Math properties
Math properties reference sheet
A printable guide to arithmetic and equality properties, with definitions, equations, equivalent names and the nonzero conditions needed for reciprocals and division.
Preview and downloadMath properties practice
Identifying math properties worksheets
Name the property shown by an explanation and example. Choose 10, 12 or 15 questions from arithmetic and equality properties, with a separate answer key.
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Read each statement and example. Write the name of the property it illustrates. Use the reference handout when you need to compare definitions.
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Customize this worksheetPaper sizes and printing help · More math properties activities
Choose the properties learners are ready to name
Choose 10, 12 or 15 questions, then select at least that many property types. Each question asks for a name from a statement and an example. The key accepts both additive identity and addition property of zero where either name describes the same rule.
An answer can be mathematically correct even if its wording differs from one textbook. Compare the meaning of the property, rather than treating an accepted synonym as an error.
Learning objective
What this activity builds
Recognize what changes and what stays the same in a mathematical statement, then name the property that explains it.
Worked example
Which property explains (4 + 7) + 2 = 4 + (7 + 2)?
The associative property of addition.
The numbers stay in the order 4, 7, 2. Only their grouping changes. A change in order, such as 4 + 7 = 7 + 4, would illustrate the commutative property instead.
Teaching notes
Make the practice count
- Ask learners to describe the change before asking for its formal name.
- Underline a changed grouping and circle a changed order in different examples.
- Accept additive identity and addition property of zero as two names for the same idea.
- Introduce equality rules after learners can explain why an equation stays balanced.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose at least as many properties as questions. Each property appears at most once, and additive identity accepts “addition property of zero” as an equivalent name.
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