Category Archives: Algebra

Stained Glass Slope Activity (Revisited)

This activity is the most popular activity I’ve ever posted and I can see why. It is fun and combines math and art. Coloring in the design lets you make so many creative choices and I’m always impressed with the results. But most importantly it provides some great practice for graphing diagonal, horizontal and vertical lined.

Start by graphing the list of equations. As you do you will notice relationships between the different lines. When you are done use colored pencils to color it in.

Get the free project printable by clicking here: Stained Glass Slope Project

Graph Paper: Free Printable

Graphing can be one of the toughest skills for math students to master. In my decade of experience as a high school math teacher I noticed that a good sheet of graph paper can make a big difference. I’d run off a bunch of double-sided copies of this before each unit on graphing so it was available and ready to go.
coordinate graph

This graph paper is my favorite design because it fits four to a page and is numbered. I also included a sheet that is specific for Algebra 1, it has space for students to label the slope and y-intercept on the graph. This is perfect for linear equations. Finally, there is one for Algebra 2 students that has space to label the vertex and x-intercepts on a parabola.

Download the free Graph-Paper-Printable-from-Kathryn-Gomes

Let us know how this resource works out for you. And feel free to share it!

The Winter Hiker

skiing and slope

This was my opener for my Algebra class this past week. Here are the discussion questions we used. Activities like this help you think about slope in a real life context.

  1. Which path do you think the hiker should definitely avoid?
  2. Which path is the easiest in your opinion?
  3. Which path leads sharply uphill?

Stained Glass Slope Activity

In my Algebra class we are studying slope. It is such an important concept, it is worth spending extra time making sure students really understand it. A fun activity to add some art into the mixture is this stained glass activity from ilovemath.org.

stained glass window- graphing linear equations

The first page gives you a list of different equations in slope-intercept from. The second page is the answer key. The fun part is coloring in with your own personalized design at the end.

stained glass example

To make it look even cooler tape a piece of tracing paper or wax paper over your graph paper. Draw the lines for the equations on top. When you are finished remove the graph paper and color in your design. Now you can tape the stained glass window graph to a window and the light will pass through.

Problem Solving in Algebra 1

In my Algebra 1 class problem solving is a main emphasis. Each week the students have a special problem to complete on Fridays. It normally involves several steps and some creative thinking. Here is one from last week:

sample POW

This problem was taken from Drexel University’s problems of the week.

When students respond their written explanation is just as important as the mathematical methods they used. Here is an excellent response I received last week:

First I made t = time in hours that has passed by since 8:15 { so at 8:15, t=0} 
then I have
(0,50) and (1.5, 62) 

for (time, temperature in Fahrenheit). Forming a linear equation here. I first had to determine the slope. That will be 
m = (62 – 50) / (1.5 – 0) 
m = 8 

Since the y-intercept (50), then I wrote the linear equation through slope-intercept form. I came up with
y = mx + b 

I replaced y with F for temperature in Fahrenheit, and x with t for time and ended up with

F = 8t + 50 

in order to answer the second question I did this

104 = 8t + 50 
54 = 8t 
t = 6.75 hrs 

6.75 hrs after 8:15AM is 3PM. 

At 5PM, t=8.75. Thus 

F = 8(8.75) + 50 
F = 70 + 50 
F = 120 

So by 5PM, the water in the tub will have a temperature of 120 degrees F. 

The water in the tub won’t be heated in a linear fashion. It will be heated in a logarithmic fashion. Because the wood-burning stove has a maximum temperature, then eventually the water can only be heated until that temperature. If  i assumed that the water follows a linear trend, then it can go beyond the wood-burning stove’s maximum temperature. Another reason why it cannot follow a linear trend is that the particles would begin to heat faster during the first few moments, but eventually slowdown in heating up.

Look all the excellent vocabulary that was included and how clearly you can follow each step. Being able to explain a problem like that in writing means a student fully understands the concepts.

Registration for 2nd Semester Algebra 1 is Now Open

This year there are spots available in my algebra class for 2nd semester students. Registration is now open.

Course Title: Algebra 1- Second Semester

Web-ex time slot: Mon 1:00 PM–2:00PM EST

Grade level: 7th and up

Cost: $299

Required texts: UCSMP Algebra 1 (3rd edition) ISBN#9780076213863

Second semester begins on January 4th and students will be jumping in right as we begin chapter 5. There is a clean break over Christmas so it should be a smooth transition. In order to succeed they will need to have a good grasp on algebraic expressions and equations.

Topics covered will include:

Chapter 5: Division and Proportions in Algebra

Chapter 6: Slopes and Lines

Chapter 7: Exponential Growth and Decay

Chapter 8: Powers and Roots

Chapter 9: Quadratic Functions and Equations

You can find reviews and video clips from the course here. If you have concerns about your student jumping in mid-year they can take a placement test before you decide to register. Please feel free to contact me through this website if you have any additional questions.

Codes

We’ve been working on problem solving skills in my algebra 1 class and lately that has meant creating and breaking codes. One of my students created this one and it was trickier than I expected.  Give it a try and post your comment below.

Using these 4 equation can you find x and y? In class we also did this where instead of variables we solved for shapes or even the operations themselves.

james code

The Top 3 Reasons You Should Take an Online Math Class

Registration for Aim Academy’s 2015-2016 classes opens on March 2nd.  Below I have listed the top three reasons you might want to consider an online math class for next year.

  1. The accountability. This is by far the number one reason students sign up for my classes.  You know that if you’re in a class with deadlines, live sessions, and a teacher checking in regularly you won’t be able to just put it off.  The easiest way to change oh yeah, I need to study for the SATs at some point into 30 hours of solid preparation is to sign up for a class.
  2. The fun. Yes, I did say “fun.” J  When I wrap up my first week of live class a lot of my students message me privately in surprise, they really enjoyed it and were not expecting that.  Who knew you could actually look forward to math class?  When we solve a problem in a new way or use math to explain a card trick I get a bunch of fun reactions (“I’m going to show that problem to my little sister!”).   I’m not offended by the tone of surprise.  If math means getting a textbook out on your own morning after morning and doing problems 1-23 odds that is just boring.  I’m a math nerd and I think that is boring!  With a class you get to have all the fun interaction between students and there is a greater opportunity for activities, lively discussions, and even the occasional math joke (see below).  Even without these added bonuses it is more fun to learn math with students from Hawaii, Alaska, and the Czech Republic.
  3. The reinforcement. One solid math course can really help a struggling student get back on track.  Most students don’t know where they went wrong they just know that suddenly they “don’t understand anything.”  But that is rarely the case. Normally there are just a few skills they never mastered.  With a teacher there to find these gaps and address them they can quickly catch up.

I’d encourage you to sign up for one of my classes.  If not for these three reasons listed above than for the math jokes J

math jokes