Aligned Division Algorithms Worksheet | Grade 11 Algebra II

This Grade 11 Algebra II worksheet teaches students to compare long division, synthetic division, and the Remainder Theorem when rewriting a rational expression as a quotient plus a remainder over the divisor. Students finish able to read, translate, and defend each form with exact work.

At a Glance

• Grade: 11 · Subject: Algebra II
• Standard: HSA-APR.D.6 — Rewrite a(x)/b(x) as q(x) + r(x)/b(x) using long or synthetic division
• Skill Focus: Comparing long division, synthetic division, and remainders
• Format: 5 pages · 12 problems · Answer key included · PDF
• Best For: Polynomial division unit practice and review
• Time: 40–50 minutes

What's Inside

Twelve tasks across 5 pages, organized in three parts: Read the Forms, Translate and Compare Forms, and Explain Agreement or Inconsistency. A reminder box states the division identity, the x − c limit on synthetic division, and the exact-answer convention. A 3-page answer key is included.

Skill Progression

• Guided practice (Part A, 3 tasks): Students interpret a synthetic division table, a given identity, and a rational equation without redoing the division.
• Supported practice (Part B, 6 tasks): Students run long division, synthetic division, the Remainder Theorem, a divisor like 2x − 1, and two reconstructions.
• Independent practice (Part C, 3 tasks): Students judge sample student work and explain in sentences, backed by calculation.

The sequence follows gradual release: I Do, We Do, You Do.

Standards Alignment

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 degree of r(x) less than the degree of b(x). The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

• After direct instruction: Assign Parts A and B as guided classwork once students have seen both algorithms.
• Before a unit quiz: Use Part C as a review discussion in pairs.

Formative tip: while students work, check whether they write a 0 for each missing power of x. Expect 40–50 minutes in total.

Who It's For

Designed for Grade 11 Algebra II students who can already divide polynomials and now need to connect methods and explain remainders. Part A works as an entry point for students who need support. Pair it with an anchor chart that compares long division and synthetic division side by side.

HSA-APR.D.6 asks students to rewrite a(x)/b(x) in the form q(x) + r(x)/b(x), where the degree of r(x) is less than the degree of b(x), using inspection or long division. This Grade 11 Algebra II worksheet builds that skill through 12 tasks over 5 pages. Students read synthetic division tables, compare long and synthetic division, apply the Remainder Theorem, reconstruct a dividend, and diagnose errors in sample student work. Because the standard rewards flexible representation rather than one procedure, each task pairs an algorithm with a reason it works. Fisher & Frey (2014) describe the move from modeled to independent work as gradual release of responsibility, and the three parts here follow that model. A 3-page answer key supports quick checking.