EngageNY
Introduction to Simultaneous Equations
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...
EngageNY
Geometric Interpretations of the Solutions of a Linear System
An intersection is more than just the point where lines intersect; explain this and the meaning of the intersection to your class. The 26th segment in a 33-part series uses graphing to solve systems of equations. Pupils graph linear...
EngageNY
Nature of Solutions of a System of Linear Equations
If at first you cannot graph, substitute. The lesson introduces the substitution method as a way to solve linear systems if the point of intersection is hard to determine from a graph. The 28th installment of a 33-part series finishes...
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Word Problems
Use several skills to solve word problems leading to systems of equations. Scholars define variables and write equations to model situations described within word problems. Pupils solve the resulting system of linear equations using...
EngageNY
Another Computational Model of Solving a Linear System
The process of elimination really works! Use elimination when substitution isn't doing the job. The 29th segment in a series of 33 introduces the elimination method to solving linear systems. Pupils work several exercises to grasp the...
EngageNY
Conversion Between Celsius and Fahrenheit
Develop a formula based upon numerical computations. The 31st part of a 33-part unit has the class determine the formula to convert a temperature in Celsius to a temperature in Fahrenheit. They do this by making comparisons between the...
EngageNY
Definition of Reflection and Basic Properties
Discover the results of reflecting an image. Learners use transparency paper to manipulate an image using a reflection in this fourth lesson of 18. They finish by reflecting various images across both vertical and horizontal lines.
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Definition of Rotation and Basic Properties
Examine the process of rotating images to visualize effects of changes to them. The fifth lesson of 18 prompts pupils to rotate different images to various degrees of rotation. It pays special attention to rotations in multiples of 90...
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Rotations of 180 Degrees
What happens when rotating an image 180 degrees? The sixth activity in the series of 18 takes a look at this question. Learners discover the pattern associated with 180-degree rotations. They then use transparency paper to perform the...
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Definition of Congruence and Some Basic Properties
Build a definition of congruence from an understanding of rigid transformations. The lesson asks pupils to explain congruence through a series of transformations. Properties of congruence emerge as they make comparisons to these...
EngageNY
Linear Equations in Two Variables
Create tables of solutions of linear equations. A lesson plan has pupils determine solutions for two-variable equations using tables. The class members graph the points on a coordinate graph.
EngageNY
The Graph of a Linear Equation—Horizontal and Vertical Lines
Graph linear equations in standard form with one coefficient equal to zero. The lesson plan reviews graphing lines in standard form and moves to having y-coefficient zero. Pupils determine the orientation of the line and, through a...
EngageNY
The Computation of the Slope of a Non-Vertical Line
Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
EngageNY
The Graph of a Linear Equation in Two Variables Is a Line
Show your class that linear equations produce graphs of lines. The 20th segment in a unit of 33 provides proof that the graph of a two-variable linear equation is a line. Scholars graph linear equations using two points, either from...
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Every Line is a Graph of a Linear Equation
Challenge the class to determine the equation of a line. The 21st part in a 33-part series begins with a proof that every line is a graph of a linear equation. Pupils use that information to find the slope-intercept form of the equation...
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Some Facts About Graphs of Linear Equations in Two Variables
Develop another way to find the equation of a line. The instructional activity introduces the procedure to find the equation of a line given two points on the line. Pupils determine the two points from the graph of the line.
EngageNY
Applications of the Pythagorean Theorem
Examine the application of the Pythagorean Theorem in problem-solving questions. Pupils apply the theorem to find lengths when given different scenarios. They finish the 17th installment in an 18-part series by applying the theorem to...
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Constant Rates Revisited
Find the faster rate. The resource tasks the class to compare proportional relationships represented in different ways. Pupils find the slope of the proportional relationships to determine the constant rates. They then analyze the rates...
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The Defining Equation of a Line
They appear to be different, yet they are the same line. Part 24 out of 33 lessons provides a theorem about the relationships of coefficients of equivalent linear equations. Pupils use the theorem to determine whether two equations are...
EngageNY
Representations of a Line
Explore how to graph lines from different pieces of information. Scholars learn to graph linear functions when given an equation, given two points that satisfy the function, and when given the initial value and rate of change. They solve...
EngageNY
Increasing and Decreasing Functions 1
Model situations with graphs. In the fourth installment of a 16-part module, scholars learn to qualitatively analyze graphs of piecewise linear functions in context. They learn to sketch graphs for different situations.
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Increasing and Decreasing Functions 2
Explore linear and nonlinear models to help your class build their function skills. In a continuation of the previous lesson, learners continue to analyze and sketch functions that model real-world situations. They progress from linear...
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Summarizing Bivariate Categorical Data in a Two-Way Table
Be sure to look both ways when making a two-way table. In the lesson, scholars learn to create two-way tables to display bivariate data. They calculate relative frequencies to answer questions of interest in the 14th part of the series.
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