Curriculum / Math / 11th Grade / Unit 3: Polynomials / Lesson 12
Math
Unit 3
11th Grade
Lesson 12 of 14
Jump To
Lesson Notes
There was an error generating your document. Please refresh the page and try again.
Generating your document. This may take a few seconds.
Are you sure you want to delete this note? This action cannot be undone.
Use polynomial identities to determine Pythagorean triples.
The core standards covered in this lesson
A.APR.C.4 — Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)2 = (x² — y²)² + (2xy)² can be used to generate Pythagorean triples.
The foundational standards covered in this lesson
8.G.B.7 — Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Ensure that students memorize the following sets of Pythagorean triples: 3-4-5, 5-12-13, and 7-24-25.Â
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Prove that if $${ x>1}$$, then a triangle with side lengths $${x^2-1}$$, $${2x}$$, and $${x^2+1}$$ is a right triangle.
Algebra II > Module 1 > Topic A > Lesson 10 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A triangle has side lengths of $${(x^2-y^2 )}$$, $${(2xy)}$$, and $${(x^2+y^2 )}$$. Choose values for $$x$$ and $$y$$. Will the resultant three sides be a right triangle? How do you know?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Generate three Pythagorean triples
Describe, algebraically, how you know that$${(x^2-y^2)}$$, $${(2xy)}$$, and $${(x^2+y^2)}$$ will always result in side lengths for a right triangle.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Identify the solution(s) to systems of polynomial functions.
Topic A: Polynomial Features and Graphs
Classify polynomials through identification of degree and leading coefficient. Graph a polynomial function from a table of values; prove degree using successive differences.
Standards
A.APR.A.1F.IF.C.7.CF.IF.C.9
Identify features of polynomial functions including end behavior, intervals where the function is positive or negative, and domain and range of function.
F.BF.B.3F.IF.B.4F.IF.B.6F.LE.A.3
Match and compare equations and graphs of polynomials, and identify transformations.
F.BF.B.3F.IF.B.4F.IF.C.7.C
Sketch polynomial functions using sign charts and analysis of the factored form of the polynomial function.
A.APR.B.3
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Operations with Polynomials
Multiply polynomials, identifying factors, degrees, and number of real roots. Identify features of a polynomial in standard form.
A.APR.A.1F.BF.B.3
Add and subtract polynomials. Identify degree, leading coefficient, and end behavior of result.
A.APR.A.1F.BF.A.1.B
Divide polynomials by binomials to determine linear factors.
A.APR.A.1A.APR.B.2A.APR.B.3
Determine if a binomial is a factor of a polynomial using the remainder theorem.
A.APR.B.2
Identify and factor with difference of two squares in quadratic and quartic polynomials. Describe identity of difference of two squares. Describe the zeros that represent the resultant factors.
A.APR.B.3A.SSE.A.2
Factor difference and sums of cubes. Explain sums and differences of cubes as polynomial identities.
A.APR.C.4
Factor polynomials by grouping in quartic, cubic, and quadratic functions.
F.IF.C.8.A
Topic C: Polynomial Extensions
A.REI.D.11
2 days
Write polynomial functions from solutions of that polynomial function.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
We've got you covered with rigorous, relevant, and adaptable math lesson plans for free