CCSS.Math.Content.HSA-APR.D

CCSS.Math.Content.HSA-APR.D is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSA-APR.D.6

  Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the ...

• 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 ...

01

What Students Need to Do

Students factor and divide polynomials to write rational expressions in equivalent forms. They add, subtract, multiply, and divide these expressions while tracking values that make denominators zero.

02

What Mastery Looks Like

Students factor, divide, and combine rational expressions accurately. They show why two forms are equivalent and keep track of values that make an original denominator zero.

03

Common Misconceptions

Students cancel terms across addition, such as canceling x in (x + 2)/x. They may add denominators when adding fractions or forget to multiply by the reciprocal when dividing. They also drop excluded values after factors cancel.

04

How to Assess It

Give the exit ticket: Rewrite (x² + 3x + 5)/(x + 1) as a polynomial plus a fraction, and state the excluded value.

1. 01

   Give pairs factor cards to build numerators and denominators, cancel common factor cards, and record excluded values before simplifying.

2. 02

   Ask students to explain why (x + 2)/x cannot become 2, then correct the cancellation error in writing.

3. 03

   Run a matching game with cards showing factored, expanded, simplified, and restricted forms of the same rational expression.

4. 04

   Use C(x) = 500 + 8x and have students rewrite C(x)/x to interpret fixed cost and variable cost per item.

• CCSS.Math.Content.HSN-RN.A.2

  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

• CCSS.Math.Content.HSN-RN.A

  Extend the properties of exponents to rational exponents.