Getting students to analyze a math word problem and find the correct solution can sometimes seem like an endless battle in the classroom. There are times when the simple fix really is teaching your students at the beginning of the year to consistently take their time when reading ANYTHING. However, all too often students choose to take the easy route when it comes to word problem solving and aim for grabbing the numbers and doing some type of calculation to them without reflection.
HOW DO YOU SOLVE THIS?
Students need a checklist or method for taking on a complex word problem. There are many out there such as 'CUBES', but I've always observed in the classroom that they were missing some of the more critical thinking aspects and metacognition that are necessary for students to truly understand what it is they've calculated.
I've created a NEW 5-STEP method that takes students through the complete breakdown of a math word problem. It is called the GU-3Q-PE method, formatted into a graphic organizer template, and it should be used at the beginning of the year consistently. This STEP-BY-STEP method was created with sequence in mind and should be done in order, each step being dependent on the next.
As a teacher, your job in teaching this 5 STEP GU-3Q-PE method will be to direct teach each component of the 5 steps by modeling them, but more importantly, giving real-time feedback to students to perfect each element. I will provide you with a FREE GRAPHIC ORGANIZER of this method and visually break down the steps below. If you'd like a more extensive and complete package of this method, the information will be provided at the end of this post.
(When first introducing this method, you can provide students with a blank template that just has the first letter of each element and ask students to GUESS what each letter stands for to engage them.)
For this STEP BY STEP guide, we will be applying this method to the following multiplication word problem.
STEP 1: G = GOAL
Have your students understand that the first step after reading the word problem 2+ times is to write down their GOAL in this word problem.
The GOAL is what they are aiming to solve in this word problem
The GOAL is the rewording of the question in the word problem
The GOAL must include important details specific to the word problem, NEVER written in general language (an example of a general goal is: My goal is to multiply __ and __)
The GOAL is worded with these possible sentence stems: "My goal is to find the weight of ____ after _____" "My goal is to round ____ to the _____ place" "My goal is to find the area of _____"
You will need to coach your students and really dive deep into analyzing how your students are writing their GOALS because it can provide you with information about how they have processed the word problem. Use a lot of group work and rotations when first having students write their GOALS so they can get comfortable comparing how each of their classmates processes this information. When giving feedback on a GOAL, aim more at letting students know that this part or that part sounds to general and is lacking details. Ask them how they can improve it and come back to them when they've revised it. Be sure to PRAISE good GOAL writing every time you see detailed GOALS that show an understanding of what is being asked in the word problem and also PRAISE students when you see that they've improved parts of their GOALS.
Possible examples of GOOD goals for the word problem above that were student provided.
GOAL: My goal is to find out how much weight all 16 cars were altogether
GOAL: My goal is to solve the total weight of all 16 cars
GOAL: My goal is to figure out how many tons all 16 cars will weigh in all
Possible examples of NEEDS IMPROVEMENT goals that were student provided.
GOAL: To add them all up (too vague, unclear understanding)
GOAL: My goal is to multiply the numbers (not written to describe what needs to be solved)
GOAL: My goal is to multiply 16 and 2.86 (this is not a goal, it is a description of an expression.)
Students that struggle with finding the correct method for solving word problems should avoid picking a strategy during the GOAL writing phase. These students should hold off on figuring out whether to add/subtract/multiply/divide until they've gone through the 5 step method first.
STEP 2: U = UNDERLINE
Have your students understand that the purpose for underlining in word problems will be to locate key words that are given in the statement and in the question of each word problem.
It is essential that students have practice all year long in locating them in word problems and in being able to identify which mathematical operation applies to them.
In the multiplication word problem above, the key words that were identified and underlined were:
-EACH
-ALL
-ALTOGETHER
Although highlighting can be used as a replacement for this step, it is advised that underlining be the main or only method of bringing out these key words to minimize distractions from various highlighting use.
Students should be held accountable for underlining in every math assignment that you assign them. If possible, use these 5 steps as part of a student's grade for each word problem, instead of only rewarding the circled correct answer. This will ensure that students are not only aiming to immediately commit to an answer, but will take more time to improve their mathematical comprehension and grade by following the process.
STEP 3: 3Q = 3 QUESTIONS
In reading, one of the pillars of comprehension is having students create questions to engage with the text and reflect on what they've read. In math word problems, this is a fundamental element that has been missing in traditional problem solving. The way questioning works is to have students create 3 simple questions that can be answered from reading the word problem. In my class, I call them "baby questions" to relate to the idea that the questions that students create should NOT be a rephrasing of the original word problem question, nor should they be questions that CANNOT be answered EASILY by a quick rereading of the text. Another way you can introduce "baby questions" to your students is by giving the example that students in lower grade levels below yours should be able to answer them. For example, if you are teaching 5th graders, then the questions that your students create should be questions that a 2nd or 3rd grader should be able to answer by reading the word problem.
