MathIsFun points out that plants grow new petals or leaves in a spiral pattern based on the Fibonacci number series and the golden ratio. You can use this to teach students about the Fibonacci number series, pointing out the pattern with positive integers. Bring in several plants that exhibit this pattern. Examples include varieties of sunflowers, aloe and daisies. Have the students find the Fibonacci number series in each example. Use graph paper to show how understanding Fibonacci numbers leads to calculating the golden ratio. Also use graph paper to create spirals based on the Fibonacci number series and then ask students to find these spirals with some plant examples.
Whether it is basic math, algebra, geometry, trigonometry or calculus, there are big and small concepts that can be broken down into interesting and memorable facts that apply to real life. Have students work in groups to create a magazine that focuses on a particular number pattern, shape, theorem or formula. Students should be required to do research to find ways to write or photograph how their topic is used in the classroom, nature, certain occupations and hobbies. The magazines should be written at a readable level for others in the class to comprehend them.
Students can learn about abstract algebra and group and set theory by writing their own musical compositions with no musical background required. Use an example in class by assigning four notes of a keyboard to the numbers 1, 2, 3 and 4. Compose a musical piece for an example. Assign the students to create a musical piece by making a hexachord, a collection of six notes. Have the students calculate all the possibilities to turn in with their compositions. Encourage students to also use some musical reasoning, such as knowing how to end a phrase. Show them that they can have chords or “simultaneities” using more than one numbered note at the same time.
Crystals can be used to show high school students naturally occurring geometric shapes, concepts of symmetry and surface area calculations. Start with individual table salt, which is a cube. Draw a cube and calculate its surface area. Show its symmetry by drawing a vertical and a horizontal line through the middle. Bring to class rock sugar candy, chrome alum crystals and fluorite. Students can explore the shapes of perfect and imperfect crystals. A long-term activity could include growing the candy and the chrome alum crystals, which helps students with understanding crystal formation in addition to calculating crystal growth and making a super-saturated solution.