Math Puzzles

My students enjoy puzzles. It often doesn’t depend on the type of puzzle. They like the trial-and-error of attempting to find patterns and eventually solutions. In math class these puzzles take on many different forms. I believe that patterns and puzzles play an important role in the math classroom. Some skills are more aligned with using puzzles than others.

Puzzles offer learners multiple entry points. Students have the option to look at a puzzle and decide to start in one section while another student decides to start in a different section. One puzzle that’s been thrown around the Internet is below.


I gave this puzzle to my fourth grade students. Students started to calculate how much each horse was worth and worked from there. I had other students that immediately looked at the horseshoes and found that the total worth would have to be divided by two. After working with each other the students then conversed in groups. The discussion was fabulous. Students started to identify where a mistake was made and corrected their papers as needed. During this time students were engaged, using math vocabulary and practicing skills that they will see again throughout the year. What I found interesting was that zero students had the correct answer the first time. It took perseverance as well as a thorough amount of collaboration to get to a consensus. The class had a conversation afterwards.

The key I find is connecting the puzzle to the skill/standard. Afterwards, students understand that this was a fun problem, but was the puzzle connected to a certain skill? Connecting the puzzle to prior skills not only shows how this fits into a continuum, but also gives students a picture of what skills are being addressed. Maybe the skills can be introduced after the lesson. I know that the exploration that students participate in is a valuable piece in the learning process. What are students exploring as they unpack the problem? The objective isn’t to just solve the problem. The bulk of the student learning experience is using the substitution process to find a solution.


After discussing the solution I drew the picture above on the whiteboard. Through this I attempted to bridge the puzzle to more of an abstract model. This made sense to some students while others were debating on whether this matched the earlier puzzle. Regardless, the transition seemed beneficial in having students use substitution to find a solution.

Next week the class is tackling a different problem.


I’m already looking forward to using this with my students.

Author: Matt Coaty

I've taught elementary students for the past 14 years. I enjoy reading educational research and learning from my PLN. Words on this blog are my own.

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