Benefits of Puzzles in Math Classes
Math puzzles are an easy and effective way of engaging students in their math and providing challenge. Implementing puzzles into math lessons encourages problem solving and logical thinking. Number puzzles provide motivation to complete math work - as Kulkarni (2013) says, these puzzles can encourage students to develop positive attitudes towards math in non-puzzle contexts. Puzzles help students develop logical thinking and strengthen their abstract capacity.
Puzzles can be introduced into math classes in many ways, I began with puzzles as early finisher activities however some students would benefit from a lesson on how to solve some of them and were generally excited about doing puzzles in math (even if it was testing their skills on the unit we were working on).
Puzzles can be introduced into math classes in many ways, I began with puzzles as early finisher activities however some students would benefit from a lesson on how to solve some of them and were generally excited about doing puzzles in math (even if it was testing their skills on the unit we were working on).
Types of Math Puzzles
Below are some math puzzles that I have used in my class. There are many more that can be found with a simple internet search.
Riddles or Brainteasers
Math riddles combine critical thinking and basic math skills. These are great lesson openers for the students to think about before class begins or as early finisher activities when they are done their daily work.
Below are some sites with good math riddles for students to work on - my students were very engaged with these and always asked to do more:
Riddles or Brainteasers
Math riddles combine critical thinking and basic math skills. These are great lesson openers for the students to think about before class begins or as early finisher activities when they are done their daily work.
Below are some sites with good math riddles for students to work on - my students were very engaged with these and always asked to do more:
- https://www.mentalup.co/blog/math-riddles
- https://www.mathwarehouse.com/riddles/math-riddles.php
- https://www.mashupmath.com/blog/free-math-riddles-for-kids
Ken Ken
Ken Ken puzzles were one of the first types of puzzles that I implemented into my classroom. I introduced these as an early finisher activity - at first when the students tried them they were not happy and many of them became frustrated easily. Now we have worked on these multiple times and the students ask if they can work on them when they have finished their math for the day.
How to solve ken ken puzzles
Example:
The ken ken example below (from education.com) is a 3x3 puzzle, it will use the numbers 1, 2, and 3 in each row and column.
The cages are outlined in the second image. Each of them have a target number in the top left corner.
The third image shows the target numbers for the cages. When there is only one box in a cage, the target number is simply that number.
Knowing that a 1 goes in the top left corner, we know that a 2 and a 3 must go in the column down from the 1 and the row across from the 1.
Ken Ken puzzles were one of the first types of puzzles that I implemented into my classroom. I introduced these as an early finisher activity - at first when the students tried them they were not happy and many of them became frustrated easily. Now we have worked on these multiple times and the students ask if they can work on them when they have finished their math for the day.
How to solve ken ken puzzles
- Fill each square cell in the puzzle with a number between 1 and the side of the grid. (in a 3x3 grid you will only use the numbers 1,2,3 and 4 whereas in a 5x5 grid you will use the numbers 1,2,3,4,5)
- Use each number only once in each row and each column (for example: a 3x3 grid will have 1,2, and 3 in each column and 1,2, and 3 in each row)
- The numbers in each cage (area surrounded by bold lines) must combine to create the cage's target number.
Example:
The ken ken example below (from education.com) is a 3x3 puzzle, it will use the numbers 1, 2, and 3 in each row and column.
The cages are outlined in the second image. Each of them have a target number in the top left corner.
The third image shows the target numbers for the cages. When there is only one box in a cage, the target number is simply that number.
Knowing that a 1 goes in the top left corner, we know that a 2 and a 3 must go in the column down from the 1 and the row across from the 1.
Ken Kens can be found on various sites, some are listed below:
- https://www.kenkenpuzzle.com/assets/KKCRWeek21-1c2f076e54e8d34b3a1e16a0403ab99a.pdf
- https://krazydad.com/inkies/
- https://iota.math.msu.edu/k12-outreach/kenken-puzzles/
Join the Dots
This puzzle uses nine dots, the goal is to connect all of the dots using only straight lines without lifting the pencil. This puzzle may be challenging for younger students but with some hints they have the potential to figure it out.
This puzzle uses nine dots, the goal is to connect all of the dots using only straight lines without lifting the pencil. This puzzle may be challenging for younger students but with some hints they have the potential to figure it out.
