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OhioMaths

Expressions and Structure

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you simplify expressions using the exponent rules, and what does a rational exponent mean as a radical?

Apply the properties of exponents to simplify expressions, including rational exponents interpreted as radicals (Ohio N-RN.1, N-RN.2).
An Ohio Algebra I answer on the exponent rules and radicals (N-RN.1, N-RN.2): the product, quotient, power, zero, and negative rules, and rewriting rational exponents as radicals such as x to the one-half equals the square root of x.
11 min answer →

How do you factor a quadratic trinomial, and how do the factoring patterns (GCF, difference of squares, trinomials) fit together?

Factor quadratic expressions, including GCF, difference of squares, and trinomials, to reveal zeros and equivalent forms (Ohio A-SSE.3a, A-APR).
An Ohio Algebra I answer on factoring (A-SSE.3a): the GCF first, the difference of squares, factoring monic and non-monic trinomials by the product-sum method, and checking by expanding.
12 min answer →

How do you read the parts of an algebraic expression, terms, factors, and coefficients, and interpret what each part means in a real-world model?

Interpret expressions that represent a quantity in terms of its context, identifying terms, factors, and coefficients (Ohio A-SSE.1).
An Ohio Algebra I answer on interpreting the parts of an expression (A-SSE.1): naming terms, factors, and coefficients, and reading what each part means in a context such as a cost or growth model.
11 min answer →

How do you add, subtract, and multiply polynomials, and why is the set of polynomials closed under these operations?

Add, subtract, and multiply polynomials, understanding that polynomials are closed under these operations (Ohio A-APR.1).
An Ohio Algebra I answer on polynomial operations (A-APR.1): combining like terms to add and subtract, distributing the minus sign, multiplying with the distributive property and FOIL, and the idea of closure.
11 min answer →

How do you rewrite an expression into an equivalent form by using its structure, such as factoring out a common factor or recognizing a difference of squares?

Use the structure of an expression to identify ways to rewrite it, and produce equivalent forms to reveal properties of the quantity (Ohio A-SSE.2, A-SSE.3).
An Ohio Algebra I answer on rewriting expressions using structure (A-SSE.2, A-SSE.3): factoring out a GCF, spotting a difference of squares, and choosing the equivalent form that reveals zeros or a starting value.
11 min answer →

How do you use units to set up and check a calculation, and how does accuracy guide how you report an answer?

Reason quantitatively with units, choose and interpret units in formulas, and report answers to an appropriate level of accuracy (Ohio N-Q.1, N-Q.2, N-Q.3).
An Ohio Algebra I answer on quantities and units (N-Q.1 to N-Q.3): unit conversion and dimensional analysis, choosing units in a formula, interpreting a rate, and reporting answers to a sensible accuracy.
11 min answer →