Tape diagrams, model drawings, visual models, bar, model, unit bar – different names for the same thing: strategies to help with the comprehension of word problems for students.
Sometimes in math, each book or teacher takes a name for a really great idea and twists it around to call it something else. Because this is often the case, and because we work with so many different math series, I’ll be calling this concept visual models.
Visual models are a comprehension strategy that is amazing for helping students solve word problems. I think back to how I taught word problems to my students. I remember thinking it made perfect sense – circle the numbers, underline the words, box important information, right? For the most part, that procedure really worked out well when students were doing part-whole addition, part-whole subtraction and part-whole missing addend problems. But I vividly remember thinking of problems that were a lot more complex, which might be what I know now as multiplicative comparison problems or additive multiplicative comparison and realizing that my fancy procedure didn’t hold up.
When we started to get more of our state testing, and the standards started to become more firm than they were when I first started teaching 20 some years ago, we had a few strategies – guess and check, make a table. There were lots of different icons at the top of the problems and I remember thinking, Gosh, how am I helping kids to know which strategy to use for which problem?
Fear of word problems is also a very real thing, for students and even adults. In fact, when I took the GRE to get into my master’s program at Oakland University in Michigan, there was a question on the test that said something like, Fran drove eight more miles than Sam to work but three miles less than and twice the amount …my eyes glazed over and I thought, “Oh no! Not one of these problems!” I tried to draw diagrams and find the best (longest!) way possible to solve the problem.
To be honest with you, most of the time, I felt like it was just kind of a guessing game and the result was that a lot of kids began to subscribe to the “guess and check” method. We also tried the chart method, where you have a T-chart with key vocabulary that indicates the type of operation the problem requires. If it says sum it will be addition, if it says difference” it will be subtraction. Kids just aren’t learning to think and analyze the problems. Usually, when the going gets tough, because they don’t understand, students resort to an appeal to their teacher for help.
When most kids read a story problem, they want to get right to the nitty gritty. They look at the problem and decide – add or subtract? Typically, these kids are really more interested in solving it and figuring out what operation they’re going to use, than really understanding what the problem is asking.
For the majority of my teaching career, up until about eight years ago, I felt like we needed a strategy to help all students with all the different types of problems. I felt like we needed a common language around problem solving, which didn’t really exist at the time.
Is there a solution? Is there a way that we could tailor problem solving for students as early as kindergarten all the way through eighth grade? There is: using visual models to solve word problems.
Much of the information for visual models comes from research that’s been done in Singapore. The process works for everything, all the different types of problems that students are going to encounter: part-whole problems, additive comparison, multiplicative comparison, additive multiplicative, fractions, and as you go up even higher, ratios and proportions.
Sometimes, people in Michigan or the US think, wait a minute, why are we doing something that is from another country? It’s just good math!! Using visual models to give students a comprehension strategy that helps them solve word problems is golden!
I really wanted a process that can be consistent from teacher to teacher, grade level to grade level, that could follow a student all the way up. In most of our M3 Building Math Mindsets project schools, we proudly display this step-by-step poster that walks students through being able to break down and answer problems, both the simple and the more complex.
Why do we need a process?
This tutorial video, Word Problems with Visual Models: Basics, will explain the need for a process for students to be able to follow with visual models, from as early as first grade, students can be doing visual models with proportional units to help them understand part-whole addition, part-whole subtraction, part-whole missing addend, and even additive comparison. As students start to get a little bit older, they start to no longer be able to use a proportional model because we’re not just talking about five jelly beans any more. We might be talking about 29 jelly beans, and we’re certainly not going to proportionally draw out 29 boxes.
Many students that are in first grade feel very frustrated, maybe thinking that there’s no purpose in being able to do a visual model because they know, from reading the problem, that we add or subtract. It’s “easy peasy”! But, what they don’t realize is that, the second a more complex problem comes up, they will stop in their tracks.
For example, if we were to say that Karen brought 48 ice cream cups to the soccer game. One third of those cups were chocolate chip ice cream, three fourths of the remainder were strawberry, and the rest were vanilla. How many vanilla cups did Karen bring to the soccer game?
Students’ reactions to a problem like this are probably pretty similar to yours: Huh? Three fourths of the remainder – what’s the remainder? Should I find a common denominator? Okay, I circled all the numbers and I underlined the words, but I don’t really know what this is actually asking!
Quite quickly, problems can go from very simplistic adding problems to really more complex problems like this one. If we teach this step-by-step process of using visual models while the problems are simple, the students will be able to use it most effectively when the problems do get more complex.
Moving towards Non-Proportional Thinking
This spring, we started talking about the journey to help kids connect proportional and non-proportional thinking with our Math4Littles series (catch up here!). Beginning with real objects in the physical world, moving to quantitative pictures, math work mats, and finally to journals beginning in Kindergarten and then 1st grade, where we really start to make the transition official.
So what comes after we have this understanding? Part-whole problems with a non-proportional representation!
For your instructional convenience, we have created some really amazing videos that you can use during face-to-face or virtual instruction that will help students gain understanding about part-whole problems! The videos come with a PowerPoint tutorial that you can use in the classroom, a reference poster, a student journal that mirrors the presentation, and a blank journal template that you can customize based on the types of problems that you’re working on with your students. Check out our sneak peeks to see what you can expect!
It’s all at your fingertips! Our M3 Members have access to download each of the six bundles at no cost, or you can buy the bundles individually in our store for less than a cup of coffee.
These Word Problems with Visual Models bundles are for you if…
- …you hate coming up with problems. Me too! And usually, the sample problems in our math books don’t flow the way we want our kids to learn. First, we want kids to learn part-whole addition, then part-whole subtraction, and then maybe part-whole missing addend. Next, I want to give them a mixed review before I add the next type of problem, which might be part-whole multi-step. You can completely customize the flow of problems by mixing and matching the bundles.
- …you love a good anchor chart/poster. Each bundle has a unique poster, featuring the studious Professor Barble, that can be blown up for a classroom wall, or printed small on a bookmark that the kids could have in their journals. The posters will help students learn to recognize, and develop familiarity with, the types of drawings and problems they’ll encounter in elementary school.
- …you don’t love creating PowerPoints. That part is done for you! Of course, we include the original PowerPoint file in the bundle, so you could always edit the presentation if you wanted to add your own problems, but if you don’t, no problem! It’s ready to go into your classroom – virtual or face-to-face – tomorrow!
Check out our new Word Problems with Visual Models series and let us know how it goes!
Coming soon – look for journals you can use in 1st and 2nd grade, all the way up through 5th grade eventually! We can’t wait!
Next week – we’ll look at visual models that go with comparison word problems! See you then!