# Tag Archives: garbage

## More on √2 – Common Crappiness Simply Seen (CCSS)

It’s strange how one can read something many times and miss the complete stupidity of it, in math at any rate.
This is from the CCSSM Grade 8:
The Number System 8.NS (Grade 8)
Know that there are numbers that are not rational, and approximate
them by rational numbers.
2. Use rational approximations of irrational numbers to compare the size
of irrational numbers, locate them approximately on a number line
diagram, and estimate the value of expressions (e.g., π2). For example,
by truncating the decimal expansion of √2, show that √2 is between 1 and
2, then between 1.4 and 1.5, and explain how to continue on to get better
approximations.

I need an approximation to √2. Just get me the decimal expansion, please. Oh, and I need it to 73 decimal places.

Do I have to explain to the authors of this garbage that the only way I am going to get anywhere with √2 is by a process of successive approximation, NOT THE OTHER WAY ROUND ! !

And just try doing this for pi.

“I know that there are irrational numbers”. “How do you know that?”. “Because my teacher told me”.

And where will I encounter π2 ? Or “estimate the value of pi-e”.

And when we get to High School we find:

Use properties of rational and irrational numbers.
3. Explain why the sum or product of two rational numbers is rational;
that the sum of a rational number and an irrational number is irrational;
and that the product of a nonzero rational number and an irrational
number is irrational.

I find real difficulties explaining the last point.

I am not proposing that we go as far as Cauchy Sequences or Dedekind cuts, but if they cannot do a better job than this the topic is best stopped at “√2 is irrational and here’s why”. How many students can prove that √2+√3 is irrational?

Filed under arithmetic, confusion, irrational numbers

## Another Common Core Math Horror

I thought I had found them all, but NO.

————-
Kindergarten
Operations and Algebraic Thinking
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
————-
What has subtraction got to do with taking apart ???
(The examples are all of the form 9 = 3 + 6 and so on).

Also there is NO mention at all of subtraction as a way of finding the difference between two numbers, or of finding the larger of two numbers (anywhere).

While I am in critical mode I offer two more, less awful, horrors from Grade 1:

“To add 2 + 6 + 4,…”  and  “For example, subtract 10 – 8″.

The poor symbols are clearly in great pain at this point. Just read aloud exactly what is written…..

Filed under algebra, arithmetic, language in math, operations, teaching

## Fractions as parts of a whole, again !

This was found on “talking math with your kids” as an example of the “strange” stuff that kids bring home and cause mystification in their parents.

“The whole is 8. One part is 8. What is the other part ?”.

Just what exactly is this supposed to mean?
That the whole always consists of two parts?
Since when did numbers have parts?
What is the definition of “part”?
Even if we are talking about 8 things, then the natural AND logical answer is “There isn’t another part”.
If I want to see ways of creating 8, using adding, then what is wrong with
8=1+7 8=2+6 8=3+5 … 8=7+1 and 8=8+0 for completeness’ sake.

To call zero a part of 8 is going to lay the groundwork for a feeling that math hasn’t got a lot to do with real life, which is a crying shame. This feeling can arise at any stage, we should give reality a chance at this level. To conclude “What a stupid question!”.

Filed under abstract, arithmetic, education, fractions, language in math, teaching

## Fractions are parts of the same whole, part 2

When is a whole not a whole ?

When it’s a hole.

(which half of the hole shall we fill first, the top half or the bottom half?)

Besides, I thought whole was an adjective.