Category: Math word problems

Help With Solving Word Problems

Word problems can be a source of frustration and anxiety for many students. So I was looking for an article to see if there was any goos advice on this topic and I found the article below on Article Directory .com.

It offers some good ideas and should prove helpful as your student takes on learning math and solving word problems.

Six Word Problem-solving Strategies To Help Reduce Math Anxiety

 

 

Many students fear and despise the mathematics story problems (word problems) they encounter in their classes. Math anxiety is a real life experience and is usually made worse by the thought of having to solve a story problem.

The truth is, life itself is made up of a long series of story problems and those whose solution requires the use of our math skills are not difficult once a few simple strategies are learned.

Story problems usually contain key words or phrases that tell what operation(s) need to be performed with the numbers. Learn to look for these word clues:

ADDITION: add (to), sum, plus, more than, increased by

SUBTRACTION: subtract (from), difference, minus, less than, decreased by, how many more?

MULTIPLICATION: multiply, product, times, twice, three (four, five, etc.) times, percent

DIVISION: divide, quotient, share equally

When attempting to solve one of these problems, if the appropriate operation to be used is not obvious – just try something. If the wrong method is selected, one will at least learn what does not work – after all, if something isn’t tried, nothing will be learned.

Here is a basic procedure to follow:

Read the problem carefully – find out what is being asked for. Don’t try to understand the whole problem the first time through – just determine what the main question is.
Go back and re-read the problem to see what information has been given that will be helpful in answering the main question.
Find any word clues that will help determine what operations are needed.
Perform the required operations.
Finally, mentally check the answer to see if it makes sense and is reasonable. Be especially aware of the units (ft., in., lb., oz., gallons, etc.) and be sure the answer is expressed in the correct units.

The following six proven strategies will be helpful in solving story problems:

Draw a Figure or Diagram: This is the basic strategy to use when help is needed to visualize what is wanted in a problem – a sure-fire way to clear out any mental fog that exists. Labeling the figure with all the known information will keep everything straight and avoid getting lost in the words.

Put Data in a Table – Look for Patterns: A table is a great method for organizing information and once the information is in the table, it is a lot easier to find a pattern in the data.

Cut and Try Method: This method involves taking a guess at the answer and checking it against the desired answer and then adjusting the first guess (and any subsequent guesses) to get closer to the desired result.
An example of this method is used in zeroing an artillery piece on its target. An observer gives his best estimate of the target coordinates, a round is fired, the location of the hit is observed and the coordinates adjusted accordingly. The process is repeated until a hit is registered on the target.

Solve a Simpler Problem: Using a simpler version of a problem can be helpful in suggesting a problem solving approach.

A well-known example of this method involves deciding how many fence posts are needed for a fence of given length if the posts are to be spaced at 10 foot intervals. Draw a diagram of a fence with two or three posts, observe the pattern and apply it to the longer fence in the problem.

Work Backward: Solving problems by working backward is exactly what we do when solving linear equations.

For example: the equation 9x – 13 = 32 means that 13 subtracted from the product of x multiplied by 9 results in 32. So we reverse those operations to find x. Add 13 to each side of the equation and then divide both sides by 9.

Dimensional Analysis: Dimensional Analysis is one of the most useful methods for solving story problems. The great thing about specifying the units of the measurements (besides clarifying what we are talking about) is that they act just like numbers in arithmetic operations. All we do to solve a problem is put the units in the right order to produce the correct units for the answer.

For example: If a car traveled 395 kilometers in 210 minutes, what was the average mph?
Put the units in order so that cancellations will result in the desired combination:
Km/min x mi/km x min/hr = mi/hr

Next, plug in the given information and carry out the arithmetic operations.
395 km/210 min x 0.621 mi/km x 60 min/hr = 70 mi/hr or 70 mph

In summary, if students afflicted with “math phobia” will take a deep breath and approach the story problems with calmness and the following tools, life will take on a new beauty and serenity:

Read the problem carefully
Look for the operations key words
Pick a logical strategy to find the solution;

Draw a figure or diagram and label known parts
Put data in a table and look for patterns
Cut and try (take a few guesses and refine)
Solve a simpler problem
Work backward
Use dimensional analysis

Review your answer to see if it is reasonable.

Don’t forget to be neat and logical and have some fun – story problems are just a puzzle to solve.

