3-dimensional figures
    Area and Volume
    Geometric probability
    Geometric Relations: Congruence and Similarity
    Geometric Representations
    Sampling as a method of estimation and prediction
  • Competencies
    Apply geometric properties of length or area to represent and calculate probabilities.
    Define and describe types of geometrical reasoning and proof, using them to verify valid conjectures as they surface in the study of geometry; develop a counter example to refute an invalid conjecture.
    Define, describe, and analyze 2- and 3-dimensional figures, their properties and relationships, including how a change in one measurement will affect other measurements of that figure.
    Extend previous understandings of the characteristics of 2-d and 3-d shapes, including the measures of area and volumes, by exploring, solving, and interpreting real world problems.
    Extend previous understandings of the characteristics of 3d-shapes to develop an understanding of, and use formulas to determine surface areas and volumes.

Description

In this lesson, students develop the area formula for a triangle. Students find the area of rectangles and squares, and compare them to the areas of triangles derived from the original shape.

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Discovering the Area Formula for Triangles

Content Provider

Illuminations

 

Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.  Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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