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From Khan Academy: Comparing Decimals

No, Sal Khan did not actually submit this question. But Andyhav3 asks:

What’s this student getting at with “the right side of the decimal,” and how might you help Andyhav3?

[Click here to see how your approach compares to how his question was actually handled.]

6 replies on “From Khan Academy: Comparing Decimals”

mpershansays:

My guess is that Andyhav3 is confusing the denominators of fractions with the right side of a decimal.

I think that I’d start by asking him to explain what 0.5 means. If we can anchor him in with the idea that 0.5 is the same as a half, I’d ask him, “half of what?” Then I’d ask him to explain whether, based on his answer, 0.9 should be bigger or smaller than 0.5.

Perhaps the confusion comes from negatives. We as teachers are very poor when transitioning from positives (one side) to reals (both sides). For example, it’s not uncommon for a student to identify -100000000 as really small, when in fact it’s REALLY BIG in a NEGATIVE direction. (Is there a better way to say that?)

Anyway, my best guess at this kid’s mistake is that he’s confusing something he learned about negatives with what he should know about place value and magnitude.

Rachelsays:

Marshall, I agree with you–it seems like this student sees the decimal point as some kind of turning point/reflection in the way that he should think about numbers. Tricky, because it is a ‘line of symmetry’ for the names of place value, but not for value comparison.

I would go back to conversations of place value, and talking about place value as a unit of comparison. Which is bigger, 675 thousandths, or 645 thousandths?

Maybe one other possibility is that he’s confused about whether having more small stuff actually means that you have less.

Or maybe he’s confused about the difference between 0.645 + 0.03 = 0.675 which adds a positive and makes it bigger, and things involving multiplying by decimals which makes them smaller.

It makes me wonder what we can do to build students’ understanding of place value when they think they’re old enough that they don’t want to hear it any more.

Also, reading that feedback on the KA site doesn’t really make me excited as a student to share my question with the world.

delisesays:

This seems like another good example of how insufficient instruction by drill & memorization really is.
Was anyone else concerned by the way Mr. Khan said the numbers in this problem? Decimal numbers can be more confusing for students if we as teachers are not precise with our language. The word form of the number 45.675 is “forty-five and six hundred seventy-five thousandths.” Mr. Khan repeatedly says “forty-five and six hundred and seventy-five thousandths” instead. Knowing that numbers can be expressed in multiple ways, the word form used here really suggests the expression 45 + 600 + 0.075 which is not equivalent to 45.675. That word “and” implies the combining of parts, or addition. Used correctly (only where the decimal point sits in a number), it makes sense. 45.675 = 45 + 0.675.
Think about the numbers 600.075 and 0.675. The way Mr. Khan was saying numbers, he would use the same word form for both of these numbers.