Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...
Mathematics Vision Project
Module 7: Connecting Algebra and Geometry
The coordinate plane links key geometry and algebra concepts in this approachable but rigorous unit. The class starts by developing the distance formula from the Pythagorean Theorem, then moves to applications of slope. Activities...
Mathematics Vision Project
Connecting Algebra and Geometry
Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates including...
EngageNY
Distance and Complex Numbers 1
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
National Security Agency
What’s Your Coordinate?
Your middle schoolers will show what they know with their bodies when they become the coordinate plane in this conceptual development unit. Starting with the characteristics of the coordinate plane, learners develop their skills by...
EngageNY
Similarity
Use the coordinate plane to show two figures are similar. The lesson incorporates congruence transformations and dilations to move a figure on to another figure. Pupils determine that if a similarity transformation exists between two...
Education Development Center
Finding Triangle Vertices
Where in the world (or at least in the coordinate plane) is the third vertex? Given two coordinate points for the vertices of a triangle, individuals find the location of the third vertex. They read an account of fictional...
Virginia Department of Education
Transformations
The coordinate plane is a popular place! Identify rotations, reflections, and dilations on the coordinate plane. Pupils work in small groups to match transformations of a figure with the description of the transformation. They perform...
Virginia Department of Education
Distance and Midpoint Formulas
Small groups work through two guided activities to derive the distance and midpoint formulas for the coordinate plane. The activities begin with concrete examples and move to abstract.
Education Development Center
Finding Parallelogram Vertices
Four is the perfect number—if you're talking about parallelograms. Scholars determine a possible fourth vertex of a parallelogram in the coordinate plane given the coordinates of three vertices. They read a conversation...
Shodor Education Foundation
Triangle Area
While the lesson focuses on right triangles, this activity offers a great way to practice the area of all triangles through an interactive webpage. The activity begins with the class taking a square paper and cutting in in half; can they...
EngageNY
Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
Mathematics Vision Project
Module 4: Linear and Exponential Functions
Sequences and series are traditionally thought of as topics for the pre-calculus or calculus class, when learners are figuring out how to develop limits. But this unit uses patterns and slopes of linear functions in unique ways to bring...
NASA
Space Vectors
How do you determine the position coordinates of objects in space? Using the provided worksheet, class members determine the location of the space shuttle based upon its spherical coordinates from the Dryden Flight Research Center.
101 Questions
Ditch Diggers
What's the best way to dig a ditch? Scholars watch a video that shows the progress of ditch digging from two ends. Using coordinate geometry, they determine whether two ends will eventually connect to form one single ditch or not.
Radford University
Getting Around Millbrook
When is the distance formula not accurate? Referencing a map of the school, pairs determine the walking distance between two locations. Creating coordinates for each location, pupils determine the distance between the two points and...
EngageNY
The Geometric Effect of Some Complex Arithmetic 1
Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into what it...
EngageNY
Complex Numbers and Transformations
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
EngageNY
Distance and Complex Numbers 2
Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th lesson in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a formula to find...
EngageNY
Examples of Dilations
Does it matter how many points to dilate? The resource presents problems of dilating curved figures. Class members find out that not only do they need to dilate several points but the points need to be distributed about the entire curve...
Math by Design
Transformations – Reflections
Scholars use interactive resources to figure out how to mathematically draw a reflection of a geometric shape viewed in a mirror. To conclude the activity, class members are asked to deduce the result of multiple reflections across...
Illustrative Mathematics
Why Does SSS Work?
While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by...
EngageNY
Discovering the Geometric Effect of Complex Multiplication
Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...
Mathematics Vision Project
Module 6: Congruence, Construction, and Proof
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This unit...
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