Hot Lava Mama Posted August 6, 2015 Share Posted August 6, 2015 How do I show the unit conversion process where you multiply to change from a larger to smaller unit and divide to change from a smaller to larger unit? My son is confused and thinks it should be the opposite. Any hands-on way to show this so it makes sense to him? Thanks! Hot Lava Mama Quote Link to comment Share on other sites More sharing options...
Lang Syne Boardie Posted August 6, 2015 Share Posted August 6, 2015 Use water -- gallon jug, quart mason jar, pint jar. (Edited: forgot to say that this is most effective when you're actually writing the conversions on the chalkboard as you work it out, so that he can see what happens to the numbers.) Quote Link to comment Share on other sites More sharing options...
73349 Posted August 6, 2015 Share Posted August 6, 2015 It didn't make sense to me until someone showed it to me as multiplying by a fraction that equals one, and you have to orient the fraction so that the unwanted unit cancels out. So 2 gallons * (4 quarts/1 gallon) = 8 quarts; or 5 yards * (3 feet/1 yard) = 15 feet; etc. 3 Quote Link to comment Share on other sites More sharing options...
SilverMoon Posted August 6, 2015 Share Posted August 6, 2015 A ruler with millimeters marked. Quote Link to comment Share on other sites More sharing options...
Kiara.I Posted August 6, 2015 Share Posted August 6, 2015 It didn't make sense to me until someone showed it to me as multiplying by a fraction that equals one, and you have to orient the fraction so that the unwanted unit cancels out. So 2 gallons * (4 quarts/1 gallon) = 8 quarts; or 5 yards * (3 feet/1 yard) = 15 feet; etc. This is a completely NECESSARY skill set, and a gift you can give your children. I aced physics quizzes I hadn't bothered studying for by looking at the units they gave me, and the units I was supposed to end up with in the answer, and building my own formula to make it work. Not that I'd *advise* that method of doing physics, of course. ;) But it's a very, very useful skill to have. 1 Quote Link to comment Share on other sites More sharing options...
Syllieann Posted August 7, 2015 Share Posted August 7, 2015 It didn't make sense to me until someone showed it to me as multiplying by a fraction that equals one, and you have to orient the fraction so that the unwanted unit cancels out. So 2 gallons * (4 quarts/1 gallon) = 8 quarts; or 5 yards * (3 feet/1 yard) = 15 feet; etc. Yes, this is the best way to illustrate it. The term you would Google for examples is "dimensional analysis." It will serve your student well all the way through college science classes. Quote Link to comment Share on other sites More sharing options...
Kerileanne99 Posted August 7, 2015 Share Posted August 7, 2015 Yes, this is the best way to illustrate it. The term you would Google for examples is "dimensional analysis." It will serve your student well all the way through college science classes. Yes, absolutely. Hubby teaches college chemistry and I tutor it. For some reason converting between units absolutely slays half the class. I have made a LOT of money simply showing students how to cancel units in the denominator with those in the numerator:) every professor I know or have had uses dimensional analysis (aka factor analysis). 1 Quote Link to comment Share on other sites More sharing options...
Hot Lava Mama Posted August 7, 2015 Author Share Posted August 7, 2015 Thanks for the help, above. I forgot to mention that this is for a 3rd grader that hasn't had fractions to any extent. He understands what fractions are, but we haven't done any addition or multiplication with them. Quote Link to comment Share on other sites More sharing options...
Hot Lava Mama Posted August 7, 2015 Author Share Posted August 7, 2015 Use water -- gallon jug, quart mason jar, pint jar. (Edited: forgot to say that this is most effective when you're actually writing the conversions on the chalkboard as you work it out, so that he can see what happens to the numbers.) Can you give me a little more detail? So, I have a gallon jug and I want to change it to cups. I take the cups out and count them (I assume?), then "multiply" by the 1 gallon. Is that correct? How would it work with the division part? Sorry if I am being dense but I have not slept well for about a week as I have had sick kids. Thanks for your help. Hot Lava Mama Quote Link to comment Share on other sites More sharing options...
Tanikit Posted August 7, 2015 Share Posted August 7, 2015 I think it might help if he understood that dividing leaves you with a smaller number and multiplying leaves you with a larger number - then he needs to know that you will have more cups than you would gallons and so on. This is definitely where manipulatives need to be used first though - has he poured and measured and wet the kitchen floor enough or is he just playing with figures in a book? You could try metric measurements first too - the concepts are exactly the same, but using 10/100/1000 is much easier to explain the concepts without him stressing about the dividing and multiplying which is a relatively new concept for a third grader. Hot lava Mama - you have 32 cups and want to change that to gallons - now you would need to divide by 16 cups/gallon 32 cups 16 cups 32 cups 1 gallon -------- divide by --------- which then gets changed to --------- x ---------- = 2 gallons 1 gallon 1 16 cups But if you know gallons hold more water than cups then you know you will have fewer gallon jars than you would need cups so you must divide and not multiply. Quote Link to comment Share on other sites More sharing options...
