Hello fellow math lovers! My name's Cameron Woods and I'm here to teach you about algebra blocks! With over 2.5 months of Algebra 1.5 experience, I am highly qualified for this job! Over the last couple of months we've gone over a number of challenging problems, algebra blocks being included many times. It's amazing how much I've learned in such a short period of time!
To begin, lets try to solve some sample problems.
To begin, lets try to solve some sample problems.
1. A rectangle whose length is x and whose width is 1 is called an x-block. The figure shows two of them.
a. What is the area of an x-block?
The area of an x-block is x, because it's simply x multiplied by 1.
b. What is the combined area of two x-blocks?
2x. This is because 1x+1x= 2x.
a. What is the area of an x-block?
The area of an x-block is x, because it's simply x multiplied by 1.
b. What is the combined area of two x-blocks?
2x. This is because 1x+1x= 2x.
c. Show that there are two different ways to combine two x-blocks to form a rectangle whose area is 2x.
d. Draw two different rectangular diagrams to show that x+2x=3x.
A few important skills you can take away from these problems are combining like terms, distributing, and a good understanding of an x-block!
2. Draw a diagram using the appropriate number of x-blocks and 1-blocks to illustrate the distributive property 3(x+2) = 3x+6
For a more in-depth explanation, visit http://www.youtube.com/watch?v=KRZSdieGN3k&feature=youtu.be
For a more in-depth explanation, visit http://www.youtube.com/watch?v=KRZSdieGN3k&feature=youtu.be
This problem is good practice for illustrating distributive properties.
3. Draw an algebra-block diagram that shows that x(x+2) = x•x+2x
If you don't understand how I drew this, please click below.
4. Label the figure at left so that it provides a geometric representation of x(x+3)
For a step-by-step video of how I labeled this, visit
http://www.youtube.com/watch?v=QaimfWw0Pb0&feature=youtu.be
For a step-by-step video of how I labeled this, visit
http://www.youtube.com/watch?v=QaimfWw0Pb0&feature=youtu.be
This problem focused more on labeling the algebra-block, and less on actually illustrating it. I found that when a distributive property is in the format of x(y+m), x is the length of one side length, while y+m is the length of the perpendicular one.
5. Draw an algebra-block diagram that illustrates the equation
(1+x)y = y+xy.
To understand how this block illustrates the equation, please visit:
http://www.youtube.com/watch?v=89UdRWydSB4&feature=youtu.be
(1+x)y = y+xy.
To understand how this block illustrates the equation, please visit:
http://www.youtube.com/watch?v=89UdRWydSB4&feature=youtu.be
This problem was similar to the ones above, but it's still useful to practice and learn! Problems like this are great for learning distributive properties!
6. Show how an xy-block and a y•y-block can be combined to illustrate the equation (x+y)y = xy + y•y
7. Write (x + 1)(x + 2) without parentheses. Explain how the diagram at left illustrates this products.
Source: Molly Mazor-Brown
In conclusion, I think this project went very well. I was able to understand a lot more about algebra blocks after this. I also was excited about viewing my classmates' websites! It's interesting to see all the different pages/topics. I really enjoyed doing a creative project in class in lieu of our usual Phillips Exeter Academy problems.