Origami
Origami provides students with hands on learning and has the potential to be very beneficial in mathematics classes. The folding of origami paper builds spatial reasoning and sequencing skills (Baicker, n.d.). Origami can be used in a variety of math lessons including patterns, fractions, geometry, division and many more. In his paper on using origami as a teaching tool in mathematics, Liu (2019) says that origami in math classes "provides an engaging context in which teachers can introduce conceptual understandings of mathematical ideas and give students hands-on learning experiences through which they can visualize abstract mathematical ideas in a concrete way."
The origami that I used in my class was a simple sonobe unit fold. These small object are not the most satisfying on their own, however when they are combined, they form lovely larger shapes.
Origami provides students with hands on learning and has the potential to be very beneficial in mathematics classes. The folding of origami paper builds spatial reasoning and sequencing skills (Baicker, n.d.). Origami can be used in a variety of math lessons including patterns, fractions, geometry, division and many more. In his paper on using origami as a teaching tool in mathematics, Liu (2019) says that origami in math classes "provides an engaging context in which teachers can introduce conceptual understandings of mathematical ideas and give students hands-on learning experiences through which they can visualize abstract mathematical ideas in a concrete way."
The origami that I used in my class was a simple sonobe unit fold. These small object are not the most satisfying on their own, however when they are combined, they form lovely larger shapes.
References
Baicker, K. (n.d.). Origami Math. "Unfold" math learning with hands-on fun and activities. Scholastic. https://www.scholastic.com/teachers/lesson-plans/teaching-content/origami-math/
Kampen, M. (February 6, 2019). 20 Best Math Puzzles to Engage and Challenge your Students. Prodigy. https://www.prodigygame.com/main-en/blog/math-puzzles
Kulkarni, D. (July 5, 2013). Recreational and Educational Value of Math Puzzles. Edutopia. https://www.edutopia.org/blog/recreational-educational-value-math-puzzles-deepak-kulkarni
Liu, Y. (May, 2019). A Comparison Study of Using Origami as a Teaching Tool in Middle-School Mathematics Class in North America and China. Major Papers. 86. https://scholar.uwindsor.ca/major-papers/86
Images:
Whitney, G. (unknown). Math Monday: Introducing the Sonobe Unit [image]. MoMath National Museum of Mathematics. https://momath.org/home/math-monday-introducing-the-sonobe-unit/
William, A. (unknown). Shallow Focus Photo of Rubik's Cube [image]. Pexels. https://www.pexels.com/photo/shallow-focus-photo-of-rubik-s-cube-2121804/
Unknown. (September 19, 2008). Getting Started with Sonobe Units [image]. Gurmeet. https://gurmeet.net/origami/modular-origami-getting-started-with-sonobe-units/
Baicker, K. (n.d.). Origami Math. "Unfold" math learning with hands-on fun and activities. Scholastic. https://www.scholastic.com/teachers/lesson-plans/teaching-content/origami-math/
Kampen, M. (February 6, 2019). 20 Best Math Puzzles to Engage and Challenge your Students. Prodigy. https://www.prodigygame.com/main-en/blog/math-puzzles
Kulkarni, D. (July 5, 2013). Recreational and Educational Value of Math Puzzles. Edutopia. https://www.edutopia.org/blog/recreational-educational-value-math-puzzles-deepak-kulkarni
Liu, Y. (May, 2019). A Comparison Study of Using Origami as a Teaching Tool in Middle-School Mathematics Class in North America and China. Major Papers. 86. https://scholar.uwindsor.ca/major-papers/86
Images:
Whitney, G. (unknown). Math Monday: Introducing the Sonobe Unit [image]. MoMath National Museum of Mathematics. https://momath.org/home/math-monday-introducing-the-sonobe-unit/
William, A. (unknown). Shallow Focus Photo of Rubik's Cube [image]. Pexels. https://www.pexels.com/photo/shallow-focus-photo-of-rubik-s-cube-2121804/
Unknown. (September 19, 2008). Getting Started with Sonobe Units [image]. Gurmeet. https://gurmeet.net/origami/modular-origami-getting-started-with-sonobe-units/