Multiplication Made Visual

In school, multiplication is taught by giving students a specific method to use (which they call the "traditional" method), and you have to solve problems with it. By only providing one of over a dozen multiplication methods, this eliminates the creativity, and quite possibly the fun, in multiplication. I'm not going to dwell on these issues; you can read my Capstone Research Paper for that.

I have discussed a few other methods of multiplication on this blog, one of which is the Criss-Cross Method. Again, I won't explain it here, but this method does lay the foundation for the new method I am going to explain today.

Rather than taking you through the steps, I will post a video tutorial on how to do it (those are usually more fun anyways). If you are wondering why it works, I encourage you to refer back to the Criss-Cross Method and notice the similarities. Try a few problems with the Criss-Cross Method, and then this method, and see how the numbers that appear throughout the problem seem to be identical.

When you watch this video, I would strongly suggest doing the examples along with the video. It can be a very useful technique for problems whose digits are of a reasonable size.

I think this is a really cool method of multiplication, and even easier to teach than the traditional method. Play around with it, and you will likely end up using it in the future.

For some more intellectual readers, it might be fun to try multiplying numbers with bigger digits using the quinary or senary number systems (base five or base six). This would make less dots in each section. I think it might be a fun exercise.

Answers to June Problem of the Week:

*For the answers to the creation of a line of best fit, it will be written as an inequality. There is no way to get the exact answer by hand, so just make sure your answer is in the interval that is written.

Easy:
a = 7¹/₃
p = 14

m = ¹¹⁸⁹⁸⁸/₆₉₂₅
n = ³⁹⁴/₂₇₇
y = 15.76
z = 12.08
g = 8
b = 112
q = 44
x = 33

Medium:
h = 105
p = 270
t = 19
n = 92925
u = 92.925
q = 135
a = 2165.2875
d = 21.652875
g = 15
j = 46.4625
k = 23.23125
r = 27
s = 45
2 < m < 3.5
45 < b < 50
175 < x < 275

Hard:
s = 107
t = 365
p = 905
q = 4096
q₀ = 4096
q₁ = 2048
q₂ = 1024
q₃ = 512
q₄ = 256
q₅ = 128
q₆ = 64
q₇ = 32
q₈ = 16
q₉ = 8
q₁₀ = 4
q₁₁ = 2
q₁₂ = 1
q₁₃ = ¹/₂
q₁₄ = ¹/₄
q₁₅ = ¹/₈
x₁ = -452.5
x₂ = -2
x₃ = 4
y = 0
a = 226.25
b = -224.25
c = -454.5
t = 2635773.77
m = 34
x = 79.53%