CCSS.Math.Content.7.NS.A.2a
The standard
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
Common Core State Standards for Mathematics
What this standard means
Students need to multiply positive and negative rational numbers, including fractions and decimals, and explain why the sign rules make sense. They should connect the rules to properties they already know, especially the distributive property, not just memorize “same signs positive, different signs negative.”
Mastery looks like solving products such as -3(2.5), (-2/3)(-9), and 4(-1/2), then explaining the sign using a model, pattern, or property. Students often get stuck when both numbers are negative, or when they mix up multiplication rules with addition rules.
Ways to teach it
- Use red and black counters to model repeated groups, including removing negative groups, then record each product as an equation.
- Ask students to explain why (-1)(-1) must equal 1 using the distributive property and the equation (-1)(1 + -1).
- Give five signed rational number products on index cards and have students sort them into positive, negative, and zero with one explanation.
- Connect products to money by having students calculate repeated debts, repeated deposits, and the effect of removing debts.
Plan a lesson for CCSS.Math.Content.7.NS.A.2a
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Related standards
- CCSS.Math.Content.7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
- CCSS.Math.Content.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
- CCSS.Math.Content.HSA-APR.D.7
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a ...
- CCSS.Math.Content.7.NS.A
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.