Numberless Word Problems

A few years ago I was doing a lot of one-on-one work with a student who struggled in math. We often met before class to do some mental math and try to improve his number sense. After school, we would revisit the skill we discussed in class that day. He made a lot of progress and was starting to feel much more confident about math in general and problem solving in particular. Then we introduced fractions.

Shortly after we started our unit on fractions, he put his head down in frustration. I asked him what was wrong, and he replied, “I was just starting to get math and then… then fractions happened.” It was as if he had contracted a deadly virus named fractions. We talked about how good problem solving doesn’t change just because we moved from whole numbers to fractions. Over the next month or so, we continued to work and his confidence with fractions improved as well.

My approach with that student would be slightly different today. Instead of moving him right into word problems with fractions, I would use numberless word problems to help ease some of the anxiety. The numberless word problems would be a sort of scaffold to the problems with fractions. This would help him see that we’re still using the same problem solving strategies we used with whole numbers.

Numberless Word Problem in 4th Grade

Numberless word problems are just that – word problems without numbers. Let’s look at the following problem.

Brian eats 1/8 of the pizza and Julie eats 4/8 of the same pizza. How much of the pizza did Brian and Julie both eat?

This is a pretty basic word problem involving fractions. Some students might struggle with this problem simply because they are intimidated by the fractions. So, why not take the fractions out all together?

Brian eats some pizza and Julie eats some pizza. How much of the pizza did Brian and Julie both eat?

Now we can have a conversation about what is happening in the problem. We can talk about how one person has some amount of pizza and another person has another amount. We want to know how much they have together. That hopefully leads students to see that this is an addition problem. Once they understand the context of the problem and have determined the operations they need to use (addition), then they can start looking at specific numbers.

Depending on the students and the problem, I might put some whole numbers in the problem before moving to fractions. This will give the student another opportunity to see the context of the problem before the fractions are introduced. I did this today with my class.

I took a problem from our math book and covered up the fractions to create a numberless word problem. This is how I introduced the problem.
After we discussed the context of the problem, and determined the necessary operation, I put whole numbers into the problem.
Then, we looked at the original problem with fractions and talked about how the structure of the problem didn’t change because of the fractions.

This is a wonderful strategy because it helps students focus on the context of the problem. The focus on the narrative portion of the problem before worrying about the numbers. They can’t worry about the numbers, because they aren’t there yet.

Teaching Students with ADHD

One year I had a boy named Jimmy in my class, and he was one of the coolest kids I ever taught. (I always change names of students on this blog.) Jimmy asked me almost every day how my previous night was. This wasn’t just something he was taught to ask, Jimmy was genuinely interested in what I did and how I was feeling. He had the hardest time sitting still. Jimmy was such a kind kid who seemed to genuinely care for everybody around him and had a heart of gold. He had an extremely difficult time staying focused during a lesson. Jimmy would often display his artistic talents by drawing me pictures. If you’ve worked in a classroom, you probably know a kid just like Jimmy – kind, talented, sweet, but has trouble sitting still and staying focused.

It was clear to me early on that Jimmy had ADHD. I don’t think I heard the team ADHD (Attention Deficit Hyperactivity Disorder) when I was kid. The term ADD was initially used in an American Psychiatric Association manual in 1980. An upward trend of ADHD diagnoses followed a 1997 survey of parents nationwide. As many educators know, that upward trajectory has continued today.

Different students with ADHD benefit from different supports in the classroom. Some students see improved attention simply by sitting near the instruction. Other students need more supports like a timer to help keep them on task or a checklist to ensure they have the belongings they need at the end of the day. I was interested in creating a list of strategies to help students with ADHD, like Jimmy. I used a few websites to help me compile a list of non-medication strategies to use with students:

  • Give minimal number of directions;
  • Give directions in written form when possible for student to reference as they work;
  • Limit the amount of work on a page;
  • Cover up some work or text on a page to minimize distraction;
  • Use color coded folders to help student stay organized;
  • Periodically help students clean out backpacks, desks, folders, etc.;
  • Use checklist for assignments or homework materials;
  • Frequent redirection;
  • Peer tutoring;
  • Think/Pair/Share and other sharing strategies;
  • Give student movement breaks throughout the lesson and day;
  • Teach study skills explicitly;
  • Give student clear expectations;
  • Give students clear deadlines when assignments are due;
  • Use brain breaks;
  • Give students choice on assignments.

This is not an exhaustive list of strategies to support students with ADHD. It is, however, a place to get some ideas to get started. They are strategies I was so glad to discover when I had Jimmy in my class. Hopefully they can help the Jimmy you have in your classroom or school.


Today I was reading a text with my students and wanted to preview some of the vocabulary. I decided to use a graphic organizer with a “Prediction” and a “It Means…” column. Students would make predictions about the meaning of each word, and then we would talk about the actual meaning.

Before students started, we had a conversation about the importance of trying to make your best guess based on what is known about the word, or its parts, but that it was okay for your prediction to be incorrect. We also talked about strategies that would help predict what the word might mean – word parts, hearing the word used before, etc.

After the three minutes I gave students to make predictions, we whipped around the room and listened to a few predictions for each word. We talked about how students got the prediction and then shared the meaning of the word. Students added the meaning to their “It Means…” column. What was really valuable was the conversation that happened after students made the prediction.

One of the words was disassemble. A student said his prediction was, “take apart.” I asked him if he’d ever seen this word before and he said no. He said, “I knew if you assemble something you put it together – like ‘some assembly required’ on commercials. So, I guessed the dis- meant to do the opposite, so I guessed that dis… assemble meant the opposite, take apart.” He even added the pause between the dis- and assemble. I couldn’t have asked for a better response, and part of me wanted to let him finish teaching the lesson.

This was a very simple way to preview the vocabulary. Students were engaged because they wanted to see if their predictions were right, and the rich conversation made the time spent extremely valuable.

As I said, these words were preselected, but choosing which words to teach is critical. We can’t teach all the word which might be unknown to students. So, how do we know which words to teach? Isabel Beck, Margaret McKeown, and Linda Kucan broke vocabulary words into a 3-tier system:

  • Tier One – Words used everyday which require little instruction (building, car, parking lot)
  • Tier Two – Words are high frequency academic language used across domains (formulate, analyze, specify)
  • Tier Three – Words specific to a field of study (denominator, insulator, legislature)

The biggest impact comes from teaching the Tier Two words because they are used across content areas, but we also need to teach the Tier Three words within units of study. Teaching prefixes and suffixes also has an enormous impact because knowing one prefix or suffix can unlock so many words. For example, our discussion of dis- meaning “not” or “opposite of” lead to a conversation about other words with the same prefix – disapprove, dissatisfied, etc.

After you’ve chosen the best words to teach, you need to determine the best way to teach them. One strategy in Robert Marzano’s Vocabulary for the Common Core is Six-Step Process for Vocabulary Instruction:

  1. Provide a description, explanation, or example of the new term.
  2. Ask students to restate the description, explanation, or example in their own words.
  3. Ask students to construct a picture, symbol, or graphic representing the term or phrase.
  4. Engage students in activities that help them add to their knowledge of the terms in their vocabulary notebooks.
  5. Periodically ask students to discuss the terms with one another.
  6. Involve students in games that allow them to play with terms.

There are tons of resources out there with ideas for vocabulary activities. What are some of the strategies that you use in your classroom?