This year I discovered the magic of numberless word problems. I work in a school in Brazil where the vast majority of students are English Language Learners. The 5th grade teachers and I noticed that students were very uninterested in talking in Zoom. It seemed like a combination of hormones and disinterest.
Numberless word problems became a way to engage and support students learning English and promote communication about real-life situations and student thinking. After trying numberless word problems in one lesson, I was convinced that this needed to be incorporated into math class more often.
I co-taught a lesson virtually with a class of 5th grade students. We worked through two numberless word problems for the entire 50 minute math block. The problem we spent the most time started like this:
We honestly spent the most time on this slide. I asked the following questions:
- What is this situation all about?
- What does “on average” mean?
- Which activity do you think he spent the most time doing?
That final question caused a very interesting discussion. One boy even explained, “I think he spent the most time playing video games because his dad is probably at work and his mom is busy in the house. His friends can’t come over because of Covid and he doesn’t have any brothers or sisters. To play soccer, he would need to find someone to play with, but with video games he can play all by himself at night or day. He can find his friends to play with online and they can stay socially distanced.” My jaw dropped. He created an entire story for Luis and he deeply understood the situation of this problem before any more information was given. This was my first time ever trying out a numberless word problem, and within the first 5 minutes, I already saw the positive results that I had read so much about.
I then revealed the next slide:
This was given to students at the end of a decimals unit. Students had already practiced adding and subtracting decimals, but rarely within context of a real life situation. I asked the following questions:
- What is new on this slide?
- What does 6.25 hours mean? Is this how people normally refer to time?
- Was our prediction correct?
- Is it possible that Luis could have spent 7 hours playing soccer? Is it possible he could have spent 5 hours playing soccer?
We spent quite a bit of time talking about what 6.25 hours could be since we don’t normally use decimals when talking about time. A few students understood this concept right away and others were quite confused, but everyone was talking and sharing their thoughts in about this low entry, high ceiling problem. We were moving slow through the problem, but the conversation was rich in mathematical concepts. After realizing 6.25 hours meant 6 hours and 15 minutes, we revealed the next slide:
I asked the following questions:
- What does 3.5 hours mean?
- What might the question be?
Students responded, “Maybe the question will be ‘how many hours did Luis spend playing in all?’” Another said, “The question could be ‘how many more hours did Luis spend playing video games than soccer?’” This already had the kids thinking like mathematicians. They were using their prior knowledge to notice mathematical structures and make predictions. They had a deep understanding of this problem situation before the question was even revealed.
We finally revealed the question:
We gave the students a few minutes to actually solve this problem. Then we came back together to discuss the result. There were a few wrong answers, but after some discussion the students agreed that the answer was 2.75 hours. We then talked for a looong time about what 2.75 hours meant in hours and minutes. One girl was convinced that it meant 3 hours and 15 minutes because she took the .75 and regrouped it into 60 and 15 which is an hour and 15 mins. This showed she had a conceptual misunderstanding about what a decimal is, and the homeroom teacher and I spent some time explaining that .75 of an hour must be less than one hour. Some other students understood quickly that .75 is like 3/4 and 3/4 of an hour would be 45 minutes. Since conversions of time does not need to be mastered in 5th grade, we kept going, but we were satisfied that the class engaged in some deep thinking and conversation.
I am happy to share the two 5th grade decimal numberless word problems with you for FREE! I hope you have as much fun with them as I did. I personally wrote these numberless word problems. To learn how to easily write your own numberless word problems, please click here.