Possible examples of GOOD "baby questions" might be the following:
How many cars were there? / How many cars did the car dealership bring?
How much did each car weigh? / What is the weight in tons of 1 or each car?
What does altogether mean? Is altogether addition or subtraction?
Will I be using the digit 4 in my operation?
These types of questions above are great examples of students reflecting on their reading and will provide you with plenty of excellent data to see how yours students are processing the reading. Encourage the use of vocabulary questions as a good question (what does altogether mean?) as it shows that students are showing you that they might have forgotten or don't know its meaning and can be open to learning it before committing to solving it.
For EL (English Learner) students, you might also encounter more language related questions such as:
What does dealership mean?
What does ton(s) mean?
What does vehicle mean?
Encouraging these types of questions at the start and openly praising them in group discussions will give your students confidence at the beginning of the year to let you know right away about these potential language obstacles.
Possible examples of NEEDS IMPROVEMENT "baby questions" might be:
What do I solve? (this is a general question that can apply to ANY math word problem, making it irrelevant)
How many tons did all these vehicles weigh altogether? (any variation of the original word problem question is NOT a baby question because it is simply a repeat and does NOT show that students are thinking about the content of the word problem)
Why did the car dealership buy these cars? / What colors were the cars? (these types of questions provide valuable data to show that this student is not processing the overall importance of questioning and that they are not tying in their questions related to the GOAL)
Based on questioning alone, you can break students up into small groups for further intervention and/or continue to expose these students to great questioning from their peers.
STEP 4: P = PICTURE
Another crucial element in reading is visualization. Having your students create pictures based on word problems or math in general is a vital skill in comprehension that requires a lot of practice for each type of mathematical concept. Students will often confuse the purpose of creating a picture to mean that you want to see a nice drawing, which can lead to some very detailed drawings of car.
Explain to students that the purpose of a picture in math is to get an overview for what is happening mathematically and that pictures should be quick representations of objects. For example, a dot, box, or circle should be quickly drawn to represent a car or any other object mentioned in a word problem.
Along with the quick pictorial representation of the object (dot, box, circle), teach students the importance of LABELING their pictures.
These labels will often be numerical based, but can also be words depending on the word problem. The visual example shows the PICTURE break down of this multiplication word problem with the labels in the process of being added in.
Circles and labels like this are the fastest and easiest way to teach picture representations for most word problems.
Model these pictures with your students as much as possible at the start of the year and slowly begin having students share their pictures in small groups, rotating frequently to get them familiar with various methods that work well for other students. Praise ALL pictures and reinforce the need for quick and easy representations that will help your students lead into the last step.
STEP 5: E = EXPRESSION
After having practiced creating pictures, you can easily transition into the last step, which is creating an EXPRESSION. You will be able to demonstrate using their pictures that although you can add 2.86 + 2.86 + 2.86 for a total of 16 times, it is much easier in math to take what you have for 1 car and multiply it by the total cars (2.86 x 16).
Have students refer back to their baby questions, which links directly with their creation of their expression. When they asked the baby question of "How much did each car weigh?" it starts the expression (2.86... )
Then, when they asked "how many total cars were there?" it gives the total amount of cars that will be multiplied by (2.86 x 16).
The two other main questions that I apply to most word problems are:
What do we have?
(16 cars)
What are we doing to that?
(finding the weight of all/ more of them)
These two questions will help students see the overview and come closer to understanding that this is multiplication.
What do we have?
What are we doing to that?
A possible grading rubric for this word problem to keep students accountable for the process could look something like the following 6 point rubric below.
GOAL: Did the student write a relevant goal? (1 point)
UNDERLINE: Did the student underline anything? (1 point)
3 QUESTIONS: Did the student create 3 relevant baby questions? (1 point)
PICTURE: Did the student draw a relevant picture? (1 point)
EXPRESSION: Did the student write an expression? (1 point)
CORRECT ANSWER or WORK SHOWN: Did the student circle the correct answer? or Did the student shown their work? (1 point)
GET 2 FREE TEMPLATES AT THE LINK BELOW
(FREE VERSIONS ARE IN THE PREVIEW DOWNLOAD OF THE PRODUCT)
What's included?
-1 blank GU-3Q-PE template sized for an Interactive Student Notebook (cut/paste)
-1 blank GU-3Q-PE template sized for standard printing (8.5" x 11")
-4 in 1 blank Mini GU-3Q-PE template for taping on student desks for quick view (recommended for all year long visual access)
-1 Acronym GU-3Q-PE template for an Interactive Student Notebook (cut/paste)
-1 Acronym GU-3Q-PE template sized for standard printing (8.5" x 11")
-1 Acronym Mini GU-3Q-PE template for taping on student desks for quick view
-1 Worded Description Mini GU-3Q-PE template for reminded students what each category means
-1 Visual Representation Mini GU-3Q-PE template for visual aids / accommodations
-24/7 EMAIL SUPPORT if you need any special requests or if any adjustments will make your teaching easier