Very cool video about how just a few minutes of a computer game, which involves no numbers, can help kids with school based math. Check this out: https://youtu.be/LFR3J9KQsNo
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Top Seattle Schools
The Seattle area has a number of excellent public and private schools. Some of the more well know private schools include Lakeside, Seattle Prep and smaller ones located on Vashon and Bainbridge. Excellent public schools can be found on Mercer Island, in the Bellevue School District and in urban Seattle Public Schools. While it's tempting to look for rankings of the area's top schools, it's also helpful to think of the needs of your child and how nearby schools can meet them. Having grown...
MoreVolume of a cylinder
A battery in the shape of a perfect cylinder has a volume of 15 cm³. Its height is 6 cm. Find the radius of the battery. h= 6 cm
volume= 15 cm³
We know the formula for the volume of a cylinder is:Continue Reading Volume of a cylinder
MoreConversion Factors
Imagine a question about average speed...take a sailboat race that spans 750 miles and is completed in 3 days, 20 hrs and 13 minutes. What is the average speed of this boat in miles per hour? Conversion factors are very helpful in questions like this, along the same lines as dimensional analysis that is often used in chemistry. First, convert the time to hours: We use conversion factors because they help us convert multiple types of units. Here, I have deleted the units that can...
MorePeriod of Trig Functions
Let's start with the general equations of: Y=A sin (B(x-c))+D In this post, we'll talk about the B term. This term helps us find the period, the distance required to complete one cycle. It multiplies the angle. For example y=sin(90°) or in radians, y=sin (π/2) is 1. But if you make B=2 instead of 1 (not shown but assumed in the previous equation), it now looks like y=sin(2(90°) which simplifies to y=sin(2(180°). Or in radians, y=sin(2(π/2)) which simplifies to y=sin(π). These now equal...
MoreOne to one functions
In algebra 1 and algebra 2, the topic of one to one functions often comes up. We know that if a function is one to one, it has an inverse, which can be useful knowledge.
Graphical approaches:
Use horizontal and vertical line tests. Draw a vertical line through the graph and it should only intersect with function at one point. Draw a horizontal line through the graph and it should only intersect at one point. example of a function that is not one to one (fails horizontal line test): e...
MoreTrig functions: Amplitude
Our basic y=sin (x) function looks like this, with the y axis coming in increments of 1 and the x axis coming in increments of π . Now, what happens if the coefficient of sin(x) is changed from 1 (assumed but not written) to -1? Here's a gif of it... all the y-coordinates are now negative where they were previously positive in y=sin(x). And for y=sin(x) all y coordinates which were negative are now positive. If we looks at a function such a...
MoreGraphing trigonometric functions
Trigonometric functions begin with a review of the unit circle and trig ratios. Y=sin(x) begins at the origin, peaks y=1, crosses the x-axis at pi, bottoms out at y=-1 and ends its first period at 2pi,0. Y=cos(x) starts at y=1, descends to cross the x-axis at pi/2, bottoms out at y=-1, crosses the x-axis at 3pi/2, and finishes its period at 2pi. Now, for all functions F(t)=A(Bt-C) + D where f(t) is a trig function, we know that: A: amplitude, B:period=2pi/|B|, C: phase shift is C/B...
MoreConverting radians to degrees
Most students in Algebra II are comfortable using degrees, as that was typically included in their previous geometry course. Radians are an alternative way to measure angles and their refer to the length of the arc on the unit circle for a given angle. For example, a 45 degree angle corresponds to π/4 radians. Think of it like this: the circumference of a circle is 2πr and with a unit circle having a radius of 1, the circumference is 2π. Thus, a circle has 360 degrees or 2πr. Now, an 1/8 of ...
MoreThe Socratic Method
Parents often ask: What's your approach to tutoring algebra or any math subject? Having volunteered and worked as a tutor for several organizations, I use a combination of training and experience to guide my approach. Generally, I use the Socratic Method. Sometimes student simply want answers to questions but this usually isn't helpful in fostering critical thinking and understanding. If they rely on my help for everything I can't prepare them for independent learning. I ask my students qu...
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