Name: Adding + Subtracting Polynomials – Leveled Worksheet
SKU: 632fc2402834d878640e48b4
Price: 39.99 USD
Availability: InStock

About this resource

What's inside this resource

Adding and Subtracting Polynomials - Leveled Checking Worksheet This math resource provides practice with adding and subtracting polynomials for high school algebra students. The worksheet features 4 sets of 3 problems each that allow students to check and reinforce their understanding at different levels. Sets A and B have students match their work to an answer bank. Set C gives a proposed answer for students to verify. Set D has students complete problems and show all work. With various levels of scaffolding and answer keys included, this resource can be used for whole-class instruction, small group practice, homework, or individual assignments to build fluency with manipulating polynomial expressions. The leveled nature of the worksheet allows teachers to differentiate to meet each learner’s needs.

What's included

Set A: three addition problems, from 3x² − 4x + (2x² + 5x), with a three-option Answer Bank in which every letter is used
Set B: three subtraction problems, from x² − 7 − (2x² + 2), with a six-option Answer Bank and the note "Not all answer choices will be used"
Set C: three problems each supplied with a proposed answer and a Correct / Incorrect choice, under the direction "Show all work that led you to your decision"
Set D: three problems with no scaffolding and the direction "Complete each problem below, showing all work!"
A two-page ANSWER KEY reproducing all four sets with a worked intermediate line and a final simplified answer for each of the twelve problems
A Name line and the ©EightGoneSideways2021 footer on every page

Resource types: Worksheets & Printables, Worksheets

In the classroom

Teaching tips & learning objectives

Learning objectives

Add polynomials by combining like terms, as in 3x² − 4x + (2x² + 5x) = 5x² + x
Subtract a polynomial by distributing the negative across every term inside the bracket, as in x² − 7 − (2x² + 2) = −x² − 9
Judge whether a supplied answer to a polynomial problem is correct, and justify the judgement with written working
Locate a simplified result among a bank of similar-looking options, distinguishing it from answers produced by a mishandled sign
Set out full working for a polynomial calculation rather than recording the answer alone

Teaching tips

The four sets are a deliberate gradient — matching with every option used, then matching with distractors, then checking someone else's answer, then solving unaided — so they can be released one at a time as a lesson progresses rather than handed out as a single sheet
Set C is the diagnostic one: two of its three proposed answers are wrong, and both go wrong at the same place, distributing the minus sign across a subtracted bracket
Set B's extra answer-bank options are not padding — they are the results of exactly that sign slip, so a student choosing one has revealed the misconception rather than simply guessing
The key shows the intermediate line as well as the final answer, so it doubles as worked examples if a set is used for whole-class modelling
All twelve expressions stay at or below degree two with small integer coefficients, which keeps arithmetic out of the way of the sign work being assessed

Skills covered

Adding polynomials — Set A combines like terms across sums such as 3x² − 4x + (2x² + 5x) and x² + 5x + (3x² + 6x − 7).
Subtracting polynomials — Sets B, C and D all require distributing a negative across a bracket, as in x − 12 − (x² + 16x − 12), which the key expands term by term before simplifying.
Checking another person's working — Set C supplies a proposed answer for each of three problems and asks students to rule on it and show what led them there.
Reading against a bank of near-miss answers — Set B lists six options for three problems, several of them results of a mishandled subtraction sign, such as −x² − 5 alongside the correct −x² − 9.
Setting out working — Sets C and D both instruct students to show all work, and the key models an intermediate line for every problem.

Good to know

Questions teachers ask about this resource

How do the four sets differ from one another?

By how much support they give. Set A is matching with exactly one option per problem; Set B is matching with three spare options that will not be used; Set C supplies an answer and asks students to judge it; Set D gives nothing but the problem. The underlying skill is the same in all four.

What exactly does Set C ask students to do?

To rule on somebody else's answer. Each of its three problems arrives with a proposed result — 12x² − 9, −4x² − 8x + 10 and −x² − 6x − 3 — and a Correct / Incorrect choice, with the instruction to show the work behind the decision. The key prints the correct simplification beside each, so the verdicts follow from it.

Why does Set B's answer bank hold more options than problems?

Because the spare options are deliberate near misses. Three problems are given six choices, and the unused ones are what a student gets by failing to distribute the subtraction across the whole bracket — −x² − 5 in place of the correct −x² − 9, for instance. Choosing one shows exactly where the working went wrong.