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...

Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....

Your algebra learners emphasize the"geometric" in geometric series as they use a common ratio between algebraic terms and find that it corresponds to a repeated similarity transformation. 

Find the area of triangles, rectangles, and parallelograms using this metric activity.

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...

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal. 

Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from...

Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...

Scholars determine distances on the coordinate plane to find areas. The instructional activity begins with a proof of the formula for the area of a parallelogram using the coordinate plane. Pupils use the coordinate plane to determine...

A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...

Designing a deck sure demands a lot of math. Future engineers and architects learn about the areas and perimeters of squares, rectangles, triangles, and composite figures. They apply their new knowledge to design a deck with a specified...

What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.

Get new flooring for as cheap as possible. Given a floor plan of a house, pupils determine the area of each room and the amount of necessary flooring. They then make selections for the flooring in every space, taking a budget into...

Investigate patterns in the binomial theorem. Pupils begin by reviewing the coefficients from Pascal's triangle. They look at the individual terms, the sums of the coefficients on a row, and the alternating sum of each row. Individuals...

Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...

If you want a bigger garden, here's a task for you. Given the perimeter of a triangular garden, scholars determine the largest possible area. They then generalize their findings and extend the idea to other polygons.

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...

Homes come in many different shapes and sizes. Building a model of a geodesic dome is the ultimate goal for the activity. Cutting and folding is the way to go here.

Put on your thinking caps because middle school math has never been more interesting in this huge resource full of thought provoking questions. Written as a newsletter, the resource has 10 two-page newsletters with a variety of...

The 21st segment in a 28-part series provides learners with area problems involving composite figures. To find the solution, pupils must decide whether to add or subtract areas. The composite figures are composed of quadrilaterals,...

Build a complete house in just a few days. Learners create floor, roof, deck, and landscape plans for a two-story house. Scholars then use their knowledge of area formulas, trigonometric ratios, and the Pythagorean Theorem to determine...

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

Use the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...

Your learners get extra practice using coordinates in calculating mid points, finding end points, deciding if points are collinear, calculations using slope concepts, writing linear equations, using triangles and quadrilaterals, and...