Word Problems All Operations Grade 3: Fill & Download for Free

I'm writing this answer geared towards parents and people who did NOT study math in college (are not mathematicians or engineers).----First, what Varun said, quoting Feynman: Math is a language. This is the first thing that really needs to be understood. Kids struggle with word problems is because they're learning math as a set of algorithms. But it's not. In fact, word problems should be the EASIEST math problems. Word problems are what you do in the kitchen when you make a recipe for twice as many people, or when you figure out how many gallons of paint to buy in the store. People have practical experience with word problems.If they learned to translate between math and whatever their spoken language is, it would make a lot more sense to them. For more about this, people with some comfort with math might like Keith Devlin's book "The Language of Mathematics: Making the Invisible, Visible." Dr. Devlin is on the faculty at Stanford University.http://www.amazon.com/Language-Mathematics-Making-Invisible-Visible/dp/0805072543/ref=la_B000APRPC6_1_2?ie=UTF8&qid=1352081409&sr=1-2Specifically math is a language without which you really can't discuss the physical world properly.But math is taught as algorithms, so to address that:Teoubleshooting Math Education(1) It's important to feel masteryIf you're getting B's in math, use Khan Academy or some other tool to roll backwards as far as necessary to the point where the student last felt he or she "nailed it". Work forward again from there.(2) If a student is getting anything lower than a B in math, whether on a specific unit or overall, they're missing stuffThat's only going to make the future painful. Do the same thing as #1. Realize that you may be a sophomore in high school who needs to go back to re-study things from 5th grade. Do it. Go all the way back to when math was fun. Counting? Start there. Remember that if something was tough when you were 7, it's entirely possible it will be obvious when you're 12 or 15 or 38.Basics:(3) Learn multiplication tables!Why? Because seeing the number 42 and knowing that it's 7*6, which means it's divisible by 2, 3, and 7 is absolutely essential to the computational math as taught in schools today. You can't get that from a calculator. Kids who are sports-oriented should learn multiplication tables by running cadence or some other sports-related drill. Kids who are music-oriented should learn multiplication tables in song. Kids who are arts oriented should be drawing representations. This is mission-critical memorization, people, pull out all the stops, and don't delay!(4) Variables are explained badly, but are actually easy to understand and useThe variable "x" is used as the first variable kids typically encounter. Anything could be used, so some thoughtless textbook writer of long ago decided to use the most confusing letter; the letter that looks like the multiplication symbol. But anyway, "x" is a bucket. Visualize a bucket. You can put anything you want in it. That's what "x" is; that's what any variable is.(5) Negative numbersThese are a construct lots of people get confused by - particularly if they encounter it too young. It requires abstract thinking, and some kids take a while to develop that ability. Other people really just don't have much capacity overall, but almost everyone eventually does.(6) FractionsThe concept of fractions is fundamental in k-12 math. Students will need to think both in terms of "1/4 = one part in four" and also in terms of algebraic expressions in the "numerator" and "denominator." I have discovered more emotional blocks related to "denominator" than you can possibly imagine. Numbers in the denominator are not humans trapped in the basement. Unsimplified fractions are not messy bookshelves. I don't know why fractions are so emotionally triggering, but I have plenty of experience that they are.(7) Logic and ProofsGeometry is the only "real math" you learn in k-12. Please pay attention; it's where you learn rigor. If you love geometry and find everything else tedious, you might actually like mathematics as taught in college... you might also like law, too. Conversely, if you love the calculation games and find geometry dull, you are likely to prefer engineering over mathematics.(8) Imaginary numbersThese are eventually used to describe oscillations (which you begin talking about in trigonometry). Oscillations are everywhere in engineering. Remember what I was saying about math as a language? You have to be able to express these oscillations as mathematical equations in order to design with them in mind. Specifically, imaginary numbers for oscillations are in the exponents of the natural logarithm, e. See how it all comes together?More advanced concepts that begin to explain the philosophical beauty:- An operation is something like multiplication, division - anything that you "do" in math. (That's why you say "order of operations.") An "operator" is the representation of the activity, for example the multiplication sign. This concept eventually becomes very powerful, but it's taught in a way that orphans it for a (long) while.- The identity is the thing that gets you back the original. An example makes this easy to understand (I only know how to say it clearly in "math" which I'm not speaking here): for addition, the identity is 0. When using the operator "add" you can add 0 to anything and get the same thing. For the operator "multiply" the identity is "1," because if you multiply any number by 1, you get back the same number that you started with.- The inverse operation is the thing that gives you an "undo." For example the inverse operation for addition is subtraction. If you add 4 to a number then subtract 4, you get back the original number. For multiplication the inverse operation is division. For raising to a power, it's taking a root (which is the same thing as taking the fractional power if you know what that is). This concept is also very powerful, particularly in algebra.- A set is a hugely useful concept, and one that bridges out of mathematics into everyday language. When you're a kid you don't learn much about it, but there is a lot that you can say about sets and how they behave mathematically. The first time you get a sense of how powerful sets are is in probability if you take that in high school.---The Real Deal:Mathematics as a discipline has little to do with the computational stuff you learn from kindergarten through your first couple years in college. It's something much more like philosophy: mathematicians are concerned about creating systems that are completely self-consistent and take into account all eventualities. As such, it's built upon logic, which is typically not taught until geometry.Statistics and probability may be more tactically useful to more people than mathematics.