By: Robert Leatherwood, PhD

Article Directory: http://www.articledashboard.com

 

  So what do you think? Did you find this article useful? Are you ready to go out and tackle some word problems?  🙂

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Math at Easter-Time

The holidays can be lots of fun for children. Not just because they get candy and gifts, but because they also get off from school!

But just because they’re off from school, doesn’t mean that you can’t still help them learn math!

Teresa Evans wrote a nice article for ezinearticles.com which helps you take advantage of Easter and teach your children math while still making it fun.

Easter Math Is Fun Math

Easter is an exciting time for kids. But the good thing is that you can use that excitement to help kids develop their math skills. Turning regular math into Easter math makes math much, much more exciting. You can use Easter math games or Easter Brain Teasers and the kids will beg you for more.

Below are some simple ways that you use Easter math in the classroom or at home.

Bunny Hop
Here is a simple Easter math game that you can use to practice any basic math skill. You start by selecting a start line and a finish line. Next two children compete to jump from the start to the finish by taking two bunny hops every time they answer a question correctly. You can use any questions that help kids to practice the skill that you want. For example you could ask ‘6 times 8’, ‘half of 34’ or ‘What is the number before 87’? The first child to answer correctly takes two jumps and the first one to reach the finish line is the winner.

Easter Counting
You may know the old favorite counting game Buzz. But did you know that you can easily turn this into an Easter math game by replacing the word ‘Buzz’ with an Easter word. Try using ‘Bunny’ or ‘Easter Egg’ instead. The kids sit in a circle and count around a circle but replace the number 7, each multiple of 7 and every number containing a 7 digit with the word ‘Bunny’. If a child says the number instead of saying ‘Bunny’ they are out.

This is a tricky game that requires concentration and a good knowledge of multiples. You can also try playing it with other digits instead of 7. For example, you could use 5 or 10 for an easier version or use 8 or 9 to make a more challenging version.

Easter Brain Teasers
Brain teasers are a great way to get kids thinking math. Many number problems can also be made a lot more interesting by using Easter as a theme for the problem. Here are a few that you can start with.

The Easter Bunny has 15 Easter Eggs in a Basket. He gives our 3 then collects 7 more then gives 6 children 2 eggs each. How many eggs in the basket now?
You can easily change the numbers in this one and then have a completely new problem to present.

Tom has been dyeing eggs. He used green and red dye. If he has dyed 17 eggs and he has 5 more red eggs than green eggs. How many eggs does he have of each color?

How many eggs did I find in the Egg Hunt? I found between 10 and 30. The number is divisible by 4 but not by 7 or 8. I found an even number of eggs.

There are many different ways to use Easter math get kids adding, multiplying, comparing and using other math skills. You’ll find that kids will definitely agree that Easter makes math loads more fun.

Terese Evans is a teacher and parent who uses games to get kids excited about learning. She shares her favorite Kids Easter Activities including Easter worksheets, board games, card games and game sheets at http://www.kids-easter-activities.com. You can receive your own printable Easter Activities for Kids when you visit http://www.kids-easter-activities.com.

While the kids may all agree, I know that I certainly do too!

Have a great Springtime and Easter (if you celebrate it)!

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Word Problems Are Fun!

You may recall getting very nervous when your teacher said “OK class, today we’re going to do some word problems to help you learn math.” I use to break out into a cold sweat! But it doesn’t need to be thaat way for you or your children. Check out this article written by Joe Pagano. Perhaps your view of word problems will change!

In Mathematics, Word Problems Can Be Fun
By Joe Pagano

One of the biggest hurdles your youngster has to overcome in school is the terrible bugaboo which is a math word problem. During my many years of private instruction, the one complaint I have heard all too many times is that of the inability to conquer the word problem. Yet word problems can be tackled successfully. This article outlines how.

Word problems are more difficult that “regular” math problems because the solution requires one to first determine what has to be done and then how to do it. Thus a word problem, unlike the solution of an equation such as x + 3 = 4, and then asking for the value of x, requires one to determine what equations can be extracted from the words, and then how to solve those specific equations.

Another difficulty lies in a student’s inability to read at a level necessary to make sense out of the words that make up the problem. Poor readers will generally make poor word problem solvers. This is why I teach students critical reading skills, among which are techniques such as “anticipatory reading” and other active reading competencies. Such methods not only give students a tremendous boost in their mathematical abilities but cross over into other disciplines requiring reading, such as social studies and English.

