EngageNY
Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first instructional activity in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear...
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 2)
Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...
EngageNY
Complex Numbers as Vectors
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
EngageNY
Using Matrix Operations for Encryption
Data encryption is an important security measure for sensitive data stored on computers. Pupils learn how to utilize matrices for creating code. They also get a great review of matrix multiplication, inverse matrices, and the identity...
EngageNY
Congruence Criteria for Triangles—AAS and HL
How can you prove it? Guide classes through an exploration of two possible triangle congruence criteria: AAS and HL. Learners connect this criteria to those previous learned and also explore criteria that does not work. The instructional...
EngageNY
Addition and Subtraction Formulas 2
Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...
EngageNY
Revisiting the Graphs of the Trigonometric Functions
Use the graphs of the trigonometric functions to set the stage to inverse functions. The instructional activity reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing...
EngageNY
Comparing Linear Functions and Graphs
How can you compare linear functions? The seventh installment of a 12-part module teaches learners how to compare linear functions whose representations are given in different ways. They use real-world functions and interpret features in...
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...
EngageNY
Exponential Notation
Exponentially increase your pupils' understanding of exponents with an activity that asks them to explore the meaning of exponential notation. Scholars learn how to use exponential notation and understand its necessity. They use negative...
EngageNY
Sequencing Translations
Investigate the results of multiple translations on an image. Scholars use vectors to perform a sequence of translations in the seventh lesson of 18. They examine the results and determine the importance of using a sequence rather than a...
EngageNY
Multi-Step Problems—All Operations
Harness the power of algebra to solve problems. Young mathematicians learn to work out multi-step problems by applying algebraic techniques, such as solving equations and proportions. They use tape diagrams to model the problem to finish...
EngageNY
Ptolemy's Theorem
Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.
EngageNY
Networks and Matrix Arithmetic
Doubling a network or combining two networks is quick and easy when utilizing matrices. Learners continue the network example in the second lesson of this series. They practice adding, subtracting, and multiplying matrices by a scalar...
EngageNY
Matrix Arithmetic in Its Own Right
Matrix multiplication can seem random to pupils. Here's a instructional activity that uses a real-life example situation to reinforce the purpose of matrix multiplication. Learners discover how to multiply matrices and relate the process...
EngageNY
Vectors and Stone Bridges
What does it take to build a stable arch? Pupils apply vectors and physics as they examine arched bridges and their structural integrity. They use vectors to represent the forces acting on the stone sections and make conclusions based on...
Curated OER
Acids and Bases - Vinegar II
Eighth graders experiment what happens when acids and bases are mixed together. In this acids and bases experimental instructional activity, 8th graders decide which of three solutions of unknown pH will neutralize a fourth solution of...
Curated OER
The Great Button Sort
Pupils practice figuring out how items have been sorted. They also sort buttons in small cooperative groups. They color and sort their own paper buttons and then give their button sort to another student to see if he or she can figure...
Curated OER
Brian's Pegboard II
Young scholars are able to assess a problem and use systematic methods to solve the problem. They also find out all the possible outcomes for a sequence of events using tree diagrams.
Curated OER
ndirect Measurement Technique: Using Trigonometric Ratios
Ninth graders find the height of an object that would be difficult or impossible to measure directly. They construct and use a Clinometer to measure the angle of elevation (or depression). Students create a sketch of the measurement...
Curated OER
Square and Triangular Numbers
Young scholars use equations to represent practical situations. They solve linear equations and quadratic equations. The use of problem solving strategies is also developed.
Curated OER
Decreasing Differences
Students identify and interpret the pattern within a set of numbers using words. Then they write rules in words using complete sentences. Students also highlight two similar sequences with the same difference in order to get the first...
Curated OER
Translating Parabolas
High schoolers make informed choices among technology systems, resources, and services. They select and apply technology tools for research, information analysis, problem solving, and decision making in content learning.
Curated OER
Exploring Similarity Using Scale Drawings
Learners explore scale factor as they create a scale drawing of a box, then determine the surface area and volume of the original and the scale drawing. The one page worksheet contains activities and procedures with four questions....