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...

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

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. 

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,...

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...

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. 

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...

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.

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...

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,...

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...

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.

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...

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...

The topic of trigonometric ratios is often covered with loads of rote memorization baked into the activity. This activity set, however, leans more on using similar triangles and discovery learning to help young geometers develop a deeper...

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...

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...

Geometric design makes a fashion statement! Challenge learners to design a hat to fit a Styrofoam model. Specifications are clear and pupils use concepts related to three-dimensional objects including volume of irregular shapes and...

Add up areas of squares to discover the pythagorean relationship. Small groups create right triangles with squares along each side. They calculate the areas of each square and notice the relationship. Groups construct other types of...

Young geometers need a clear understanding of perimeter, volume, and area. This lesson plan provides a worksheet to help small groups of learners to calculate various measurements of objects and choose the proper units for measurement....

A learning task that involves creative ways of thinking permits children to use paper models as a way to visualize the fraction one-half. Learners can fold or cut their models in such a way that the unshaded regions, and shaded...

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...

Take a similar approach to three dimensions. Pupils develop the relationship between areas of similar objects and see how they relate to the ratio of the sides. Building upon area formulas, small groups put together volume formulas for...