EngageNY
Triangle Congruency Proofs (part 1)
Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...
EngageNY
Modeling with Quadratic Functions (part 2)
How many points are needed to define a unique parabola? Individuals work with data to answer this question. Ultimately, they determine the quadratic model when given three points. The concept is applied to data from a dropped object,...
EngageNY
Basic Properties of Similarity
Does the symmetry and transitive property apply to similarity? The 10th segment in a series of 16 presents the class with a group of explorations. The explorations have pairs show that similarity is both symmetrical and transitive. It...
EngageNY
Proofs of Laws of Exponents
Apply pupil understanding of exponent properties to prove the relationships. In the sixth lesson of the series, individuals are expected to prove relationships using mathematical statements and reasoning.
EngageNY
Factoring Expressions
Factor in an informative resource when teaching about factoring. The 11th instructional activity in a 36-part module shows pupils how to factor algebraic expressions by applying the distributive property. Some of the problems involve...
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The Distance from a Point to a Line
What is the fastest way to get from point A to line l? A straight perpendicular line! Learners use what they have learned in the previous lessons in this series and develop a formula for finding the shortest distance from a point to a...
EngageNY
Matrix Multiplication Is Not Commutative
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
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 strengthen...
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Adding and Subtracting Expressions with Radicals
I can multiply, so why can't I add these radicals? Mathematicians use the distributive property to explain addition of radical expressions. As they learn how to add radicals, they then apply that concept to find the perimeter of polygons.
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Trigonometry and the Pythagorean Theorem
Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...
EngageNY
Using Trigonometry to Determine Area
What do you do when you don't think you have enough information? You look for another way to do the problem! Pupils combine what they know about finding the area of a triangle and trigonometry to determine triangle area when they don't...
EngageNY
Matrix Multiplication Is Distributive and Associative
Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous lesson plan in the series, pupils now test the associative and distributive properties. The...
EngageNY
Review of the Assumptions (part 1)
What was the property again? Tired of hearing this from your pupils? Use this table to organize properties studied and as a reference tool for individuals. Learners apply each property in the third column of the table to ensure their...
EngageNY
Base Angles of Isosceles Triangles
Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...
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
Estimating Quantities
Apply the concept of magnitude to estimate values and compare numbers. The ninth lesson of the 15-part series asks learners to write numbers to their next greatest power of 10 and then make comparisons. Scholars begin to understand the...
EngageNY
Definition of Translation and Three Basic Properties
Uncover the properties of translations through this exploratory lesson. Learners apply vectors to describe and verify transformations in the second installment of a series of 18. It provides multiple opportunities to practice this...
EngageNY
Solving Equations with Radicals
Show learners how to develop a procedure for solving equations using radicals with the fifth instructional activity of the 25-part module that challenges learners to use properties to solve multi-step quadratic and cubic equations....
EngageNY
Dividing Fractions and Mixed Numbers
Class members discover how to extend division to fractions to mixed numbers. Individuals first review how to convert mixed numbers to improper fractions and then apply division strategies learned in previous lessons. A memory game tests...
EngageNY
Absolute Value—Magnitude and Distance
Do you want to use the resource? Absolutely. Scholars learn about absolute value and its relation to magnitude and distance on a number line. They compare numbers in context by applying absolute value.
EngageNY
The Order of Operations
Future mathematicians learn how to evaluate numerical expressions by applying the order of operations. They evaluate similar-looking expressions to see how the location of parentheses and exponents affects the value.
EngageNY
Understanding Box Plots
Scholars apply the concepts of box plots and dot plots to summarize and describe data distributions. They use the data displays to compare sets of data and determine numerical summaries.
EngageNY
From Equations to Inequalities
Sometimes, equality just doesn't happen. Scholars apply their knowledge of solving equations to identify values that satisfy inequalities in the 34th installment of a 36-part module. They test given sets of numbers to find those that are...
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...