High School Number and Quantity Tests
As students advance from kindergarten to the middle school years the concept of a number makes several transitions. Values begin as your basic 1, 2, 3s and then eventually we come across a zero and it attribute it to nothing or the lack of anything. In middle school students begin to learn the difference between rational and irrational numbers. In this curriculum the concept of a number is taken to new heights by the introduction of imaginary numbers and complex numbers. The definition of these numbers requires you to evaluate a system. In the sense of an imaginary number, they are values that when squared have a negative outcome. Students at this level begin to model systems and encounter a wide range of math applications. Being able to quantify values is fundamental to learning higher level scientific concepts. I find this section of the high school curriculum to be the biggest mash-up, if you will. There are so many skills that overlap other high school course that it amazes me.
- Question Sampler - When I was done putting this together I realized that all of the sections of the core curriculum have a page each here.
- Multiple Choice Questions Form A - A major publishing company has requested to license this test from me, it must be written well.
- Short Response Questions Form B - I rewrote this one due to a complaint that I used too many cute pictures. Is the toy box all right?
What Is This Curriculum All About?
There are three primary focuses in this high school level curriculum. The main focus is on the uses and applications of real and complex numbers. To a slightly lesser extent students are introduced to the concept and application of both matrices and vectors. Within this scope students spend a great of time algebraically breakdown everything and work towards understand patterns and the relationships that are created within these areas.
We begin, normally, with the real number system. Students get a quick reminder on the use of roots and exponents. We go through all the common operations and then begin to write slightly complex expressions. We than learn about writing radical expressions and the concept of irrational numbers. The goal is for students to just begin to understand how these values can be used to help them model mathematic situations that they may come across.
One of my favorite areas of this curriculum is the study of quantities. It may just be because my background is rooted in science and engineering. Students will primary learn how to model and communicate data to other people. Understanding which formula, you should use in certain situations based on the level of accuracy and precision that you are centered on becomes paramount in this section of the curriculum. We also explore the concept of significant digits and how to decide how accurate your solution is required to be.
Complex number systems is most likely why students view this section as difficult. I would argue that this is primarily because all the material in this section is completely brand new to most students. The other sections tend to all build off of prior knowledge. Students not only learn how to process operations with complex numbers, but how to graph them and apply them to polynomial identities.
We finish off the curriculum concentrating on the use and application of matrices and vectors. Just like all the other units, we focus on operations at first and then we transition over to two-step operations. Teachers than spend a good bit of time showing how you can use both of to not only display, but analyze data.