I really love doing Facebook LIVE presentations. I particularly enjoy it when I have the opportunity to talk about something that strikes a chord with homeschool parents. We did a Facebook LIVE video talking about working with students and mathematical word problems. It was like touching that third electrified rail in so far as how people feel about word problems! It would be fair to divide us into two groups:
1) Those who find word problems to be fascinating puzzles.
2) The rest of us, who really do not have an affection for word problems.
In the interest of true confession, I have never been a particular fan of mathematics. You can assign me the task of diagraming sentences all day long. In my opinion, word problems can be sometimes inscrutable.
Steve Demme (the author of Math-U-See) said to me once, “Well, Gretchen, you know when you solve math problems as an adult, they ARE word problems.” Point taken. While I would not say I love word problems to this day, I no longer have an adversarial relationship with them. One of the things I’ve always loved about Math-U-See is taking the sting out of word problems by making them a part of the daily lessons. What, however, do you do if you did not start your mathematical journey with Math-U-See?
We as parents have to be able to model for our children how to meet the challenge of word problems head on, and toward that end I want to share with you some of the tips that were shared in the Facebook LIVE video. I also have some things to say about math anxiety in adults.
You can also watch the video below, if you prefer.
Below you will find several tips to implement when working with word problems with your children. These tips are applicable, regardless of the age of your student, their mathematical experience, or even the level of Math-U-See in which they are working. As always, I am indebted to our tremendous customer service team. They are the contributors of much of my list here. You do know, of course, that being a member of the Demme Learning family means that you can call our team and ask for help if you are having a struggle. We want your success!
10 Ways to Make Word Problems Fun
1) Start With Fresh Eyes
If you are just completing a math lesson, and have already been at it for 15-20 minutes, take a break before you begin the word problems. Stand up and do some jumping jacks, have a snack, take a break. Then sit back down to the word problems.
2) Read the Word Problem All the Way Through First
Read the word problem all the way through first; don’t worry about the numbers in the word problem. Then ask yourself and your student, “do we understand what it’s all about”? Are there any new terms we are unsure of here? Are there words we don’t know?
3) Reread the Word Problem Again
Reread the word problem again; out loud is best. I know that reading out loud seems silly, but it is tremendously helpful.
4) Skip the Numbers
Sometimes in the reading out loud is it helpful to just skip the numbers altogether. Instead of reading the number, add some humor by saying “BEEP” instead of the number. Humor really DOES help learning! You can change the names of the people in the word problems to your children, their friends, or even their favorite super hero.
5) Circle Keywords
Are there keywords you can circle? “Sum”, “in all” and “all together” usually mean addition. “How many are left/remaining”, or “What is the difference” usually means subtraction. The word of is an important one as in “1/4 of 12” or “5/10 of a dollar” means you are being instructed to multiply. There are other key math words that may help you analyze a word problem – but be careful.
Depending on key words alone does not encourage students to think mathematically about a problem or use logic to reason toward a solution. Sometimes key words do not appear in problems, or additional operations may be required to find the final answer Encourage them to take the whole of the word problem in context. Make sure you both understand what the problem is asking before seeking out those individual words.
6) Rewrite the Word Problem
If word problems cause anxiety in your child, help them become the drafter of word problems. For example: 12-7= ? That is the computation. Have your student create a situation to accompany those numbers. Developing a proficiency in creating word problems really helps students develop confidence in analyzing them.
7) Word Problem Writers Are Sneaky
Remind your student that those who write word problems are a sneaky lot. They will put in information that is not necessary just to throw a student off track. If irrelevant information is a challenge for your student, try creating some word problems that contain unnecessary information. Help them become proficient in knowing what is not necessary – that is a life skill in and of itself!
Consult the Instruction Manual
Consult the Instruction ManualIf there is a lesson in the Math-U-See curriculum that is giving you a particular challenge, make very sure you have consulted the corresponding lesson pages in the instruction manual. We always provide instruction for the how as well as the why, and often, if a family is challenged with a lesson, we find that the answers they seek can be found in the lesson manual pages.
9) Review the Questions
Word problems need to be answered in words too. Make sure that you have answered the question in words. Further, does your answer make mathematical sense? Can you plug your answer back into the word problem and work it out to to see that it is indeed correct? Remember this step. This leads to frustration for a student who has worked hard, and perhaps not found the right answer.
10) Relax
Just like any skill, learning to negotiate word problems is something that happens over time. You are not going to be an overnight success (most of the time). But if you, as the parent, can stay affirmative and encouraging, you can make a tremendous difference for your student.
In conclusion, I realize that this blog post is long. The information will be helpful to you. If you still want more, we offer more help with word problems on our parent resource page:
Word Problem Tips [PDF]
We do need to have a conversation about what our math anxiety does to our children. Look for that blog post to come in the near future. We want you and your student to have success in all your mathematical endeavors!
Solving word problems is difficult for students, but teaching students how to read the word problem and understand the context or situation of the world problem sets a good foundation for future work with complex word problems. The Separate Word Problems are similar to the Join Word Problem type in structure, but ask students to subtract or separate two things rather than add or join them together.
