Reteaching Decimals And Fractions Fractions: Fill & Download for Free

That is a great question. Teaching time is a difficult concept to teach out of context (i.e., in a lesson) One my team of teachers worked on for over two years to better define and prepare lessons for grades K-3. Here is what we discovered.Digital and analog are like decimals and fractions. Digital and analog are two ways to measure time just like decimals and fractions are two ways to measure distance and volume. The way you read time is the same for both digital and analog. So, we focused on teaching analog visually and wrote the time in digital.Analog is inherently more difficult. Give yourself time to teach analog. The short hand is easy to understand as the hour hand, but it is difficult for students to understand visually. It is hard to see what the short hand is pointing to and if it is not exactly the hour, the short hand is often between the current hour and the next. Students often confuse the current hour as the hour that has past already so they naturally often want to read the number that is next. Conversely, the long hand reads the tick in increments of five between the cardinal numbers of 1–12. Like denominators in fractions, you have to teach students that for the long hand, the cardinal number 1 is really 5, 2 is really 10, 3 is really 15, and so fourth. Make sure students understand this concept before having students read out the minutes by skip counting. It can be confusing for students when they are asked to read our 3:27 as 3 and 5, 10, 15, 20, 25, 26, 27. Other than 5 and 10, those numbers are not on the analog clock. I have had teachers cover the hour numbers with the corresponding minute numbers with success. In our opinion, it was easier for students to learn to see the larger number and remember the smaller number than the other way around. Plus, I think it helps learning to read analog when no numbers are present. This is not a problem with digital, it gives you the numbers to read.The research (for us anyway) is out whether to teach common benchmark times (whole hour, quarter hour, half hour) before teaching hours and minutes. Either way, these terms are easy to memorize but difficult to understand. We mostly tried to stay away from those terms until they were being taught in fractions.In analog, “Showing Time” is easier than “Reading Time”. We learned that students are more confident when you ask them to manipulate the hands to make a given time than trying to read the hands set for a particular time. These are two different set of skills that are often taught at the same time. We chose to teach “Showing Time” to some level of mastery before “Reading Time”. It saved a lot of intervention time later.Here’s the kicker. We often wondered why should we spend so much time on analog if digital was so much easier. Well, it makes a difference when teaching students “Elapsed Time” later. We found that the students who understood analog did better counting up/down hours and minutes for elapsed time. Students really struggle retaining the hours when crossing over 12. For example, if the question is, “If John when to school at 9:15 and got home at 4:30, how much time did John spend away from home?” A lot of students would just subtract 4:15 from 9:30. Analog proficient students could count up knowing 1:00 was counted as the 4th hour.Here is an observational note: try to avoid reading time chorally. Specifically, when reading time like the example in point number 2. There are students who will chime in chorally after the class and teacher have started. These students will often not make the connection between the skip counting and the minute intervals on the clock. The hard part, the teacher will not catch this until independent practice leaving a chunk of students needing reteaching while the rest of the class is advancing.Well, that is what we learned. I hope it helps you and your team plan successfully!

A negative decimal, for instance, [math]-0.5[/math] can’t be converted into a positive fraction! Maybe a fraction, but certainly not positive!If you owe someone money, say $1,000, this is the same as having -$1,000 in your balance. The only way to make your balance positive, i.e. +$1,000, is to give that person a $1,000 and then gain ANOTHER $1,000. There is no possible way to just omit that negative sign!So a negative decimal like [math]-0.5[/math] can be rewritten as [math]-\dfrac{1}{2}[/math].Or you may put a pair of parentheses around the fraction with a negative upfront. But don’t you dare omit that negative sign! It’s a crime for which mathematicians are going to hunt you down and reteach you what’s 1+1 equal to.EDITThe OP might be asking about the absolute value of a negative number, in which case it doesn’t matter if the input of the absolute value function is positive, negative, fractional, or decimal. The absolute value of any number is always the positive of that number.

Of course. It's the same as with any other knowledge. There are PLENTY of things I learned in elementary, middle, and high school math and did tons of practice problems doing that I've had to reteach myself over the years. For example, when I started learning linear algebra last semester, I was really struggling to solve systems of equations using matrices and I finally realized it was because I was out of practice just using algebraic elimination to solve them. I'd learned that method years ago, doing practice problems, but then never really used it afterwards, always defaulting to substitution. However, Gaussian elimination (the method first introduced to solve systems of simple linear equations using matrices) is an extension of the simple elimination method. Once I retaught myself how to use basic elimination (and understood it better than I had the first time around I think), Gaussian Elimination became easy and even a little fun (primarily because it felt really good to suddenly be easily able to solve problems that had been making me want to bang my head against the wall in frustration).Another example is converting between decimals, fractions, and percents. I learned how in elementary school and I'm sure I did plenty of homework problems, but for years afterwards I could never remember how to do it except for particularly easy ones, like 0.5 to 1/2 to 50%. Now I can do it easily and I've been able to years because I learned to how derive the formulas algebraically, which is quite simple.Something I currently still struggle with is remembering the difference between “injective”, “surjective”, and “unto.”. I always have to look them up, even though I have no trouble understanding the differences when I'm told them. If anyone has a good way of remembering those definitions, please tell me in the comments.I also remember when I learned trig about a year and a half ago with Khan Academy, I didn't move on to the next section until I felt confident in my ability to solve the problems in the current section, but when I got to the unit tests I found I'd already forgotten stuff from the earliest sections. I realized later that this was at least partly because I was too focused on learning the algorithms and not on where they came from, why they worked, or what they meant. That made the whole thing too much of an exercise in memorization and meant I later had to go back and reteach myself some of the stuff I had only partially learned.Don't beat yourself up if you find that some of your math skills are rusty or even that you've completely forgotten stuff. That doesn't make you bad at math, it just means you're a human with imperfect memory like everyone else (I hope that doesn't come off as patronizing because it's not meant that way. It's something I've told my students many a time when they're feeling like they just aren't capable of learning something and it usually seems to help.)