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Exploring the Isometric Drawing Tool

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Exploring the Isometric Drawing Tool

Grade Levels

10th Grade, 11th Grade, 12th Grade, 7th Grade, 8th Grade, 9th Grade

Course, Subject

Geometry
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.2.3.8.A.2 CC.2.3.8.A.2
Understand and apply congruence, similarity, and geometric transformations using various tools.
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 attributes of objects are measureable, e.g., length, mass, capacity, and can be quantified.
    Some geometric relationships can be described and explored as functional relationships.
    Spatial reasoning and visualization are ways to orient thinking about the physical world.
    The same number sentence (e.g., 12 - 4 = 8) can be associated with different concrete or real world situations, AND different number sentences can be associated with the same concrete or real world situation.
    The set of real numbers has infinite subsets including the sets of whole numbers, integers, rational, and irrational numbers.
    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.
    Two- and three-dimensional objects can be described, classified, and analyzed by their attributes, and their location can be described quantitatively.
  • Concepts
    2- and 3-dimensional figures
    Distance, Pythagorean Theorem
    Estimation: Products, sizes, distance
    Geometric probability
    Geometric Relations: Congruence and Similarity
    Geometric Representations
    Polygons and Polyhedra
    Polygons: Area and the relationships between the different polygons
    Proportionality: Similar figures and objects, scale factors, unit rate
    Representations
    Sequence: Numbers and objects
    Symmetry: Mirror
  • Competencies
    Apply geometric properties of length or area to represent and calculate probabilities.
    Compute fluently and solve problems using positive and negative rational numbers (including integers).
    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.
    Understand and apply the Pythagorean Theorem to find distances between points in a coordinate plane and to analyze polygons and polyhedra.
    Understand area as a measurable attribute and select appropriate units, strategies (e.g., decomposing) and tools to solve problems or make estimations. Use properties of 2-dimensional shapes to find the area of polygons; connect the area/array model of multiplication to the area formula for rectangles, and use this connection to justify the formula.
    Use fundamental facts about distances and angles to describe and analyze figures and situations in 2- and 3-dimensional spaces and to solve problems including those with multiple steps.

Description

Students explore using the isometric drawing tool and gain practice and experience in manipulating drawings.

Web-based Resource

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Exploring the Isometric Drawing Tool

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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