Illustrative Mathematics
The Intersection of Two Lines
Here is an introduction to solving simultaneous linear equations. Start by drawing a line through two points. Create a second line which goes through the intersecting point. Background knowledge of how to find the equation of a line and...
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...
Inside Mathematics
Graphs (2007)
Challenge the class to utilize their knowledge of linear and quadratic functions to determine the intersection of the parent quadratic graph and linear proportional graphs. Using the pattern for the solutions, individuals develop a...
Illustrative Mathematics
Cell Phone Plans
Turn your classroom into a local cell phone store. Then, have your cell phone agents use linear equations to visually display three cell plans and their advantages. It makes for a great group project. Discuss how to decide which plan is...
Illustrative Mathematics
Equations of Lines
The intent of this resource is to show algebra learners that there is a proportional relationship between two lines that have an intersecting point. As the coordinate x increases by a constant, the y coordinate also increases. It...
Illustrative Mathematics
Fixing the Furnace
This comprehensive resource applies simultaneous equations to a real-life problem. Though the commentary starts with a graph, some home consumers may choose to begin with a table. A graph does aid learners to visualize the shift of one...
Illustrative Mathematics
Two Lines
Here is a resource that helps your algebra learners understand the connection between the graph of two lines, the equations of lines, and the solutions and intersecting points of lines. It would make a great assessment question, but can...
Concord Consortium
Shooting Arrows through a Hoop
The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils...
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...
Illustrative Mathematics
Global Positioning System II
Intricate details of a modern technology that many of us take for granted in our phones, computers (and some cars) are laid bare in a short but deeply investigative activity. The math behind a seemingly simple GPS device...
Inside Mathematics
Picking Apples
Getting the best pick of the apples depends on where to pick. The short assessment presents a situation in which class members must analyze a real-world situation to determine the cost of picking apples. The pricing structures resemble...
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using...
Illustrative Mathematics
The Circle and The Line
Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...
Curated OER
Linear and Quadratic System
Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.
Concord Consortium
Look but Do Not Touch
We seem to keep missing each other. A short task provides pupils with a quadratic function, as well as a linear function with a missing coefficient. They must determine the value of the coefficient for which the graphs do not intersect.
Concord Consortium
Circling
Come full circle in learning about conic sections. Learners first look at the type of conic section formed when concentric circles intersect a standard coordinate plane. They then see which type forms when two sets of concentric circles...
Illustrative Mathematics
Graphs of Power Functions
There are parent functions, and then there are parent functions with a really interesting way to explore them. High schoolers are asked to graph different combinations of parent functions together and determine the point of...
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...
Concord Consortium
Short Pappus
It's all Greek to me. Scholars work a task that Greeks first formulated for an ancient math challenge. Provided with an angle and a point inside the angle, scholars develop conjectures about what is true about the shortest line segment...
Curated OER
Global Positioning System I
Geometry learners touch the surface of how a global positioning system works. The end goal is to find the intersections of three different spheres geometrically and algebraically given their algebraic representations.
Curated OER
Circumcenter of a Triangle
Your geometry learners will discover and show the construction of the circumcenter of a triangle. Guided by the steps in the activity, they construct perpendicular bisectors of each side that have a point of concurrency called the...
Concord Consortium
Twinkle, Twinkle
Take a look at a star resource. Young mathematicians use a graphing calculator to draw intersecting lines that look like a star. They then apply translations to move the entire star and also consider what transformations must occur to...
Curated OER
Symmetries of a Quadrilateral I
Learners examine the properties of quadrilaterals from the point of view of rigid motion. Different types of quadrilaterals are characterized by their symmetries, so learners explore the symmetries of a described quadrilateral to...
Illustrative Mathematics
Proportional Relationships, Lines, and Linear Equations
The resource is a good introduction to what makes a proportional relationship between two lines. Discuss the similarities of both lines and the possibility of intersection. Use this opportunity to list other acceptable forms of each...