Editing to show the new cover for my CUBES posters:
Word problems just never ever go away. They pop up in nearly every math lesson, and oftentimes in other subject areas as well. Why? Because they are “real” life problems.
I agree, some “real” life word problems are a bit ridiculous (someone buying 60 watermelons, for example!), but some problems are more true to life, which makes the ability to solve them much more valuable.
Word problems come in so many different forms, and so many different levels. My current dilemma is the multi-step word problems. At the 4th grade level, we are actually encountering 3, 4, and even 5 step word problems! My strugglers are in head-deep even with tried and true strategies.
In large group and small groups, I use dry-erase boards with my students – A LOT! It is so easy to see which students show understanding, and which are still struggling (although I do catch them peeking at their neighbor’s dry-erase boards – not quite sure how to stop that problem – any suggestions???).
Right after I present the lesson, I like to pull my hardest struggling students into small group right away before they have a chance to become overwhelmed by the assignment. The greater the struggle, the smaller the group – at least that’s the rule I try to follow.
I give each student a mini-poster card to remind them of the steps we take in order to tackle the problems. The card is from my CUBES/CUBED Strategy Kit for teaching word problems.
**To be honest, there are other strategies and sets out there that are similar to my version, but I do like the CUBED (with the letter “D”) strategy best because of the emphasis with Common Core to have students represent the math problems with pictures or drawings (Drawings = D in the CUBED strategy).
Step 1: Read the problem out loud. Then read it again. This is before even picking up a pencil to circle or underline or highlight. This is the time to use those reading skills that the students have been learning during LA class! They need to visualize – what is happening in this problem? Here is the clincher – don’t let them off the hook! Make them tell you what is happening. They won’t want to. Or maybe they can’t because they truly don’t understand what is happening. My low readers often don’t digest the information as they are reading. Word problems call on a lot of different types of skills, like comprehension, sorting out needed and unneeded information, deciding on the operation, etc. It’s hard for students to organize their thoughts at this point – but that’s exactly what we need them to do! And that’s exactly why they must read and re-read the problem until they understand what is happening. I constantly tell my students that I, personally, have to read word problems several times before I “get” them. The strugglers often don’t even want to read the problem once. This is often where it becomes difficult. They may need to focus on just one sentence at a time, breaking each sentence down and thinking about what it really means.
The problem for us as teachers, is that all of the reading and discussion takes time – very valuable time. It also takes practice for the students, and perseverance – which is what we Common Core teachers are supposed to be focusing on. My struggling crew is often given fewer problems to complete – I’d rather have 5 problems done correctly than 15 incorrect problems that have been rushed through.
Strategy 2: Circle the numbers AND LABELS! In my opinion, the labels are super important to the students’ level of understanding. And without that understanding, they are totally stumped.
Strategy 3: Underline the question – not just underline it, but understand it and be able to put it in their own words. Ask them, “Now, what is the problem asking you to find?” They should be able to answer. Often, they will look at me and say the dreaded, “I don’t know.” That’s when we backtrack and re-read the problem again and discuss it. This is where we have the part versus whole discussion. What information are we given? Do we have part of something, or is it a whole/total amount?
If a student truly doesn’t know what he’s looking for, there is no real way that he can select the correct operation and proceed to solve the problem.
Step 4: Box the key words. Key words are given in many word problems and students should be able to recognize them. But key words can also be tricky. Some key words can be used for more than one operation, such as altogether. Altogether represents the total amount, but it can be used to represent either addition or multiplication (How many shells does Freddie have altogether?), and students need to rely on understanding the problem more deeply in order to know which operation to use.
This is also the time to discuss what operation(s) will be used.
This is also the time that confidence wanes, and they look at you with their sad little puppy-dog eyes and use their charms to prompt you into giving hints and clues, and maybe – the answer! Don’t do it! Stay strong!
Step 5: Eliminate information that is not necessary to the problem. I ask them to draw one line through the information, otherwise you get a student who scribbles out information that is actually needed, and then they rip their papers trying to erase.
Step 6: Drawing a picture, or really, representing the problem with a picture, table, array, or tally marks. Of course, concrete manipulatives are useful in this step and should be available to students who need to hold or manipulate items.
And while we’re still on drawings, it’s important to point out that the drawings can simply be quick sketches, arrays, bars, lines, etc. Sometimes I have students who try to draw a masterpiece and become so absorbed in their drawing that they lose focus.
Step 7: Determine if the problem is multi-step. The first few times a student encounters a multi-step problem, they are confused. I have had success by writing a 1 by or above the first step, or the first answer that they need to find. Then they should write a 2 beside the second step. Often students will complete only one step and stop. I’m constantly telling my fourth graders that they are big kids now, their problems are getting tougher, and they won’t have just one step any more.
Then they need to actually solve the problem. Use the operation that makes the most sense to the student. Sometimes they want to add, when they could be multiplying. Repeated addition isn’t as efficient, but a student can still arrive at the correct answer.
It all sounds so easy while I’m typing this, and you are reading it. I know that you have taught word problems before, and maybe much of this is a simple review for you, but I hope that maybe there was even one little idea that got you thinking a bit more deeply about word problems in your own classroom. Teachers are natural collaborators – we make each other better teachers just by sharing ideas and discussing them.
Please stop by again, or leave me a comment below, just so I know you are out there somewhere! Take care!