In Grade 5, students sort triangles and quadrilaterals into categories based on their properties, and explain why a shape does or does not belong.
Categories can overlap. A square is also a rectangle (4 right angles), a rhombus (4 equal sides), and a parallelogram (2 pairs of parallel sides).
Official benchmarkClassify 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.
On the FAST test: part of the Grade 5 reporting category Geometric Reasoning, Measurement, and Data Analysis and Probability, which is about 23–29% of the test.
Worked Examples
Worked Example 1
Naming a Triangle Two Ways
A triangle has three equal sides.
1By sides: three equal sides make it equilateral.
2By angles: an equilateral triangle has three 60° angles, so it is also acute.
Answer: Equilateral and acute
Worked Example 2
Is a Square a Rectangle?
A square
1A rectangle is a quadrilateral with 4 right angles.
2A square has 4 right angles.
3So a square is a special kind of rectangle.
Answer: Yes
Common Mistakes to Watch For
Thinking a shape can belong to only one category
Wrong:A square is not a rectangle
A square has every property of a rectangle (4 right angles), so it is a rectangle too.
Reversing the relationship
Wrong:Every rectangle is a square
A rectangle needs 4 right angles, but its sides do not have to be equal. Only some rectangles are squares.
Helpful Math Tip
List the properties of each category, then check the shape against each list. If it has all the properties, it belongs.
Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.
