CCSS.Math.Content.HSA-APR.A.1
The standard
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Common Core State Standards for Mathematics
What this standard means
Students need to combine polynomial expressions by adding, subtracting, and multiplying them. They should understand that when you do these operations with polynomials, the answer is still a polynomial. They also need to handle like terms, signs, exponents, and distribution accurately.
Mastery looks like clean, organized work with correct use of the distributive property and exponent rules. Students can explain why a product like (x + 3)(x - 5) is still a polynomial. Common trouble spots are subtracting a whole polynomial, multiplying binomials without missing terms, and adding exponents instead of multiplying coefficients.
Ways to teach it
- Use algebra tiles to model (x + 2)(x + 3), then have students write the matching expanded polynomial.
- Ask students to explain why adding two polynomials can never create a square root or variable in the denominator.
- Give a four-question exit ticket: one sum, one difference, one monomial product, and one binomial product.
- Have students write a polynomial for the area of a rectangular garden with sides x + 4 and x + 7.
Plan a lesson for CCSS.Math.Content.HSA-APR.A.1
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Related standards
- CCSS.Math.Content.HSA-APR.A
Perform arithmetic operations on polynomials
- CCSS.Math.Content.1.OA.B
Understand and apply properties of operations and the relationship between addition and subtraction.
- CCSS.Math.Content.HSN-CN.C.9
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
- 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 ...