CCSS.Math.Content.7.NS.A.1d
The standard
Apply properties of operations as strategies to add and subtract rational numbers.
Common Core State Standards for Mathematics
What this standard means
Students need to use properties like commutative, associative, and additive inverse to make adding and subtracting rational numbers easier. They should work with integers, fractions, decimals, and mixed numbers, including negatives, and explain why a strategy works.
Mastery looks like choosing efficient moves, such as pairing opposites, regrouping friendly numbers, or changing subtraction to adding the opposite. Students often get stuck with negative signs, subtracting a negative, and mixing fraction and decimal forms in one problem.
Ways to teach it
- Hands-on: Give students signed number cards and have them physically group opposites and friendly sums before writing matching equations.
- Prompt: Ask students to explain two ways to solve -3.5 + 8 + 3.5 - 2 and compare which is cleaner.
- Quick check: Show 7/8 + (-2.25) + (-7/8) and ask students to solve and name the property used.
- Real-world: Use a bank account ledger with deposits, withdrawals, and refunds, then have students reorder entries to find the balance efficiently.
Plan a lesson for CCSS.Math.Content.7.NS.A.1d
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Related standards
- CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- CCSS.Math.Content.3.OA.B.5
Apply properties of operations as strategies to multiply and divide.
- CCSS.Math.Content.7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
- CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract.