Created by Christopher Malavar
12 questions
9th Grade
Math
Updated Oct 2026
The Closure Property worksheet is designed for Grade 9 mathematics students learning to determine whether a set remains within the same set after an operation. Across 12 questions—11 multiple choice and 1 multiple-select item—students identify that rational numbers are closed under addition and distinguish which operations polynomials are always closed under: addition, subtraction, and multiplication, but not division. This free printable worksheet gives students repeated practice interpreting closure statements in true-or-false, operation-selection, and select-all-that-apply formats. It helps teachers check whether students can distinguish a valid closure property from an operation that does not preserve polynomials, while the included answer key supports efficient review and feedback. Use it for Grade 9 math instruction, independent practice, or a quick formative assessment of students’ understanding of polynomial operations.
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WorksheetsAnswer KeyAddition
, c)Multiplication
, d)Subtraction
Division
True
False
True
True
This Grade 9 mathematics worksheet covers identifying closure under operations, with a rational-number item focused on addition and polynomial items focused on addition, subtraction, multiplication, and division. Its 12 questions use true-or-false, multiple-choice, and one select-all-that-apply format to help students determine which operations keep the result within the set of polynomials.
Introduce closure as a question of whether performing an operation keeps the result in the same number set, then model one polynomial example before students complete the worksheet. Have students explain why addition, subtraction, and multiplication are selected for polynomials while division is not, and use the select-all-that-apply item to prompt discussion about why more than one operation may be correct.
Students may assume that every familiar operation is closed for polynomials and incorrectly select division alongside addition, subtraction, and multiplication. They may also treat a true-or-false statement as asking whether an operation is sometimes possible rather than whether it is always closed, or miss one correct choice in the multiple-select polynomial item.
On Wayground, you can assign the Closure Property worksheet as a printable PDF or use it as a digital quiz. It includes a complete answer key for the rational-number and polynomial operation questions, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.
Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size when students need more visual room to read the operation choices and true-or-false statements. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the multiple-choice and select-all-that-apply format intact.
Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