From the Common Core for Mathematics Grade 3 there are four focus areas for the year. The first is relevant to the test.(1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, usingincreasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.The actual standards referenced at the top of the test sheet are:CCSS.Math.Content.3.OA.A.1Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.CCSS.Math.Content.3.OA.A.3.Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.The child’s version of the objectives are:“I can use multiplication strategies to help me multiply”And finally, we get to the discussion’s question:“Use the repeated addition strategy to solve : 5 x 3”What we notice is that the test question is an attempt to determine if the child retains the conceptual understanding of “5 x 3”, not just as symbols, but as a representation that could be of physical manipulatives, i.e., the objects arranged in groups in groups cited in the standard. This is important and should be validated.The problem begins with failure to cue the child to some physical objects. This is not a creative writing class. The question should suggest the manipulatives. Maybe: breadsticks and baskets.But, no. The question takes a shortcut to sneak in a little bit more testing, and immediately asks that a certain strategy be used – the repeated addition strategy. In the process, it fails an objective.A strategy is a template for action. The action follows a strategy in a context.The test has not provided the context, which would determine the action. It has only asked for an example of the strategy, and has skipped the anchoring to objects and groups for which the strategy can be applied in context.The author of the question took a shortcut and produced a defective question. The child produced a repeated addition expression, an otherwise arbitrary artifact with no requirement to relate to anything physical, at all.If the child had imagined 5 rows of three pennies, even though that not required, the child could simply rotate the mental image 90 degrees to get a simpler repeated sum, which was all teacher asked for.But the child was not asked to show the understanding that the symbols related to physical objects, even though that WAS part of the lesson objective.The answer was marked wrong because the teacher graded the test against expected answers to questions that were not actually asked.

I love that everyone is predominantly putting up problems from statistics, probability, or some upper level math courses, because a lot of them are simple to work out, but difficult conceptually. You asked for simple problems so I'll point to problems with the weight of evidence behind them: anything with ORDER Of OPERATIONS!Think about it, how often does a minor debate break out on some social media network when another grade school problem goes viral? When people have to take remedial mathematics, what tends to be the most heavily practiced unit? It happens all the time and the weight of the viral problems tend to be word problems or order of operations. (In classes, it tends to be OofO.) Of the two of them order of operations are the simpler problem, because they've given you the equation they want you to solve. In a word problem, half the difficulty (even when simple) is figuring out what you're trying to solve. In other words, getting to the point of order of operations.Something like 9 minus 3 divided by 1/3 + 1 = ? People will plug it into a calculator as 3/1/3 and the calculator won't realize the 1/3 is actually one third and not 1 divided by 3. Which is an important distinction because 3 / .333 = 9, but 3/1 = 3/3 = 1. That's an 8 point swing. What's the reason for this issue? You could argue notation, but I'd maintain it's a misunderstanding that fractions are fundamentally a division problem for a number less than 1. Which means, it should be written 3/(1/3) where you solve what's in the parenthesis first based on your order of operations.Please Excuse My Dear Aunt Sally.() ^ x / + -