Triangular Numbers

In this college level mathematics worksheet, students solve use the Pythagorean Theorem to find the missing side of a right triangle and explore the connection between the Pythagorean Theorem and the distance formula....

Get to the root of the problem with an instructive lesson! Learners find the roots of a function using the quadratic formula. A video shows the process and includes an explanation of the substitution steps. 

Geometry to the rescue. By watching a video, scholars see how geometric concepts help explain derivative formulas: areas of rectangles and volumes of rectangular prisms for the Power Rule and similarity and trig ratios for the Sine Rule.

Perform parallel calculations to find equal slopes. Using the formula for the equation of the tangent line to a point, the resource sets out to find two points with a difference of one that have parallel tangent lines.The 25th video in a...

Using a slider, scholars build triangular numbers and their associated rectangles and use the geometric display to find the pattern to determine the next triangular number. They then relate that number to the area of the rectangle to...

Build an explicit formula using tiles. Pupils develop a tile representation of a term within a sequence given figures of previous terms. Using the diagrams, learners develop the explicit formula by recognizing the common difference and...

One-to-one means the answer is simple, right? Given four graphs, pupils use a vertical line to test each graph to find out if they are one-to-one. By using the resource, learners realize that not all one-to-one relations are functions....

Explore the building blocks of the Fibonacci Sequence. Given the lengths of sides of squares, pupils deduce the pattern to determine the lengths of two more squares. Learners continue to work with recursive formulas to generate numerical...

Have some fun building squares out of triangles. Pupils investigate the partial sums of odd numbers. Using the sum of the first four odd numbers, learners see that it can be rewritten as a sum containing a triangular number. Simplifying...

Topple misunderstandings of geometric sequences. Using a context of creating ever-increasing sizes of dominoes, pupils develop a geometric sequence. The scenario provides the size of the first domino and the common ratio between...