# Tag Archives: ratio

## Huh? Making sense of Common Core

OK, I get it. The Common Core State Standards are about large-scale coherence. Stay focused on the big picture of getting everybody going in the same direction, then tweak things later, blah, blah, blah… I get it.

And yet kids’ education is at stake. And teachers’ jobs in the era of No Child Left Behind and Race to the Top. And the quality of curriculum that has to bend over backwards to align with these standards.

So when I dig into the details in my capacity with Connected Math, I get indignant about places where things don’t make sense. Consider the case of ratios at sixth grade:

6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger.”

I’m OK with this. I’m not thrilled with the “unit rate a/b” part, but it’s not a train wreck. Let’s look ahead to seventh grade, shall we?

7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Huh?

The complex fraction (1/2)/(1/4)? Are you kidding me? Just try verbalizing this:

I walked one-half-over-one-fourth miles per hour.

Does anyone ever talk about rates this way? Ever?

No way! The only way to even come close would be to say,

I walked a half a mile in a quarter of an hour.

But then that’s not a unit rate. For some reason Common Core is obsessed with unit rates-strictly defined. If I thought this were a throwaway line, I wouldn’t be worried. But it’s not a throwaway. That sixth grade standard above? It had a footnote:

Expectations for unit rates in this grade are limited to non-complex fractions.

So the Common Core writers didn’t just make this (1/2)/(1/4) unit rate nonsense up on their first pass through seventh grade. Oh no-it was important enough to go back and exclude it from sixth grade. And important enough to use up one of only three footnotes in the entire 6-8 math standards. The other two? Here’s the next one:

Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

Are you sensing a theme here?

Right, it’s this other odd obsession with complex fractions (i.e. fractions in the numerator and/or denominator).

And the third footnote:

Function notation is not required in Grade 8.

Phew.

UPDATE: Reader Sean steps up to defend this standard in the comments below. I highlight his objections in a later post, and then respond in yet one more post on this topic.

## 50/50

### The setup

The Walker Art Center in Minneapolis has an exhibit titled “50/50″. The premise is that half of the exhibit was selected by public vote online and the other half of the exhibit was selected by museum curators in response to the public selections.

### The questions

In the photo below, we see the public half of the exhibit on the left. The curators’ side on the right is masked in black. In fact, you can only see about 2/3 of the public’s side; the remainder is past the left-hand edge of the photograph.

(1) How many works are in the exhibit?

(2) How many did the public choose?

(3) How many did the experts choose?