Below is a Facebook Live video that I recorded on Separate Word Problems by Problem Type. The text below has some highlights from the video, but the video goes more in-depth with explanations and examples.
One thing I did emphasize in this video, over the Join Word Problems video, is the use of number lines. I took a more in-depth look at how the number line changes with each unknown in the problem.
Three Types of Math Separate Word Problems
There are three types of separate word problems. The video and this blog post go in-depth about using keywords to solve these types of problems.
Here are three examples of separate word problems. As you read across these examples, think about the context or the verb in the problem and ask yourself, what is happening in the problem and what is unknown.
SRU (Separate Result Unknown)
There were ___ kids on the playground. ____ kids went home. How many kids are left on the playground?
SCU (Separate Change Unknown)
There were ___ kids on the playground. Some kids went home. Now there are ___ kids on the playground. How many kids went home?
SSU (Separate Start Unknown)
There were some kids on the playground. ____ kids went home. Now there are ___ kids on the playground. How many kids were on the playground at the beginning?
Teaching Separate Word Problems
I go in-depth about teaching word problems in the Join Word Problems Video Post. I follow a specific routine when I teach Join and Separate word problems to students, which includes using consistent vocabulary, solving for an unknown, labeling the word problem, writing an equation, and giving students the numbers. You can read more about each component of the routine in the Join Word Problems Video Post.
You can find out more about why I don’t give students the numbers until the very end in this blog post.
Facebook Live Video for Separate Word Problems
This video highlights each of the problem types above and also focuses in on how to use a number line when solving two-digit equations. You can find out additional models and strategies that I use with students in this blog post, although a number line is by far my favorite.
Free Word Problems by Problem Type Including Separate Word Problems
Do you want a free sample of the word problems I use in my classroom? Click here or the image below. FREE Sample of Word Problems by Problem Type
Word Problems Teaching Resources
Are you teaching word problems to your elementary students? Do you need more teaching resources for them?
Check out these word problem resources for your classroom!
-
Multiplication Division Word Problems Number Puzzles – OA3
$3.75
-
Two-Step Word Problems Number Puzzles – OA8
$3.75
-
Addition and Subtraction Word Problems by Problem Type
$24.75
-
Multiplication and Division Word Problems
$19.75
-
Word Problem by Problem Type BUNDLE
Product on sale
$38.80
-
Second Grade Math BUNDLE
$200.00
More Ideas for Teaching Word Problems
Do you want to learn more about teaching word problems? Check out these blog posts that go in-depth about teaching strategies you can use in your classroom!
Equations & Word Problems are practically always included in the GED Math Test.
These questions may look easy, but it takes a lot of practice if you want to achieve consistency. So let’s begin learning.
Fast & Easy Online GED Classes
Get Your Diploma in 2 Months.
It doesn’t matter when you left school.
This lesson is provided by Onsego GED Prep.
Video Transcription
Here are the needed steps: First, we set up an equation. All solutions to word problems need to include carefully crafted equations that accurately describe the constraints in that problem statement.
Solving the Equation. In the previous step, we always must solve the equation set up.
Then, answer the question. This is an easily overlooked step.
Let me give you an example; the problem may be asking for Jane’s age, but the solution to your equation is giving the age of Liz, Jane’s sister. So be sure you’re answering the initial question that was asked in the problem.
Your solution needs to be written in a sentence that has appropriate units.
For example, Amelie has withdrawn $125 from her savings bank account. Because of this withdrawal, her account’s current balance is now $1,200.
What was the account’s original balance before the withdrawal?
B − 125 = 1200 is the original equation.
B − 125 + 125 = 1200 + 125 (we’ve added 125 to both sides of our equation).
B = 1325 (On the left, by adding 125, we “undo” the subtracting 125 effect, which brings us back to B. On the right side: 1200 + 125 = 1325.
The answer to the question is: The original balance in the account was $1,325.
One more example: A triangle’s perimeter is 114 feet. Two of the triangle’s sides are measuring 30 feet and 40 feet, respectively. What is the measure of the triangle’s third side?
114 = x + 30 + 40 is our equation.
114 = x + 70
114 − 70 = x + 70 − 70 (we subtracted 70 from both sides).
44 = x
On the right side of the equation, subtracting 70 will “undo” the adding 70 effects and bring us back to x.
On the left side: 114 − 70 equals 44.
The answer to the question is:
The unknown triangle side is 44 feet.
Word problems are often dreaded by students. To try to help the grandmother who wrote about her frustration with helping her fourth-grade granddaughter with word problems, I replied with the following message:
Instead of focusing on traditional word problems at this time, which seem to be dreaded by both of you, maybe it would be better to focus on math questions in a more playful way. Try posing problems that have more than one right answer, more in the spirit of math riddles. Here’s an example of a traditional word problem that a fourth grader would be expected to solve, followed by a problem that’s more like a riddle:
Traditional Word Problem: Billy had $163 and spent some. He has $15 left. How much money did Billy spend?
