Dimensional Analysis for Elementary?

[Earthmerlin]

I was talking to a friend briefly about my 9 year old's need for instruction on word problems. She mentioned 'dimensional analysis' & how it might just help her in math. Anyone care to give me a brief intro. to this concept as it applies to 4th grade?

Edited October 19, 2018 by Earthmerlin

[Lori D.]

Well, I had never heard of this term before, and looked it up. For elementary math, it looks like it would be getting comfortable with unit conversion. And being able to convert from one type of measurement to another can make it easier to do word problems.

So for 4th grade, dimensional analysis would be understanding the relationship between inches and feet, minutes and hours, centimeters and maters, cups/pints/quarts and gallons. And understanding the relationship of fractions -- how to add/subtract/multiple/divide fractions, but also understand that a fraction is a division problem (numerator divided by denominator), and the relationship between fractions and decimals and percents (although that's usually much more of a 6th-8th grade/Pre-Algebra connection).

I would guess why dimensional analysis was suggested is because for some word problems, it is easier to understand and solve if you convert from one unit of measurement to another -- for example, converting hours and fractions of hours into total minutes.

Examples:

How many minutes is 1.5 hours?
1 hour = 60 minutes
1.5 hours = 1 hour + 1/2 hour = 60 min. (1 hour) + 1/2 hour (half of 60 min. = 30 min.) = 60+30 = 90 min.

How many inches is 3/4 of a foot?
1 foot = 12 inches
3/4 of a foot = 9 inches
(several ways to get to that: 12/1 (12 inches in 1 foot) x 3/4 (3/4 of a foot) = 36/4 = 9)
(or, another method: 3/4 = 1/2 (half of 1 foot) + 1/4 (1/2 of 1/2) --> half of 1 foot = 6", half of half = 3", 6"+3"=9")

But, I could be completely off the mark about what was meant by dimensional analysis and how it would help, LOL. (:D

Edited October 19, 2018 by Lori D.

[EKS]

Does your friend have experience teaching fourth grade math?  If not, I'd disregard.

What I did with my (advanced) students at that level, if I did anything at all, was to show them how you can "do math" on units the same way that you do with numbers, and if the units don't come out correctly, then you know you did something wrong.  But I didn't expect them to actually do anything with this on their own until they were doing high school level work.

Edited October 19, 2018 by EKS

[domestic_engineer]

We just did dimensional analysis in Rightstart Level F, 2nd edition, where it's placed near the end of the book.  It's building upon a firm (Rightstart) foundation of fractions, though.

Dimensional analysis is generally helpful with solving word problems, but in fourth grade, I would guess that it's more of a plug-and-chug, follow-my-pattern "trick" rather than an understanding of why it works.  OP, are you asking how and why it works?  I don't doubt that you could teach a 4th grader how to do dimensional analysis, just like you could teach a 4th grader to use a calculator; but I'd personally hold off until they can understand *why* it works.

[Gil]

2 hours ago, Earthmerlin said:

I was talking to a friend briefly about my 9 year old's need for instruction on word problems. She mentioned 'dimensional analysis' & how it might just help her in math. Anyone care to give me a brief intro. to this concept as it applies to 4th grade?

Well, there is a very healthy chance that your friend was throwing around "edu-speak buzz-words", perhaps without knowing what they mean fully. (Also possible that I have a limited view/understanding of the term. That's perfectly plausible as well)

Dimensional Analysis is usually taught in chapter one of any Physics of Chemistry text, since units matter in science words problems, but students in the US can get through their entire K-12 education without ever having to pay attention to the unit in math class (and yes, this boggles my mind)

It's a step that requires you to parse out and understand the units and interplay of the units used in the problem. In science texts that I've seen, its done with units of measurement because science we're weighing, measuring and counting specific things. But I think that your friend meant Dimensional Analysis more as a fancy way of saying "pay attention to your units" and thing logically about them.

Part of the problem that trips kids up so badly with rate problems, and ratio problems,  in middle school is not understanding units and how they work in relation to the context of the math itself. I don't think that 4th grade is too early to teach kids to pay attention to their units in a math problem.

For example, when I tutor kids in arithmetic, I make the kid figure out what operation to use, then set up a blank equation with only the units put in.

So some problem like

"Mikey and Clara want to hike a 713 mile trail on their 11 day vacation. How many miles do they need to hike each day to complete the trail in time?", would be set up like this

                     ________________   miles of the trail per day that Mikey and Clara should hike.
______days ) ______ miles of the trail

 

Or, if the kid preferred like this:

_____miles of the trail [division sign]  ____ days of vacation =  ______miles of the trail per day of vacation

Or even as a fraction with _____ < miles of the trail  = _________ miles of the trail per day.
                                                      < days of vacation.
 

Like wise, if you wanted to solve a problem like "If Tom and Marco hike 37 miles each day of their 2 week vacation, how far will they hike on their entire vacation?"

You might have to ask some leading/guiding questions, but eventually the kids should set up something that looks a lot like this:

____ miles per week * _____ weeks of vacations = _____ miles hiked on the entire vacation


Or like this.

____ miles per day * _____ days of vacation  = ______ miles hiked on the entire vacation.
 

Once they get to this step, they realize that they aren't directly given the exact number of days, so they use the information that they are given to find out how many days Tom and Marco are on vacation. Some kids will know that a week is 7 days, and 2 weeks is 14 days, others will have to add or multiply to get that its' 14 days.

If I were you, I would be tempted to call up this friend and ask them for more explanation. 

 

 

[Earthmerlin]

It was a brief conversation & I think she may have not given much thought as to its applicability to 4th grade. Since it's a new phrase and concept for me, I cannot give an opinion but just wanted to post here in case anyone is familiar with this at this age. Thanks!