go_go_gadget Posted August 7, 2015 Share Posted August 7, 2015 Can you give me a little more detail? So, I have a gallon jug and I want to change it to cups. I take the cups out and count them (I assume?), then "multiply" by the 1 gallon. Is that correct? How would it work with the division part? Sorry if I am being dense but I have not slept well for about a week as I have had sick kids. Thanks for your help. Hot Lava Mama I would start without the math terms, and demonstrate finding out how many cups are in a gallon. Observe that there are 8 oz in each cup, then the number of cups in a gallon to finding out how many of 8 in 64. If multiplication and division are well-understood, then the relation is clear. If not, I'd focus on those concepts with c-rods, and revisit unit conversion later. Quote Link to comment Share on other sites More sharing options...
justasque Posted August 7, 2015 Share Posted August 7, 2015 Thanks for the help, above. I forgot to mention that this is for a 3rd grader that hasn't had fractions to any extent. He understands what fractions are, but we haven't done any addition or multiplication with them. Then, frankly, I would wait. The unit analysis method described by other posters is by far the best approach, but you can't do it until you have a basic understanding of multiplying fractions and cancelling units. I know some texts obsess over it in the lower grades (ABeka, I'm looking at you), but I don't think it's worth the stress if the child isn't picking it up after some explanations and a bit of hands-on work. By 6th grade, give or take, they will be ready for unit analysis, which will serve them VERY well in the high school years and beyond. 3 Quote Link to comment Share on other sites More sharing options...
swainsonshawk Posted August 7, 2015 Share Posted August 7, 2015 This is a concept all my kids have struggled with. I teach it, we draw pictures, I help them through each instance if they need it. Not all of my kids "get it". Eventually, they've gotten it, but not necessarily at age 8. Quote Link to comment Share on other sites More sharing options...
Kuovonne Posted August 7, 2015 Share Posted August 7, 2015 How about using units that he is already very familiar with, where he already has an intuitive sense of the relative sizes of the units. rulers: inches, feet, and yards. There are more inches in a food, so you must multiply to go from feet to inches. There are fewer feet than inches, so you must divide to go from inches to feet. You can use 1" tiles, a ruler, and a yardstick to make it tactile. (If you don't have 1" tiles, just cut out 1" paper strips.) time: seconds, minutes, hours, days, weeks, months, years Use the same process as above. He should already know when you need a bigger or smaller number when you convert; multiplying yields the bigger number and dividing yields a smaller number. You can use an analog clock for seconds, minutes, and hours. You can use a calendar for days, weeks, months, and years. Part of the beauty of using these units (length and time) is they have different conversion factors. Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted August 7, 2015 Share Posted August 7, 2015 Thanks for the help, above. I forgot to mention that this is for a 3rd grader that hasn't had fractions to any extent. He understands what fractions are, but we haven't done any addition or multiplication with them. In this case, I would NOT teach any rule at all. Rules are abstract shortcuts, but they only work short-term. In the long run, they get all jumbled up in memory and lead to confusion. I would approach each problem as a logic puzzle: "We measured 59 inches, but we'd really like to know how many feet that is, and how many extra inches left over. How can we figure it out?" If he can't logic it out, then try doing more real-life measuring until he internalizes what the units mean and how they are related. Don't let your textbook rush him through this. Measuring is important, so spend the time you need so it makes sense. Then in middle school (or some time before high school chemistry), he needs to learn dimensional analysis. 1 Quote Link to comment Share on other sites More sharing options...
AnthonyPaul359 Posted August 7, 2015 Share Posted August 7, 2015 Get a couple of graduated cylinders and color code with marker or something the units in liters, oz, and milliliters so your kid can visualize how much liquid is in there and make comparisons. Quote Link to comment Share on other sites More sharing options...
go_go_gadget Posted August 8, 2015 Share Posted August 8, 2015 I would start without the math terms, and demonstrate finding out how many cups are in a gallon. Observe that there are 8 oz in each cup, then the number of cups in a gallon to finding out how many of 8 in 64. If multiplication and division are well-understood, then the relation is clear. If not, I'd focus on those concepts with c-rods, and revisit unit conversion later. Having said this, it occurs to me that I've always started my kids with metric unit conversions. Imperial is for masochists. 1 Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted August 10, 2015 Share Posted August 10, 2015 Having said this, it occurs to me that I've always started my kids with metric unit conversions. Imperial is for masochists. Lol! But really, imperial is for FRACTIONS. Almost everything is a half, third, quarter, or twelfth of something else. Lots and lots and lots of fractions. :) 1 Quote Link to comment Share on other sites More sharing options...
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