Lesson Plan
EngageNY

The Volume Formula of a Pyramid and Cone

For Teachers 9th - 10th Standards
Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from...
Lesson Plan
EngageNY

Recursive Challenge Problem—The Double and Add 5 Game

For Teachers 9th - 10th Standards
Math is all fun and games! Use a game strategy to introduce the concept of sequences and their recursive formulas. The activity emphasizes notation and vocabulary.
Lesson Plan
EngageNY

Properties of Trigonometric Functions

For Teachers 11th - 12th Standards
Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the lesson plan...
Lesson Plan
EngageNY

Introduction to Simultaneous Equations

For Teachers 8th Standards
Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...
Lesson Plan
EngageNY

Existence and Uniqueness of Square Roots and Cube Roots

For Students 8th Standards
Teach cube roots by building on an understanding of square roots. The third installment of a 25-part series asks learners to solve simple quadratic and cubic equations using roots. Scholars compare square roots and cube roots throughout...
Lesson Plan
EngageNY

Pythagorean Theorem, Revisited

For Students 8th Standards
Transform your pupils into mathematicians as they learn to prove the popular Pythagorean Theorem. The 16th lesson in the series of 25 continues by teaching learners how to develop a proof. It shows how to prove the Pythagorean Theorem...
Lesson Plan
EngageNY

Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities

For Teachers 7th Standards
Cultivate the tree of knowledge using diagrams with two stages. Pupils create small tree diagrams to determine the sample space in compound probability problems. The lesson plan uses only two decision points to introduce tree...
Lesson Plan
EngageNY

Interpreting and Computing Division of a Fraction by a Fraction—More Models II

For Teachers 6th Standards
No more inverting and multiplying to divide fractions. Applying concepts of measurement division from the previous instructional activity, pupils consider partitive division using fraction bars and number lines. They first convert...
Lesson Plan
EngageNY

Even and Odd Numbers

For Students 6th Standards
Even or not, here I come. Groups investigate the parity of products and sums of whole numbers in the 17th lesson in a series of 21. Using dots to represent numbers, they develop a pattern for the products of two even numbers; two odd...
Lesson Plan
EngageNY

Ordering Integers and Other Rational Numbers II

For Students 6th Standards
Individuals build on prior knowledge to order a set of rational numbers from least to greatest or greatest to least. As part of the lesson, they order rational numbers written in different forms.
Lesson Plan
EngageNY

Comparing Distributions

For Teachers 9th - 10th Standards
Data distributions can be compared in terms of center, variability, and shape. Two exploratory challenges present data in two different displays to compare. The displays of histograms and box plots require different comparisons based...
Lesson Plan
EngageNY

Sine and Cosine of Complementary Angles and Special Angles

For Students 9th - 10th Standards
Building trigonometric basics here will last a mathematical lifetime. Learners expand on the previous lesson plan in a 36-part series by examining relationships between the sine and cosine of complementary angles. They also review...
Lesson Plan
EngageNY

Equations for Lines Using Normal Segments

For Students 9th - 12th Standards
Describing a line using an algebraic equation is an essential skill in mathematics. The previous lesson in the series challenged learners to determine if segments are perpendicular with a formula. Now they use the formula to...
Lesson Plan
EngageNY

Secant Angle Theorem, Exterior Case

For Teachers 9th - 12th Standards
It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous lesson to investigate angles created by secant lines that intersect at a point exterior to the circle....
Lesson Plan
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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.
Lesson Plan
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EngageNY

The Remainder Theorem

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

Comparing Rational Expressions

For Students 10th - 12th Standards
Introduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result. 
Lesson Plan
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EngageNY

Graphing Systems of Equations

For Students 10th - 12th Standards
Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous instructional activity, pupils learn algebraic methods of solving the systems. 
Lesson Plan
EngageNY

Using Sample Data to Estimate a Population Characteristic

For Students 10th - 12th Standards
How many of the pupils at your school think selling soda would be a good idea? Show learners how to develop a study to answer questions like these! The lesson explores the meaning of a population versus a sample and how to interpret the...
Lesson Plan
EngageNY

Ruling Out Chance (part 1)

For Students 10th - 12th Standards
What are the chances? Teach your classes to answer this question using mathematics. The first part of a three-day lesson on determining significance differences in experimental data prompts learners to analyze the data by...
Lesson Plan
EngageNY

Drawing a Conclusion from an Experiment (part 2)

For Students 10th - 12th Standards
Communicating results is just as important as getting results! Learners create a poster to highlight their findings in the experiment conducted in the previous lesson in a 30-part series. The resource provides specific criteria and...
Lesson Plan
EngageNY

Euler’s Number, e

For Teachers 9th - 12th Standards
Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson is the discovery of Euler's number. 
Lesson Plan
EngageNY

Graphs Can Solve Equations Too

For Students 9th - 10th Standards
There are many equations Algebra I students are not ready to solve. Graphing to solve gives them a strategy to use when they are unsure of an algebraic approach to solve the problem. The lesson exposes learners to a wide variety of...
Lesson Plan
EngageNY

Multiplying and Factoring Polynomial Expressions (part 2)

For Students 9th - 10th Standards
If you can multiply binomials, you can factor trinomials! This is the premise for a lesson on factoring. Pupils look for patterns in the binomials they multiply and apply them in reverse. Examples include leading coefficients of one...