In order to better understand these strategies, we will look at a specific word problem at the pre-algebra/algebra level, and then see how to implement such techniques. The problem we shall discuss is on the topic of systems of equations in algebra.

Word Problem Example: Five hockey sticks and three hockey pucks cost $23. Five hockey sticks and one hockey puck cost $20. How much do two pucks cost?

Word Problem Strategies:

First Pass: This is the stage at which we just read the problem to get a “feel” for what is going on within. During this stage, we are not trying to solve the actual problem but just get an overall sense of what the problem deals with.

Second Pass: This is the stage when we re-read the problem, paying careful attention to the situation at hand, what the problem deals with, who the main players are, and so forth. During this stage, we start to mull over some problem solving strategies and start to plan our attack.

Third Pass: This is the brainstorming stage. At this point we clearly determine what the nature of the problem is, what we know, and what we are asked to do. This is when we start to convert words to numbers and equations and quantify everything within the problem.

Fourth Pass: This is the stage at which we begin to solve the problem using the information we gathered in the third pass. At this stage, we also double check our brainstorming phase to insure that we took the right approach.

Fifth Pass: This is the final stage at which we check the solution obtained in the fourth pass for consistency.

Let us go through these stages with the problem at hand. During the first pass, we read the problem and see that it has something to do with hockey sticks and hockey pucks and the price of two pucks. Note we have been thrown a curve ball here in that we are asked to state the price of two pucks not one. Keep this in mind for the end of the problem.

Now during the second pass, we notice that indeed we are dealing with the sport of hockey, that we are limited to the two pieces of equipment, pucks and sticks, and that we are given the prices for certain combinations of the two, and that we are asked specifically for the price of two pucks.

At the third pass, we start to create the initial mathematics. We have that 5 sticks and 3 pucks cost $23. We also know that 5 sticks and 1 puck cost $20. At this point, we should even take a guess at some numbers that might work just to make sure we have a good feel for the problem. For example, you may guess that a stick might be $4 and a puck $1. Then 5 sticks and 3 pucks would cost $23 so this seems like a good choice. However, those values do not satisfy the second condition, that of 5 sticks and 1 puck costing $20. Remember the final values have to satisfy both conditions in order to be the correct ones. But at least we are in the ballpark with our initial guess.

In our fourth pass, we choose letters to represent our items in the problem, and we then put our equations together. Since we are dealing with pucks and sticks, a good choice of letters would be S for stick and P for puck. Gee. Really? Okay, so now we have the following two equations:

5S + 3P = $23
5S + 1P = $20

Now you see that you are looking at a simple system of linear equations. You can solve by using the method of elimination. Thus if we subtract equation 2 from equation 1, we end up with 2P = $3, or by simple division, that P = $1.50. If we plug this value for P back into either equation 1, we get that S = $3.70. Now going back to what was asked for, the price of two pucks, we have 2x$1.50 = $3.00.

At the fifth pass, we should ask ourselves if our answer is reasonable. It seems that the cost of the stick should be more than that of the puck, even if the price of the stick seems a bit inexpensive. If we plug these values for S and P into equation 2, we get a check and thus we can feel comfortable that our solution is correct.

By using this simple step strategy, your children can confidently conquer word problems. No matter whether the problem involves hockey pucks and sticks, or giraffes and elephants, or whether the solution involves systems of equations or mixed rate problems. Reading critically, solving actively, and applying this five step process will insure impressive success in the oft regarded ghoulish realm of word problems. Goblins beware!

Joe is a prolific writer of self-help and educational material and is the creator and author of over a dozen books and ebooks which have been read throughout the world. He is a former teacher of high school and college mathematics and has recently returned as a professor of mathematics at a local community college in New Jersey.

Joe propagates his Wiz Kid Teaching Philosophy through his writings and lectures and loves to turn “math-haters” into “math-lovers.” See his website http://www.mathbyjoe.com for more information and for testimonials, and try out one of his ebooks here http://www.mathbyjoe.com/page/page/2924777.htm to achieve better grades in math.

Joe breaks down the process very well – eh? So simple that a child could do it!  (Well after a little coaching. 🙂 ) 

By the way, I found this article at ezinearticles .com. They have some very interesting reading on many different and varied topics.

Hope you have a wonderful Thanksgiving if you live here in the USA!

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