A Lesson Plan using Shikaku Puzzles

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Some Introduction

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We were in the last week of Term 2, it was Wednesday, and my Year 7 Maths students were adding the final touches to their last assessment before the holidays. The second to last Maths lesson for the term was wrapping up, and I realised that we still had one more to go. Friday, the lesson directly before lunch. Awesome! Twenty-six Year 7's, all eagerly waiting for that final bell before being released to enjoy three weeks of freedom. The lesson(s) directly before lunch can sometimes be tedious with middle-schoolers, but the lesson(s) directly before lunch on the last day of term with middle-schoolers can often be a whole new ball game.

Don't get me wrong. This group of students are fantastic. They are well-behaved and have slowly been increasing their work ethic as the year has progressed. It's just that when you're 12 or 13, you tend to still get excited about things, and the holidays are no exception!

I'm a big believer that whatever you do in the classroom, must be authentic. Lessons really need to have real-world applications (despite how difficult this can sometimes be to convince the students of - 'how will I ever use linear graphs when I leave school?'!), otherwise, it is easy to lose even the most dedicated of students. This is why, even for a stand alone lesson, one where you are just enjoying something more relaxed that the formalities of using the textbook questions, I still like to have ties to the curriculum. It might not directly relate to the current unit we are doing, or have just done, but I like to try and keep it within the parameters of a unit that will, or has, been studied during the year.

And so, this is where I found myself. One lesson to go. All assessment completed. Reports already sent home. How to find a lesson that the students would enjoy, learn from and not think a complete waste of time. I'll tell you, I went through the list of go to lesson plans for when you just need something, but struggled to come up with something that I thought would add value for their final few hours of the term.

Thursday morning I was sitting in the staffroom, reading the newspaper, when a colleague approached and began telling me of a seminar she had been to earlier in the week. The seminar had featured a well known Maths teacher from New South Wales who used part of his time to workshop a few Mathematical game-type activities that teachers could use with students, and she happened to think that they might have been of use in Year 7 Maths, so she gave me the information and pretty much just left me with it. Well, I can tell you, I ran with it.

I looked at the three different ideas that she had been presented with, and found that of the three, the one that seemed most relevant, in as much as it would offer a 'teaching' angle as well as a fun activity, was Shikaku. Now, if you're like my, you might instantly think, 'Oh, Sudoku. I know that!', well, you would be (and I'm sorry to say) incorrect. Shikaku is not Sudoku. It would be fair to say, that it is actually nothing like Sudoku at all!

Shikaku is a square grid with some numbers on it. The aim of the game is to successfully divide the grid into smaller sections based upon the numbers. The numbers represent how many consecutive grid squares you should include within that selection. For example, if you have a grid square with 2 in it, then you draw around that square and one other consecutive square, creating a 'selection' of two squares. If a square has 4 in it, then you draw around that square and three consecutive squares, and so on. You can see how this works in the image below.

This image is fairly self-explanatory, as you can see, on the left is the incomplete puzzle, and on the right is the completed one. This example is a relatively easy one. They can get quite complex, but it's fair to say that the students really enjoyed them, and became quite engaged once they had really got the hang of them.

By now, you might be wondering: 'Where's the learning in this? You said earlier that you didn't like to give an activity if it didn't have some sort of real-world application. You said that you believed that authenticity is important, and tha...!' Yes, I did say that, and Shikaku is underpinned by the use of and understanding of square numbers. You can see in the example above, that both of the 4's are encapsulated to form a square, and that is the crux of a square number. To quote the Year 7 textbook:

If a number can be represented by a square arrangement of dots, it is called a square number or perfect square.

Shikaku puzzles can be solved much easier if students find the perfect squares and draw the boxes around these numbers first, ensuring that they are creating a square, and not some other shape around these. Such as the two 4's above. Once that have done this, the other numbers fall into place quite (but not always - remember, these puzzles are designed to be challenging!) easily.

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The 'Rules' of the Game

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While completing some of these puzzles would be fun in itself, I decided to create somewhat of a game around the use of these as well. Being their last Maths lesson for the term, I wanted my students to enjoy themselves as well as learn something small. We had already looked at square numbers in Term 1, so this was going to form more of a refresher than anything else.

What You Will Need

1. A puzzle 'pack' for each student. I gave my students (total of 5 sheets of paper):
   • an example like the one above;
   • 2 of the 5x5 puzzles (printed on one A4 piece of paper);
   • 2 of the 8x8 puzzles (printed on one A4 piece of paper);
   • 2 of the 10x10 puzzles (printed on one A4 piece of paper), and
   • 1 of the 10x15 puzzles (printed on one A4 piece of paper).
2. Answer sheets for the selected puzzles for yourself.
3. Some rewards - I used some individually wrapped fruit chew lollies, but something like Minties or Fantales would suffice.

The Rules

I made these up to fit my circumstances, but you could adapt and change them as needed.

1. Prizes are awarded for the following (this means that students could potentially win a total of 8 prizes during the lesson (4 for completing puzzles, and 4 for good colouring):
   1. Completing both puzzles on a sheet correctly, and
   2. Colouring both puzzles on the sheet in a creative manner.
2. Students could only bring one sheet to the front for marking at a time.
3. If they wanted the bonus 'colouring' prize, than they had to do this before coming to the teacher for marking the page.

Students wouldn't receive a prize if they had done the following:

1. Created shapes on the puzzle other than squares or rectangles - no 'L' shapes were allowed.
2. They hadn't coloured neatly - I was quite meticulous in this.
3. The hadn't completed both puzzles on the sheet.
4. They tried to get me to mark more than one page at a time

I was quite brutal, in some instances, when it came to marking and assigning prize, but, hey, when there are lollies up for grabs, they can be precise and follow the rules!

A Simple (Very Simple) Lesson Plan

If this interests you, and you would like to give it a go, I followed a fairly simple lesson plan. I managed to cram this into 50 minutes, but it would probably work better in a 90 minute double lesson. Most students didn't;t get through all of the puzzles I gave them because there were simply too many (most opted to get the bonus prizes for colouring as well!) and also because we stopped about ten minutes before the end of the lesson so I could explain about the concept of completing the square numbers first.

1. Introduce the concept of Shikaku and explain what they are. I did this as I distributed the handout (puzzle pack).
2. Run through the example sheet (as the image above) so that students understand how to complete the puzzles. Allude to the idea that there is a Mathematical process they can use to complete these easier, but don't tell them immediately. (I purposely didn't tell then to find and complete the square numbers first.)
3. Explain the rules - I didn't write these on the board, but in future lessons, I would do this. I think it will help clarify for students exactly how they can win prizes.
4. Take questions - there were only a few - mainly on how to win prizes!!
5. Students complete puzzles - obviously, the bulk of class time.
6. **Optional - I chose to stop them with about 10 minutes remaining to remind tham of our lessons earlier in the year on square numbers, and to tell them how finding the square numbers in a Shikaku puzzle first, will help them to solve it easier.
7. Wrap up.

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Conclusion

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I hope that this post has provided you with some inspiration, or at the very least, something that you can use in a practical sense. For me, this was one of those lessons where you walk away feeling good about teaching. They were all engaged, and they were all taught something small about Maths, while having fun too. A successful lesson.

If you do decide to use plan, or tailor it to you classroom, I would love to hear about it, so please drop a comment in the comments section outlining your experience with this. If you would like to use it, but something here is unclear, also, please drop a comment below, and I'll try to clear up any grey areas as quickly as possible.

All images were created by myself, or used from Pexels.

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