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Polynomial Functions unit opening page with title and teacher launch guide — Page 1

Graph reasoning, end behavior, turning points, and rational zero theorem page — Page 5

Polynomial inequalities, ten-item exit ticket, and student reflection page — Page 9

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Polynomial functions unit assignment

A standards-aligned Algebra II unit with terse theory, worked examples, 70 sequenced questions, rational and complex zeros, identities, finite differences, transformations, inequalities, modeling, a ten-item exit ticket, and a separate teacher key.

High school / Algebra II
9 pages
Unit assignment + Teacher key

Student unitThirteen concise subtopics, worked examples, investigation, 70 questions, model, and exit ticket
Teacher keyAll answers, reasoning expectations, acceptable alternatives, and scoring notes
Multiplicity graphEditable local visual showing crossing and touching behavior

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Teaching

5 resources

Opening page of the Cramer's rule lesson with learning goals, lesson sequence, and prerequisite check

Three-variable Cramer's rule derivation and complete worked example showing all four determinants

Advanced reasoning questions, six-item exit ticket, student reflection, sources, and classroom-use review note

7 pages

High schoolLesson

Cramer's rule lesson and practice set

Teach students to derive, apply, check, and limit Cramer's rule for two-variable and three-variable linear systems.

Student lesson and practice
Teacher key

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Handout page one: title block, the factored form showing that a cubic behaves like its leading term, a callout bounding where the real roots can lie, and the derivation of the stationary points from b squared minus three a c

Handout page two: the four-case classification table for the number of distinct real roots, the three-panel figure of y = x cubed minus 3x plus k for k = 0, 2 and 4, a note on repeated roots, the reduction to the classical discriminant, and the first worked examples

Handout page three: the two parameter examples, the ten exercises in two columns, the recording table for questions one to four, ruled working space, and the sources with a note on the calculus prerequisite

3 pages

High schoolHandout

How many real roots does a cubic have?

Let students decide how many distinct real roots any cubic has by computing b squared minus 3ac and the product of the two stationary values.

Student handout
Teacher key

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Lesson page one: title block, the opening section introducing a logarithm as the exponent that undoes a power, the two-machine figure sending 3 to 8 and 8 back to 3, the boxed definition with its restrictions on base and argument, the two inverse identities, and the start of the section on domain and range

Lesson page two: the graph of y = log base 2 of x against y = log base one half of x on shared axes, the identity that changing the base to its reciprocal negates the logarithm, a table of the sign of a logarithm on each side of 1, and the figure showing the exponential and the logarithm as reflections in the line y = x

Lesson page five: the exercise section with a strategy callout, fifteen exercises in two columns rising from direct evaluation to short proofs, a recording table for the answer and restriction used in the first eight questions, ruled working space, and the list of sources

5 pages

High schoolLesson

Logarithms: definition, graphs, and laws with proofs

Let students define a logarithm as the exponent that inverts a power, read its domain, range and monotonicity off the graph, and prove every standard logarithm law from the index laws.

Student lesson
Teacher key

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9 pages

High schoolUnit assignment

Polynomial functions unit assignment

Teach polynomial structure, operations, zeros, graphs, identities, transformations, inequalities, data patterns, and modeling in one coherent sequence.

Student unit
Teacher key

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Lesson page one: title block, distinction among a quadratic expression, function, and equation, the general equation, a table comparing standard, factored, and vertex forms, and a triangular diagram showing what each form reveals.

Lesson page three: geometric area model for completing the square, derivation of the general completed-square form and vertex, monic and nonmonic worked examples, and the opening of the quadratic-formula derivation.

Lesson page seven: exercises twenty-three through forty-two on the discriminant, proofs, error analysis, and models, followed by a compact working record and curriculum sources.

7 pages

High schoolLesson

Solving quadratic equations: choosing and connecting the methods

Connect factored, completed-square, and standard forms so that a solving method can be selected from the structure of a quadratic equation and every solution can be interpreted algebraically and graphically.

Student lesson
Teacher key

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