When we hear, "Make sense of problems and persevere in solving them" (the first of the eight Standards for Mathematical Practice), we often think of word problems and strategies for comprehension. This standard, however, addresses more than word problems. It is an opportunity for students to seek an entry point and consider ways in which to solve the problem. Students need to self-monitor their progress and try a different strategy if they feel they are not moving towards their goal. While solving problems, students should frequently be asking themselves, "Does this make sense?" Yohaku puzzles are one way you might introduce this thinking into your classroom. I learned about Yohaku puzzles when I attended a meeting of preservice teachers at Baldwin Wallace University a couple of weeks ago. They were doing an activity from NCTM's Teaching Children Mathematics based on a submission from Mike Jacobs to the March 2018 issue. Yohaku means "blank space" in Japanese. Students work to complete the puzzle with numbers that will make the statements true. What a great opportunity for students to practice calculations as they work to confirm whether or not a set of numbers will work! There are often multiple solutions to a puzzle - which can lead to conversations where students prove to one another that their solution is valid. Another topic might be how students know whether or not they have found all possible solutions. I can't wait to try these puzzles with students! If you are looking for an extension to Yohaku puzzles, KenKen puzzles might be a good fit. I used KenKen puzzles with my 5th grade students and they loved them! You can learn more about KenKen puzzles here.
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