Implementing Geography Into Mathematics

Integrated curriculum's are a great way to make classes fun and exciting by combining two different topics from different subjects. This is great for learners who have interests outside of math and allows them to learn about how mathematics applies to the subjects that they be more interested in. In today's blog I will be talking about an activity introduced to our class that integrates geography into the mathematics curriculum and can be used to teach many different topic areas!

For this activity students will need access to a computer or some sort of device that can access the internet. A computer would work the best though as the activity requires precise clicking.

Google maps/Google Earth has an interesting feature built in where you can place markers at various points on a satellite image and measure the distance between these markers. This is great for the measurements unit in the grade 9 locally developed, applied and academic classes and allows students to explore shapes found all around the world!

It can be used as a great way to teach perimeter to students as the measurement tool on Google Earth/Maps allows students to measure the distances from different markers. You can give students the coordinates of various famous places that replicate the shapes that need to be covered in the curriculum such as rectangles, squares and pyramids and ask students to determine various things such as perimeter and even ratios! For example, students can be asked to determine the perimeter of BMO field which is a rectangle. Once they find the perimeter of the field they can find the perimeter of any other rectangular shaped object they want. Once they have both perimeters you can ask them to use a ratio to find out how much bigger/smaller BMO field is compared to their object, which covers two topics at once.

Image retrieved from: http://travelingcanucks.com/wp-content/uploads/2011/10/Pyramids-of-Giza-Egypt-20.jpg

This activity is excellent too because it provides important geography and technology skills such as how to use coordinates to locate an object and how to use google maps to locate objects which is a very useful skill in today's technological world.

Strategies for Teaching Trigonometry

Various topics in trigonometry are covered in the mathematics curriculum throughout high school. In grade 10 students are introduced to similar triangles, right angle trigonometry and the sine and cosine law to calculate missing angles or side lengths. In grade 11 and 12 trig concepts become even more prevalent and abstract involving topics such as the ambiguous case, trigonometric identifies and the graphing and transformations of trigonometric functions.

In an earlier blog post I discussed the use of spaghetti to produce a graph of the sine function, which was one activity to make trigonometry more hands on. In this post I will discuss a few more options that can make trig a little more hands on within the classroom.

One of the ways trig can be used within the classroom is to look at Pythagorean's theorem and ride angle trigonometry. All you need is some tape, protractors, measuring sticks and square floor tiles. Students can use the tape to cover the gaps between multiple floor tiles, if the tape goes over 4 tiles then the length of that side will be 4. The tap can be used to create a right angle triangle where the length of each side is visually determined by how many squares the tape crosses. The math involved here will be with the angle and the hypotenuse side length as it goes diagonally through multiple squares, making an exact length calculation difficult. Students can measure the lengths of each side with a meter stick or calculate the length of the missing side using Pythagorean's  Theorem. The angle can also be determined using a protractor. Various groups within the classroom can create triangles of different size and record their results to share with other groups. After each group has created a triangle and calculated their missing variables a class discussion can be had about the results discussing how different size triangles effects the angles.

 

Image retrieved from: https://www.teachengineering.org/activities/view/nyu_triangles_activity1

Trigonometric identities, another trig topic seen in the senior level classes, are often infamous among students for being one of the more challenging topics. My goal within my classroom would be to eliminate that stigma against trig identities by creating a classroom culture where student's know its okay to be wrong sometimes, what's important is that you learn from your mistakes and move on! Which is why its important to tell students with trig identities that they require lots of trial and error sometimes, they don't always work out perfectly the first time which is perfectly okay. Another good way to introduce identities is by using non-trig examples first such as:

3x + 4 = 7

Hopefully these strategies can help eliminate the stigma in our classrooms surrounding trigonometry and make the topics fun and intriguing for all the different types of learners in our classrooms!

Grade 12 Mathematics

The content in grade 12 mathematics classes are often difficult to make hands-on and interactive due to the abstract nature of the topics. In class we presented a few activities that can be done in grade 12 data management, advanced functions and calculus and vectors that can be used.

One of the most interesting activities presented was a math escape room. If you are unfamiliar with escape rooms, escape rooms are rooms that are full of puzzles that need to be solved in order to achieve a certain goal (usually escaping the room) but within a classroom the goal can be to open a box. Escape rooms involve a large amount of collaboration and problem solving. They are also an excellent team building activity.

Escape rooms are a great activity to do in mathematics classrooms because they allow all students to collaborate and work together regardless of mathematical ability. This is because the escape room can be designed so that all types of learners can excel at the activity. For advanced functions the clues can be designed to reflect many different topics covered in the course such as trigonometry, transformations of functions or exponential growth.

Escape rooms are an excellent activity to do at the end of a unit as a review class, but could also be supplemented with a formal review session as well. The escape room is not only limited to grade 12 classes either. It can be used in any math class as long as the clues are designed accordingly to your classes mathematical ability.
Overall escape rooms are a great review activity for any mathematical topic!