In 2021, I stumbled upon a transformative teaching tool – numberless word problems. Working in a school in Brazil with predominantly English Language Learners in the 5th grade, my colleagues and I faced the challenge of keeping students engaged during virtual lessons. The solution? Numberless word problems.
These problems became a catalyst for meaningful discussions, promoting communication about real-life situations and encouraging students’ critical thinking. After a single lesson, I was convinced that incorporating numberless word problems into our math classes was a game-changer.
During a virtual lesson with a 5th-grade class, we delved into two numberless word problems for the entire 50-minute math block. The most intriguing problem sparked a captivating discussion.
Setting the Stage
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 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.
Complexity: Decimals in Real-Life
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 the 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 about this low-entry, high-ceiling problem. We were moving slowly through the problem, but the conversation was rich in mathematical concepts.
Puzzle: Adding Depth to Learning
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.
Reflection and Growth: Nurturing Mathematical Minds
We finally revealed the question:
We gave the students a few minutes to 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 do 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! Download them here. If you’re curious about crafting your own numberless word problems, click here for a simple guide.
I hope you enjoy using these problems as much as I did creating them.
