EngageNY
Scale Factors
Is it bigger, or is it smaller—or maybe it's the same size? Individuals learn to describe enlargements and reductions and quantify the result. Lesson five in the series connects the creation of a dilated image to the result. Pupils...
EngageNY
The Remainder Theorem
Time to put it all together! Building on the concepts learned in the previous lessons in this series, learners apply the Remainder Theorem to finding zeros of a polynomial function. They graph from a function and write a function from...
EngageNY
Fundamental Theorem of Similarity (FTS)
How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line...
EngageNY
Comparing the Ratio Method with the Parallel Method
Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
Flipped Math
Remainder Theorem
Don't divide! Pupils view three examples relating the remainder of a polynomial division and the polynomial function evaluated at a related value. Learners notice how to find a missing coefficient in a polynomial given the remainder of a...
Mathematics Vision Project
Quadratic Equations
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
Mt. San Antonio Collage
Synthetic Division and Zeros of Polynomial Functions
More than just a learning exercise, this guide provides the description of many of the polynomials theorems to assist the learners. Starting with synthetic division, class members are then guided through the remainder theorem and linear...
EngageNY
Obstacles Resolved—A Surprising Result
The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors.
EngageNY
First Consequences of FTS
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to...
Mt. San Antonio Collage
Quiz 2: Polynomials
Four questions that get right to the polynomial point. High schoolers list all the attributes of a polynomial function, including finding all complex zeros. The last two questions prompt them to write a function based on the given...
Mathematics Vision Project
Similarity and Right Triangle Trigonometry
Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...
EngageNY
How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.
West Contra Costa Unified School District
Polynomial Division
How do you apply the traditional division algorithm to polynomials? Here is an Algebra II lesson that extends the use of the division algorithm to polynomials. After establishing the concept of long division, synthetic division and the...
EngageNY
Informal Proof of AA Criterion for Similarity
What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...
Mathematics Vision Project
Module 7: Connecting Algebra and Geometry
The coordinate plane links key geometry and algebra concepts in this approachable but rigorous unit. The class starts by developing the distance formula from the Pythagorean Theorem, then moves to applications of slope. Activities...
Flipped Math
Unit 2 Review: Polynomial Functions
Wrap it all up in a box. Pupils review the key concepts from an Algebra 2 polynomial functions unit by working 19 problems. Problems range from using the Remainder Theorem to find remainders and finding factors; sketching graphs by...
EngageNY
Making Scale Drawings Using the Ratio Method
Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements.
EngageNY
End-of-Module Assessment Task - Grade 8 Mathematics (Module 3)
Everything the class knows about similarity in one small package. The last portion of a 16-part series is a three-question assessment. In it, pupils demonstrate their application of similar figures and their associated...
EngageNY
Scale Drawings
Are you searching for a purpose for geometric constructions? Use an engaging approach to explore dilations. Scholars create dilations using a construction method of their choice. As they build their constructed dilation, they...
EngageNY
The Special Role of Zero in Factoring
Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...
02 x 02 Worksheets
Factoring
Factor in this resource when teaching how to factor polynomials. Scholars use algebra tiles to factor linear and quadratic expressions. They practice their skill by working on example problems from a worksheet.
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
Mathematics Vision Project
Module 3: Polynomial Functions
An informative module highlights eight polynomial concepts. Learners work with polynomial functions, expressions, and equations through graphing, simplifying, and solving.