### Pet peeves with Common Core Standards, part 2

QUOTE from Common Core standards for 7th grade:

Okay, I am not with this totally.

For example, let's say you are supposed to find the distance between −4/7 and −5/9. Two negative fractions. They want the student to construct the difference −4/7 − (−5/9) and then find its absolute value. Remember we are in 7th grade.

I find a more natural approach (and isn't it easier to SHOW this to students?) is to find the distance between 4/7 and 5/9, which is of course equal to the distance between −4/7 and −5/9.

I feel students might have difficulties if they are supposed to take the difference of two negative numbers, and find the absolute value of that. They might make mistakes even in writing out the expression −4/7 − (−5/9) correctly.

ALSO, the standard actually words it as "SHOW that...". In other words, IF I understand this correctly, students aren't only supposed to know how to find the distance, but also to be able to PROVE that "the distance between two rational numbers on the number line is the absolute value of their difference."

In mathematical symbols, do they really want the STUDENTS to show/prove that

When it gets to dealing with negative fractions & decimals, I feel it would be enough for 7th graders to show INFORMALLY, using a number line, HOW to find the distance, without having to write it with symbols (where you need to use the absolute value OF the difference).

I mean exercises such as these:

Any thoughts?

**The Number System 7.NS**c. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Okay, I am not with this totally.

For example, let's say you are supposed to find the distance between −4/7 and −5/9. Two negative fractions. They want the student to construct the difference −4/7 − (−5/9) and then find its absolute value. Remember we are in 7th grade.

I find a more natural approach (and isn't it easier to SHOW this to students?) is to find the distance between 4/7 and 5/9, which is of course equal to the distance between −4/7 and −5/9.

I feel students might have difficulties if they are supposed to take the difference of two negative numbers, and find the absolute value of that. They might make mistakes even in writing out the expression −4/7 − (−5/9) correctly.

ALSO, the standard actually words it as "SHOW that...". In other words, IF I understand this correctly, students aren't only supposed to know how to find the distance, but also to be able to PROVE that "the distance between two rational numbers on the number line is the absolute value of their difference."

In mathematical symbols, do they really want the STUDENTS to show/prove that

*The distance of p and q = | p − q| , for all rational numbers p and q.*When it gets to dealing with negative fractions & decimals, I feel it would be enough for 7th graders to show INFORMALLY, using a number line, HOW to find the distance, without having to write it with symbols (where you need to use the absolute value OF the difference).

I mean exercises such as these:

- Explain how to find the distance between -0.8 and 4.9.
- How far apart are −1/2 and −1 1/4?
- Explain how to find the distance between −200 and −1,600.

Any thoughts?

## Comments

When my 6th grader was in 4th grade, they had "problem of the week". These weren't graded, but were, roughly speaking, impossible. Add the numbers from 1to 100. Simple. It's 5,050. Just bang it out on a calculator. Opps, pressed a wrong button, so start over. Opps, ran out of attention span. Or, just go to a computer and type gcc < "main() { int i, s; s=0; for (i = 1; i <= 100; i++) s+=i; printf("%d\n", s);}"

Then "./a.out". (Sorry for any typos.)

Or, use the closed form x*(x+1)/2, for x=100. These approaches are beyond most 4th graders.

Gauss was said to have solved this in first grade, in a minute or so. I doubt it. He's said to have said that 1 + 100 is 101. 2 + 99 is 101. The numbers meet at 50 + 51, which is 50 numbers. So 50 * 101 = 5050. But i learned multiplication in 4th grade. I think it's taught a bit earlier now, but not in 1st grade.