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Lesson Plan
Mathematics Assessment Project

Generating Polynomials from Patterns

For Teachers 9th - 12th Standards
Patterns and polynomials go hand in hand. Budding mathematicians analyze sequences of dot diagrams to discover the patterns in the number of white dots and black dots. They use the identified patterns to write and simplify a polynomial...
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Assessment
1
1
CCSS Math Activities

Smarter Balanced Sample Items: High School Math – Claim 3

For Teachers 9th - 12th Standards
Communication is the key. A presentation provides 25 sample items for Claim 3, Communicating Reasoning, for the Smarter Balanced High School Math assessment. Items require pupils to answer the question and provide logical reasoning to...
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Assessment
Concord Consortium

From Tan to Ten

For Students 10th - 12th Standards
Combine simplifying trigonometric expressions with evaluating them! An open-ended question presents a trigonometric expression and numeric values for additional expressions. Learners must determine a value for the original expression by...
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Interactive
CK-12 Foundation

Factor Polynomials Using Special Products: Difference of Two Squares

For Students 9th - 11th Standards
Factoring patterns are not magic! Show your classes how to model the difference of two squares' factors using an area model. Learners manipulate the width and length of two squares to represent the polynomial a^2-b^2. They use the model...
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Interactive
CK-12 Foundation

Sum and Difference of Cubes: Stacking Blocks

For Students 9th - 11th Standards
Investigate polynomial factoring patterns by finding a connection to volume. As learners build a three-dimensional solid from smaller solids, they convert the visual model to a mathematical expression. Their models represent the sum of...
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Assessment
EngageNY

End-of-Module Assessment Task - Algebra 2 (Module 1)

For Students 10th - 12th Standards
A series of assessment tasks require learners to process information and communicate solutions. Topics include graphing parabolas, solving linear-quadratic systems, factoring polynomials, and solving polynomial equations. 
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Lesson Plan
EngageNY

The Power of Algebra—Finding Pythagorean Triples

For Students 10th - 12th Standards
The Pythagorean Theorem makes an appearance yet again in this lesson on polynomial identities. Learners prove a method for finding Pythagorean triples by applying the difference of squares identity. 
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Lesson Plan
1
1
EngageNY

The Power of Algebra—Finding Primes

For Students 10th - 12th Standards
Banks are responsible for keeping our financial information safe. Mathematics is what allows them to do just that! Pupils learn the math behind the cryptography that banks rely on. Using polynomial identities, learners reproduce the...
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Lesson Plan
1
1
EngageNY

Dividing by (x – a) and (x + a)

For Students 10th - 12th Standards
Patterns in math emerge from seemingly random places. Learners explore the patterns for factoring the sum and differences of perfect roots. Analyzing these patterns helps young mathematicians develop the polynomial identities.
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Lesson Plan
1
1
EngageNY

Putting It All Together

For Students 10th - 12th Standards
Shuffle 'em up and deal! Learners practice operations with polynomials using cards they pass around the room. The activity works with pairs or individuals, so it offers great flexibility. This is the fifth installment in a series of 42...
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Lesson Plan
EngageNY

The Division of Polynomials

For Students 10th - 12th Standards
Build a true understanding of division of polynomials. Learners use their knowledge of multiplying polynomials to create an algorithm to divide polynomials. The area model of multiplication becomes the reverse tabular method of division.
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Lesson Plan
EngageNY

The Multiplication of Polynomials

For Students 10th - 12th Standards
If you can multiply multi-digit integers, you can multiply polynomials. Learners use an area model to compare multiplying numbers to multiplying polynomials. They progress to using the distributive property. 
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Assessment
EngageNY

Mid-Module Assessment Task - Algebra 2 (Module 1)

For Students 10th - 12th Standards
Challenge classes to think deeply and apply their understanding of polynomials. The assessment prompts learners to use polynomial functions to model different situations and use them to make predictions and conclusions.
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Lesson Plan
1
1
EngageNY

The Special Role of Zero in Factoring

For Students 10th - 12th Standards
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...
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Lesson Plan
1
1
EngageNY

Radicals and Conjugates

For Students 10th - 12th Standards
Make the irrational rational again! Continuing the theme from previous lessons in the series, the lesson plan relates the polynomial identity difference of squares to conjugates. Learners develop the idea of a conjugate through analysis...
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Lesson Plan
EngageNY

Mental Math

For Students 10th - 12th Standards
Faster than a speedy calculator! Show your classes how to use polynomial identities to multiply numbers quickly using mental math. 
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Lesson Plan
EngageNY

Comparing Methods—Long Division, Again?

For Students 10th - 12th Standards
Remember long division from fifth grade? Use the same algorithm to divide polynomials. Learners develop a strategy for dividing polynomials using what they remember from dividing whole numbers.
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Assessment
1
1
Mathematics Assessment Project

Arithmetic with Polynomials and Rational Expressions

For Students 9th - 12th Standards
It all starts with arithmetic. An educational resource provides four items to use in summative assessments. The items reflect the basic skill level required by the standards in the domain and are designed to have pupils reason abstractly...
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Unit Plan
2
2
EngageNY

Polynomial, Rational, and Radical Relationships

For Teachers 9th - 12th Standards
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
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Lesson Plan
1
1
Curated OER

Trina's Triangles

For Teachers 8th - 11th Standards
Practice evaluating polynomial expressions at the same time you find Pythagorean Triples. Look for patterns and find examples when the "formula" does and doesn't work. Finally, verify the formula by proving the identity true.
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Lesson Plan
Curated OER

Area, Arithmetic and Algebra

For Teachers 8th - 9th Standards
Explore the concept of this perfect square trinomial and difference of squares lesson. A hands-on activity that uses paper rectangles and squares to illustrate the perfect-square trinomial and difference of squares formulas.
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Lesson Plan
Curated OER

Finite Differences

For Teachers 9th - 12th Standards
Young mathematicians solve problems with polynomials. As they graph and analyze polynomial functions, learners define constant and finite, and determine the relationship between the constant set of differences and the slope of a linear...