• MA.5.GR.1 Geometric Reasoning

Classify two-dimensional figures and three-dimensional figures based on defining attributes.

MA.5.GR.1.1

Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not
belong to a category.

Benchmark Clarifications:
Clarification 1: Triangles include scalene, isosceles, equilateral, acute, obtuse and right; quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.

Purpose and Instructional Strategies
The purpose of this benchmark is for students to understand that shapes can be classified by their attributes and these attributes may place them in multiple categories. In Grade 3, students identified and drew quadrilaterals based on their attributes (MA.3.GR.1.2). In Grade 4, students explored angle classifications and measures in two-dimensional figures (MA.4.GR.1.1). This past work built the understanding required for students to classify triangles and quadrilaterals in Grade 5. Classification of geometric figures will return in high school geometry (MA.912.GR.3.2) using another Grade 5 concept, the coordinate plane.

 The work in Grade 5 will help students to understand that triangles can be defined by two different attributes that students can actually measure: the length of their sides (3 congruent sides, 2 congruent sides, or 0 congruent sides) or by the size of their angle measures (3 acute angles, 2 acute angles and a right angle, or 2 acute angles and an obtuse angle).

 During instruction, it is important for students to have practice with classifying figures in multiple ways so they can better understand the relationship between attributes of the geometric figures. In addition, students should practice this concept by using graphic organizers such as, flow charts, T-charts and Venn diagrams (MTR.2.1).

 This benchmark requires a strong understanding and use of geometry vocabulary. Allow students to use math discourse throughout instruction to compare the attributes of geometric figures. For example, pose questions such as, “Why is a square always a rhombus?” and “Why is a rhombus not always a square?” Lesson activities should require students to justify their thinking when making mathematical arguments about geometric figures (MTR.4.1).

Common Misconceptions or Errors

 Students may think that when describing and classifying geometric shapes and placing them in subcategories, the last subcategory is the only classification that can be used.

 Students may think that a geometric figure can only be classified in one way. For example, a square (a shape with 4 congruent sides and 4 congruent angles) can also be a parallelogram because it contains 2 pairs of sides that are congruent and parallel.

Part A. Roll a number cube twice and write a statement based on the key below.
Number Cube Key
1 – Equilateral
2 – Acute
3 – Right
4 – Obtuse
5 – Isosceles
6 – Scalene
Part B. Write a statement that reads, “A(n) ___________ (roll 1) triangle is ______________ (always, sometimes or never) a(n) ____________ triangle (roll 2).” Complete your statement by determining whether the category of triangle from roll 1 is always, sometimes, or never the category of triangle from roll 2. Complete this process three more times for a total of four statements.
Part C. Choose one of the statements that you said is sometimes true. Give an example of when the statement is true and when the statement is not true using picture models or words. If none of your statements are sometimes true, then create one to give an example.

Instructional Items
Instructional Item 1
Choose all the shapes that can always be classified as parallelograms.
a. Trapezoid
b. Rectangle
c. Rhombus
d. Square
e. Equilateral Triangle

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