A Different Word Problem: The answer to a subtraction problem is 15. What might the problem be?
What interests me when I pose a problem such as the second one is the size of the numbers students choose. That can provide information about their level of numerical comfort. Also, then I can ask them to write a word-problem situation that would match the math problem they created. And, as always, I’m interested in how students solve problems. I think it’s very, very important to encourage students to reason mentally, without paper and pencil, and at all times to explain their thinking.
Reflections on My Message
This one activity probably won’t be sufficient for helping the fourth grader. Students need a great deal of experience with interpreting situations, connecting them to the appropriate mathematical operations, and finding and justifying solutions. But it can shift the focus from being right or wrong to connecting situations to math problems. (See Classroom Suggestions below for instructional suggestions.)
A caution: Teachers often resort to helping children solve textbook problems by providing word cues. For example, teachers might tell their students that if a problem says “altogether,” they are supposed to add, or if a problem says “how many more,” they should subtract. Teachers provide these cues to help students be more successful with word problems. However, instruction of this type does little more than offer students tricks for figuring out answers. The cues focus on doing something with the numbers at hand, instead of making sense of the situation and modeling it mathematically.
Watch a Short Video
Here’s a typical word problem that’s useful for seeing if students can interpret a remainder and give an answer that correctly responds to the situation.
There are 295 students.
Each school bus holds 25 students.
How many buses are needed to fit all of the students?
For a revealing and vivid example of how word cues can interfere, watch this one-minute video clip of Mallika Scott asking Marisa, a fifth-grader, to solve the problem. inappropriately using word cues.
Classroom Suggestions
Following are ideas about how to approach word problem instruction with students.
-
-
- Give students problems to solve that have more than one right answer, such as the one suggested above: The answer to a subtraction problem is 15. What might the problem be? For other problems like this one, my two go-to resources are both titled Good Questions for Math Teaching: Why Ask Them and What to Ask. One book is for grades K–6, written by Peter Sullivan and Pat Lilburn, and the other is for grades 5–8, written by Lainie Schuster and Nancy Canavan Anderson.
-
-
-
- Another way that I’ve had success is to present word problems in a different way. For example, using the traditional word problem I described earlier, I would write on the board:
-
Billy had $____.
He spent $____.
Billy has $____ left.
I’d read aloud what I’d written: “Billy had ‘blank’ dollars. He spent ‘blank’ dollars. Billy has ‘blank’ dollars left.” Then I would have the students read it aloud with me. Next I’d insert numbers in two of the blanks. For example, for the problem I presented above, I would write:
Billy had $163.
He spent $____.
Billy has $15 left.
Using the think-pair-share instructional strategy, first I would ask students to work individually to solve the problem, then I’d have them talk with their partners, and finally I’d lead a class discussion for them to report their results. As always, I would have students explain how they reasoned. To continue, I’d change the numbers, always filling in two blanks but changing which amount was unknown. And, for independent practice, I sometimes ask students to choose their own numbers. As with having them write subtraction problems that have a specified answer (like 15), this gives me insights into students’ numerical comfort.
Word Problems with Median and Mean
Transcript
Welcome to this video lesson on word problems that involve median and mean.
We are often intimidated by questions that involve doing two types of data interpretation, especially if they are word problems.
Today we will discuss and learn how to approach a word problem that asks you to interpret information based off an average and then use that to help you make a decision regarding the median… this all sounds scary now, but I’ll walk you through it.
Let’s get started.
A company boasts that its mean starting salary is $61,000. Below is the list of the starting salaries on which the company based its claim. New Employee Starting Salary A $27,000; B $29,000 C $37,000; D $42,000 E $45,000; F $49,000 G $55,000; H $60,000 I $92,000; J $110,000 K $125,000 Determine what an astute job seeker should inquire about when presented with a mean starting salary figure.
Okay, as usual, let’s break down this word problem. It’s in two parts. Part one talks about how a company is saying it’s great because it’s mean (or average) starting salary is $61,000. What’s nice is the work is already done for us here, because it tells us the mean and then tells us all the wages. So, what are we supposed to do then? That’s part two.
The second part of this question tell us to figure out what someone should ask about given the average starting salary. This is tricky because it doesn’t explicitly tell us to do anything… it just tells us to find what question a job seeker should ask… it’s very broad. Let’s look at the data for a second. Do you notice anything about the different salaries, especially as they relate to the average of 61 thousand? Most of the salaries are lower than the average… by quite a bit.
What the creators of the problem want us to do then, is find out what question the job seeker should ask instead of “What’s your average salary?” What we should ask is what is the median salary. Remember, the median is the middle item in a set. In this case, we want to know what the middle salary is because the average is so deceiving. So, we see that we have 11 salaries, what’s the median? $49k. This is important to the job seeker because the median starting salary is a better indicator of the salary that can be expected, since this will not be inflated by salaries that are much larger or lower than the average. The median salary in this case is $49,000. This is likely to be closer to the starting salary of an average
I hope that helps, thanks for watching this video lesson. Until next time, happy studying.