Illustrative Mathematics
Converse of the Pythagorean Theorem
Use the given tasks and detailed teacher's commentary to introduce your 8th graders to the Pythagorean theorem and its converse. Embedded links to information about Egyptian geometry make your presentation interesting. Consider giving...
Illustrative Mathematics
Applying the Pythagorean Theorem in a Mathematical Context
Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...
Curated OER
Two Triangles' Area
Need an activity for teaching the Pythagorean Theorem? Geometry juniors apply the Pythagorean theorem to two triangles to determine a final calculation.
Illustrative Mathematics
Running on the Football Field
Make your class into Pythagorean theorem fanatics in no time. What a great resource to get your sports enthusiasts into the math game! Read the commentary so you can you can strategize how to apply the three math practices.
Illustrative Mathematics
Area of a Trapezoid
Here is a straightforward example of how to apply the Pythagorean Theorem to find an unknown side-length of a trapezoid. Commentary gives additional information on proving that the inside of the trapezoid is a rectangle, but is...
Illustrative Mathematics
Shortest Line Segment from a Point P to a Line L
One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the class...
Illustrative Mathematics
The Missing Coefficient
This activity highlights the use of the remainder theorem to solve for the unknown coefficient of a specified polynomial when given one of its factors. Use this single problem as a warm-up exercise, a quick check-in at the end of a...
Teach Engineering
Stay in Shape
Using their knowledge of right triangles, pupils find out how far a ship is from a light house. Class members determine how far around the world a ship would be sailing at a constant speed.
101 Questions
Viewmongous TV
Just how big of a TV do you need?! The task at hand asks individuals to compare the area of 80-inch and 55-inch TVs. The length of the TV is given and learners must use the Pythagorean Theorem to determine the width to calculate the areas.
Illustrative Mathematics
Zeroes and factorization of a quadratic polynomial I
This activity uses the division algorithm and the definition of a zero/root of a function to guide your class to see the relationship between zeros and factors of a general quadratic, which can later be generalized to the Remainder...
Curated OER
Explaining the equation for a circle
By first starting with an explicit example of a radius and center point, this challenging lesson tries to help high schoolers gain an understanding of the Pythagorean theorem and the equation of a circle. Once they have accomplished the...
Teach Engineering
Catching the Perfect SAR Waves!
Zero in on an interesting resource involving radar technology. Groups construct a radar sensing unit and learn to calibrate the system. Using the radar system and the Pythagorean Theorem, they calculate distances between objects.
Curated OER
Narrow Corridor
Buying a new sofa? Learn how to use the Pythagorean Theorem, as well as algebra and graphing techniques, to determine whether the sofa will fit around a corner (which I'm sure you'll agree is a very important consideration!).
5280 Math
Pythagorean Triples
From Pythagorean triples to the unit circle. Learners use the Pythagorean Theorem to find Pythagorean triples and then relate their work to the unit circle in a fun algebra project. Their discovery that x^2+y^2 is always equal to one on...
101 Questions
Snail's Pace
Time doesn't fly when you're watching a snail cross a sidewalk. Combining the concepts of the Pythagorean Theorem and the distance, rate, and time formula, learners determine how long it takes a snail to go from one corner of a sidewalk...
Illustrative Mathematics
Joining Two Midpoints of Sides of a Triangle
Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel lines cut...
Curated OER
Task: Grain Storage
Farming is full of mathematics, and it provides numerous real-world examples for young mathematicians to study. Here, we look at a cylinder-shaped storage silo that has one flat side. Given certain dimensions, students need to determine...
Curated OER
Access Ramp
Just about every public building that your high schoolers are familiar with has an access ramp which complies with ADA requirements. As it turns out, designing such a ramp is an excellent activity to incorporate slope, the Pythagorean...
Illustrative Mathematics
Eratosthenes and the Circumference of the Earth
The class gets to practice being a mathematician in ancient Greece, performing geometric application problems in the way of Eratosthenes. After following the steps of the great mathematicians, they then compare the (surprisingly...
Illustrative Mathematics
Extensions, Bisections and Dissections in a Rectangle
Gaining practice in translating a verbal description into a diagram and then an equation is the real point of this similar triangles exercise. Once the diagram is drawn, multiple methods are provided to reach the conclusion. An effective...
DiscoverE
Build a Cable-Stayed Bridge
Large or small, bridges are architectural wonders! Construct a large-scale cable-stayed bridge during a whole class project. Scholars work in groups to erect the towers, build the roadway, and secure the cables of their very own bridges....
Curated OER
T Points from Directions
Here is a lesson that starts with having geometers translate points using compass directions into an accurate picture of the problem. Then they must use their knowledge of the Pythagorean theorem or similar triangles to solve. This makes...
Curated OER
Bird and Dog Race
Your pupil's pet dog and bird are racing down the city streets. In order to know who is going to win, they better know something about calculating rates, the Pythagorean Theorem, and applying those topics to the map of the city.
Illustrative Mathematics
Similar Triangles
Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...
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